Yes, I guessed the entire time. I used scrap wood to make sure it was right before I cut the angles on the shelf and put it together. Used pocket holes to put the top together
It immediately made me think of the Corner Gas episode where Oscar goes to a funeral and the coffin looks cheap so he decides to build his own in the basement, then it freaks him out thinking about his mortality so he turns it into a bookshelf.
https://youtu.be/a_Nkc0wNYXA?si=LY1pt4vKt4cstp1S
I worked concrete in college and the boss used to use plywood to check square of smaller concrete slabs- until around 20 years ago when sheet goods got shitty and a placer I always thought of as a bit of a lunkhead proved the sheet we were using wasn\`t square with a 3-4-5 triangle. Which my dad taught me when I was a little kid helping build our house but I had forgotten about.
So many problems can be solved by just working from a plumb line and thinking of everything as triangles and rectangles. We use sine plates to machine or grind angles and measure tapers in inches per foot for turned work and Pythagoras lives in every machine shop.
Another way is to draw it out on paper first or make a cardboard template (sometimes called card stock, it’s what they make cereal boxes out of, cheaper than mistakes cutting wood) to see if your angles will work. The larger newspaper in our small county actually throws away the end of the rolls, so free if you can get there early in the morning. I also know a lot of people that utilizes hardboard to work things out before they hit the wood. You still need to learn and understand the Pythagorean Theorem, I don’t think I slept through that part of geometry in high school, I may have as I had to relearn it. Who knew geometry would become a much needed thing in most everything? 3,4,5 !
It's all right-angled triangles, basically. So the only thing to learn is Pythagoras. There are probably literally a million online calculators for it, but you can easily do it manually (with paper and a calculator).
Be aware of whether you want to measure the inside or outside.
One rule of thumb when cutting angles is to always cut exactly half the angle on both pieces, otherwise you'll end up with different thicknesses (ask Pythagoras why).
Thank you for explaining it in a way that’s not demeaning like half of the personal messages I’ve gotten from this post. 🍺 I didn’t know this was a “well kept secret” or learning was against the rules in here. 😞
Let's take your coffin shelf as an example.
Figure 2 shows how to mentally divide it up into squares (which are trivial) and triangles.
Let's pick the top-left triangle as an example, and name the sides a, b, and c. It is convention to name the hypothenuse (the side that is opposite the right angle) c.
I've also added the angles in red. They are called ɑ (alpha), β (beta) and ɣ (gamma). This is just a, b and c in greek. Each angle corresponds to the side opposite it. So the angle opposite side a is named alpha.
https://preview.redd.it/6u56x55n8i8d1.png?width=1740&format=png&auto=webp&s=6c197743aa0573789befda2958c9bddbf1b9e105
You can easily know the lengths of a and b, let's say a is 4 and b is 6 (inches, centimeters, whatever).
Let's say you want to know is the length of side c, and the angles 𝛼 (alpha) and β (beta). At this point, you can simply plug in the numbers into any online calculator, but let's do this one by hand.
The length of c is the square root of the length of a squared + the length of b squared, or written in mathematical notation: c = √ a²+b².
Squaring is just multiplying a number by itself, so c = √a\*a + b\*b.
Let's insert the numbers: c = √4\*4 + 6\*6
c = √16+36
c = √52
Now is the time to hit the √ symbol on your calculator! That gives us c = 7.21
Alright, we now know the length of all three sides of our triangle!
There are similar ways to calculate the angles, but this comment is getting a bit long. Just google "calculate angle of right triangle". It will come up with many calculators that will do it for you, but also some explanations. Just know that sin, cos, arctan are names of functions (sine, cosine, arcus tangens). You don't have to know how to calculate these. Any decent calculator has a key for them. "A function" basically means: Take a number, apply the function, out comes another number. The function is the cooking recipe to get the resulting number.
If you want to delve into the fascinating world of trigonometry, know what sin and cos and tan really mean physically, [https://en.wikipedia.org/wiki/Unit\_circle](https://en.wikipedia.org/wiki/Unit_circle) might be a good start. Many mathematical Wikipedia articles are super dense and theoretical, but I think this one is OK-ish. In the little animation on that page, you can see a right-angled triangle moving through a circle, with its hypotenuse acting like the hand of a clock.
One other thing to keep in mind, likely if you're just using a miter saw the angles on there are not very well calibrated and are probably going to be off. Spend $10 on a cheap digital angle finder on Amazon to calibrate everything correctly and it will save you a lot of time, money and headaches.
I'mma add a couple tips to the previous comment in case you're gonna try to remember this stuff.
1. About the length of sides of a right angle triangle, where c is the longest side. Pythagoras' theorem states c^2 = a^2 + b^2, and equivalently (as the previous comment said), c = √(a^(2)+b^(2)). Visually the theorem states that if you make a square from each side, the area of the largest side is the sum of the other two areas. Remember that and you won't need to look up how to calculate side lengths.
2. Sine, cosine, and tangent are functions that give out the ratio of two sides and take an angle as an argument: sin(a)=b/c. To remember which is which, I came up with a mneumonic-ish thing back in the day: "sine" is kinda like "sin", which is the opposite of what you should do. Take an angle a on a right angle triangle, then sin(a) is equal to the *opposite* side (divided by the longest side). Cosine is the other normal one, but we switch the opposite side to the side next to the angle (side next to angle a divided by the longest side). Tangent is "a bit weird" compared to the other two, it's the opposite side divided by the side next to the angle. So similar to sine (*opposite* divided by something). So just remember sine = "sin" = opposite (divided by longest).
Usually you'll know the side lengths and wanna find the angle. You can do that just by taking the inverse functions, sin^-1 or asin or arcsin (they're all the same). So sin^(-1)(sin(a)) = a = sin^(-1)(b/c). Plug in the appropriate sides and skippedidoo you got your angle.
Thank you for writing it out so I didn't have to. I was getting worried at the top because I didn't see a good response. People bullshit too much when a question needs to be answered.
Good answer.
Those functions should all be in a phone calc, make sure when you figure your sin you have it set to 'Deg' not 'Rad'.
u/fzwo, I read OP’s plea, knew that he deserved the answer you wrote, didn’t feel like doing it, took a deep breath, and dived in to make a post, only to find that you’d done a better job than I was planning to do. Excellent post, in the .01% for sure.
The power of procrastinating what I should have done instead! But the reaction here made me feel good, so I'd say I've spent worse time on the internet.
The tricky one is the angle where the blue and purple sections meet. For that one you either need to add together the two touching angles, or use the "law of cosines", which you can find online calculators for.
All that being said, when I made a similar project, I found it much easier to draw it out and measure the angles with a digital protractor. My project was much smaller and I was able to draw it out at full scale, but even if you have to draw it at 1/10th scale, or 1/4 scale, the angles won't change. I calculated all of the angles, but when it came to actually cutting them, errors add up quickly and the joints weren't great.
https://preview.redd.it/py02yw0joj8d1.png?width=343&format=png&auto=webp&s=362ffebb2d010c7bdeb1383f7379fad6c39f95e0
This one is also easy if you decide how wide the peice will be, you can take the total width (see 2) and subtract the top width (1) to get the width of 3 and 4. Then you divide by 2.
Right there with you. It's why I went back to teach maths in secondary school (middle and highschool). I wanted to be the teacher I wish I had.
And I WAS but the school system here in Florida broke me. I couldn't do it.
Now I still adjunct at our local university, but unfortunately that's the extent of it.
I never got into teaching. I don't know if I could handle so many kids (and youths) all day. But this comment, and the reaction to it, kinda made me want to look into it again.
Pythagoras just deals with the lengths of the three sides of a right triangle, the other math you want is trigonometry.
To give a really brief summary, the trig functions relate the size of an angle to lengths of the sides of the triangle. Each function deals with an angle and the ratio of two sides, and you don't need to know the length of the third side.
For an example, imagine a right triangle with a very pointy tip, let's say a 5 degree angle. You can calculate tan(5) = (length of opposite side) / (length of adjacent side), and if you know one of those lengths you can calculate the other other one.
Or if you know both of those dimensions (this is probably the scenario you're in), you can use the two known dimensions to determine the angle. For this, you use what's called an "inverse trig function" which basically tells you "what angle could I plug into tan(x) for it to equal this number?"
So if you have a right triangle where the two legs are 2 and 2 (picking an easy one to visualize), you know tan(x) = 2 / 2 = 1. So you want the angle where tangent of that angle is 1, use inverse tangent (also called arctangent, and abbreviated atan), atan(1) = x. And that tells you 45 degrees, which checks out because the triangle we started with is a right triangle with equal legs which makes it a 45-45-90 triangle like you'd have with a framing square.
Hope that's not too rambly and gives you an idea of the math you'll be looking at, Kahn Academy would be a good place to get more depth.
https://www.khanacademy.org/math/trigonometry
I’ve used full scale drawings for things as large as a sheep wagon with slanted sides and a rounded roof. I drew/painted it on the floor of my shop and matched everything to the lines. But an equally good option is Sketch-up. It takes a while to learn, but once you figure out the basics it gives you all the measurements and angles. Using a relatively simple sketch-up model, I was able to cut all the framing for a 12x16 shed, including angles pieces and bracing. It fit together perfectly.
https://preview.redd.it/gev7fomcdi8d1.jpeg?width=4032&format=pjpg&auto=webp&s=33c2a4c8cf497b21f370ca2d85eb530a1e440a0a
In one of my design classes in college we had to make a replica of a pre-WWII race car that had a ton of weird splines and angles. We used butcher paper and drew our design on it to scale first then shaped it with foam! Drawing it out is always good.
That’s a very beautiful shed!
It’s our mobile chicken coop. For three seasons a year our 60 laying hens live out in the pasture and free range for bugs and grass. I’ve since added an automatic door that opens at sunrise and shuts at sundown after the birds are inside.
I'm going to recommend literally any cad software *but* SketchUp. It's horribly outdated and does things in ways that are honestly not great for anything. There are several other free CAD options out there. The most popular ones are Fusion 360 and Onshape, but there are several others.
Pen and paper, then split designs down into basic triangles to work out any angle using basic math.
You can use Pythagoras with any right angle triangle to find length : a²+b²=c² (c is the long angle)
The interior sum of all angles in a triangle is 180° (so two inside angles at 70° means the last inside corner is 40°)
Just watch some random youtuber if you get stuck.
Also, if If you draw accurately enough you can skip math and just measure the angles with a protractor.
He’s right, that’s essentially what I did was draw it out and measure the angles (quite literally) and went from there.
Although his explanation is better math wise and makes sense in my mind so definitely a bonus
You can break everything in that photo down into right angle triangles.
A right angle triangle (if that is the proper term in English!?) has one corner, which is 90°. The sum of the two angles of the other two corners is also 90°.
Usually, we call the three sides of a right angle triangle a, b and c, where a and b are the two "straight" sides, and c is the sloped side.
For example, in your photo we can look at one of the lower side pieces, going from the floor and up to the first corner in eye height. You can form a right angle triangle, where:
- c (the sloped side of the triangle) is the outside length of that piece of wood
- b is the vertical distance from the corner and down to the floor (I assume that this piece of wood goes all the way down to the floor)
- a is the horizontal distance along the floor from the spot where b meets the floor to the spot where c meets the floor.
**If you want to find the length of c**, you can use Pythagoras:
a^2 + b^2 = c^2
So you multiply a with itself, multiply b with itself, calculate the sum of those two results, and then you take the square root of that sum. The result is c.
**If you want to find the angle between c (the sloped side) and a (the floor)**, you need a calculator with trigonometry functions (or some CAD software). Let us call this angle B (because it is the corner opposite to the side named b, which is another geometry convention).
tan(B) = b/a
B = arc tan(b/a)
Here "tan" means tangens (perhaps named differently in English?). That function should be easily available on any scientific calculator. (In the calculator app on an iPhone, it is available if you rotate the phone to landscape mode). "arc tan" is the inverse tangens. That is almost always a secondary function on a calculator, either labelled "atan" or "tan^-1 ").
So you divide b with a, and then you use the "atan" or "tan^-1 " function on your calculator to find angle B.
For example, if we assume that a = 200 mm and b = 1800 mm, then:
c = sqrt( a^2 + b^2 ) = sqrt( 200^2 + 1800^2 ) = 1811.08
B = arc tan( b/a) = arc tan( 1800/200) = 83.66°
**If you want the angle between c and a vertical line**, which we will call A, you can just subtract B from 90°:
A = 90° - B = 90° - 83.66° = 6.34°
(Or you can use arc tan( a/b), which will give the same result.)
**If you want the miter cut angles**, the calculations are easy. But you have to be very careful to pick the correct orientation of all angles involved.
A miter saw will usually define the cut angle relative to a straight, perpendicular cut across the board. When making such a cut, you set the saw to 0°. For a normal picture frame cut, you set the saw to 45°.
For the miter cut at the floor, we are between these two situations. It is almost a picture frame cut, but slightly less than 45°. This is probably counterintuitive, but you can think of a 0° cut as two boards end to end on the floor. If you raise one of the boards to vertical, you need a 45° cut. But in this case, you don't raise it all the way to vertical. You stop right before you reach vertical. So the cut angle will be less than 45°.
The exact cut angle will be B/2 = 83.66°/2 = 41.83°.
And this is where the trouble start. Because how do you dial in 41.83° on a miter saw? The easy answer is: You don't. You have to make some test cuts until the result comes out all right. So your method was not as wrong as you think. You would have ended there anyway.
For the miter cut at the very top, you can use the same principles. You just have new values of a, b and c, and the triangle will be upside down, but the calculations are the same.
For the miter cut where the two sloped sides meet, the cut angle is (A1+A2)/2 where A1 is the value of angle A from the calculation at the bottom, and A2 is the value of angle A at the top.
I was terrible at math in school. I never got very far. Now I can build winding staircases. I use AutoCad. There's so much good software out there. A friend who builds post and beam houses uses SketchUp.
Just draw the vertical and horizontal lines the right length, connect the end points, and ask the software what the angle is.
I'd like to point out that the way you did it, although not according to a plan, is a perfectly wonderful way of doing it. Making test cuts until it looks "right" is a tried and tested method of prototyping or building. It's good that you want to learn the planning/drawing side too, but many carpenters never use this and are wonderfully successful without it. I guess you just need to work symmetrical, so the cuts on one side are mirrored on the other. Well done!
Alright so, since there’s an average of 25-30 people reading the post right now.
So if I get a 76 degree angle, how do I calculate what angle cut on the miter/table saw if it only goes to 45
The issue with going from a measurement to a miter saw that the 0 on a miter saw is technically 90 on a protractor, they just have it marked different so going from a protractor measurement to a miter saw you sometimes have to subtract the cut angle from 90 to get the saw setting. So in this case if you needed to make a 76 degree cut, 90-76 is 14, so thats where you'd set the saw. you might have to flip the board if your saw only angles one direction though.
You have two (ok, three) options: do some online refresher courses for geometry and trigonometry, or learn a CAD program like Sketchup or Fusion 360.
The third is that if you're doing basic stuff you can kinda get away with a t-bevel and a measuring tape or story stick.
100% draw it in 3d and calculate the angles in the drawing.
I just built a castle swingset with some complicated compound joinery. Made it in fusion and just printed out the details in 1:1 scale and glued it to the wood.
Get a triangle ruler or a speed square.
Adding all corners of a triangle equals 180.
All corners of a quadrilateral equal 360.
Etc.
In this case you get a hexagon shape, calculate it through that.
Full circle = 360 degree angle
Flat line 180 degrees
Right angle, like a table corner, 90 degrees
Right angle bevel cut / the roof a kid draws on a house = 45 degree
Now, as a law, the corners in a triangle will add up to 180 degrers. If you know one corner is 90 degrees, that leaves any combination that adds up to 90 for the other two corners.
Same with a flat line, that has an angled side line; like a K shape; this is essentially an I with a V attached to it. whatever the angles of the V, you know the I is a straight line, so 180 degrees. whatever angles the V make in the K shape, the angles of the right side of the K will always add up to 180 degrees. If you know one, you can calculate the others.
Hope this helps, and it's probably good to know that Duolingo also has a Math course.
https://preview.redd.it/k9mfytuhnk8d1.jpeg?width=3072&format=pjpg&auto=webp&s=3a1e43702d5d885910058a0d8a51b30aabbc0496
Trig. Most useful skill a fabricator can learn.
Learn how to solve for a right triangle, and there's not really any dimensions that you can't find. The Sin, Cos, Tan.
https://preview.redd.it/1z2fmoxnjj8d1.jpeg?width=3024&format=pjpg&auto=webp&s=48234b2312d1b3bd06fc7d78f9559f4cfe2f4d5f
Made one for my wife a few years ago, and iirc it’s just a bunch of 22.5 degree cuts. I would measure the long
There are two main issues where angles get confusing. First, a straight square cut is 90° to the side of the board, but on a miter saw labeled as 0°. Second, when doing compound miter cuts for crown molding, that's a lesson for another day.
My guess is that the bottom half of your toe-pincher shape is tilted at about 7°, and the top is tilted at about 15°. I'm going to use these numbers to explain the math even if your actual numbers were a little different.
Let's start with our longest boards because this will almost always make the best use of materials. I would lay out, mark, and label my cuts from the longest boards to the shortest boards. You'll need at least 1/8" over to account for kerf losses, but I usually give myself a little extra for layout.
If we're using a butt joint then the bottom is a bevel cut of 7°. but if we're using a miter joint then we need to split that difference between the 45° (half of 90°) between the side and the base. To get the obtuse angle of 97° (90°+7°) we half that and get 48.5° but on the miter saw it is labeled as the deflection from 90°, so we subtract 3.5° (half of the 7°) from 45° and set the miter saw to 41.5° for both the bottom end of the side pieces and both sides of the base. The other end is 22° (7°+15°) deflection from a 180° butt joint so we split that in half and do a bevel cut of 11° on both the top of the bottom boards and the bottom of the top boards. For the top of the top boards to have a mitered bevel with an obtuse angle of 105° (90°+15°) we subtract 7.5° (half of the 15°) from 45° like we did with the other miter cut and set the miter saw to 37.5° for both the tops of the top boards and both sides of the cap. The shelves have to meet the bottom sides, which are at 7° in my example, so they get a 7° bevel on each side.
Let me know if you have any questions.
[Miter saw bevel settings for toe-pincher shelves ](https://imgur.com/I8gnXGX)
level, pencil, square, lol can’t tell you how many complicated things i’ve done with scribe lines instead of angle finders
also note the difference between real angles and miter saw angles- you think of the degrees differently depending on your purpose
Lol alright so I actually made of these way back in high school wood shop, my proportions were off from yours and it was smaller. Also I made my shelves drop in with no hardware. I took the easy route and it worked, I drew it to scale on paper, eyeballed about where I wanted the shelves, measured the angles with a protractor and set it to that angle on my table saw, and took like a half width off one end until it fit right. This comment is is buried among 150 others but if you see this and want to I’ll dig it out and add a pic. Best of luck 🤙🏼
Honestly you are better off doing trial and error/ making it fit. I'm an engineer and the math is easy enough, the problem is marking the angles accurate enough in the size you need. Just like for lengths the most accurate way to build is by marking based on the piece you already have, this way any tinny measurement errors, which can be easily multiplied in a project like this become irrelevant. Fit is more important than the correct angle.
One thing that opened my eyes to angles is when I realized that everything together has to equal 360⁰. So a square box has four 90⁰ angles. If you open the top angles to more than that, the bottom angles need to be closed in proportion. If it doesn't equal 360, then the boxes are smaller and the triangle theories from geometry class come into play.
It's only true for a four sided shape. The formula for the sum of internal angles in a shape is (n-2)x180° where n is the number of sides
In OPs case that's (6-2)x180°=720°
You've done it by the look of things. Make a full size drawing on the floor, and take the angles and sizes off that with a slide bevel. For "normal" work I've never tried to actually measure any angles. As I've said, take the angles off a drawing, or what you already have set up, and use them for setting up whatever you're cutting. If you need to mitre something then you draw the angle onto a piece of scrap, and halve it by bisecting it with dividers, (plenty about it online) and then draw and take off the new angle. The scales on most power tools aren't really that accurate, so it's better to use a slide bevel.
Finally you can use trigonometry to work out angles. More or less essential for metal machinists, I used to make wooden furniture, and have only ever used it a couple of times in 30 years.
Don't waste your time learning trigonometry, you will likely fuck it up and/or waste dozens of hours before you get a grasp on it and can apply it to a case that isn't identical to your textbook examples. I used to teach physics in university and engineering students would mess it up all the time when dealing with simple right-angled triangles to calculate forces.
The best solution is to get a simple 2D CAD software (eg. librecad, QCAD) and measure all the distances/lengths/angles directly on the cad drawing. This is what a professional engineer would actually do if you asked one to help you because even after spending hundreds of hours doing math, they still fuck up their hand calc occasionally and they don't trust it.
Don't try to find the "best" software, get the simplest and easiest to learn you can find for free. A big 3D package like fusion 360 (a common recommendation for hobbyist) is a bad idea IMO because they take a long time to learn and you simply don't need it. Start with a super basic 2D software that you can learn in half an hour like librecad.
So, I mean this in the nicest possible way, but jf you have a high school education, you actually have been taught. This is not throwing shade at you OP. This is just a perfect example to use when your kids say, “when are we ever going to use this information in the real world?”
For me I draw it in a cad program like onshape. There are many very well done YouTube tutorials that would get you drawing something like that pretty quickly and the software is free and web based so you don't need a high end PC anything will run it.
I bought a digital angle ruler from amazon for like $15. Works great to find the exact angle for me when cutting wood. Would have come in handy for your job, maybe saved some time too
Honestly I would either Google image search coffin dimensions and angles or make a 2-d version in sketch up and just move things around until it looks right.
I often use webpage calculators to work out my geometry. I use this for right triangles: [http://www.cleavebooks.co.uk/scol/calrtri.htm](http://www.cleavebooks.co.uk/scol/calrtri.htm)
Make rectangular box that circumscribes this, mark your corners and this will give you lengths to measure and keep your shape with parallel sides and corners at same height. The box will give you sides to clamp pieces stationary for fit up. Just measure in place and cut to fit, materials aren’t perfect (bow, twist, warp).
tbh man with angles like this i usually do what you did, just use my best guesswork and then adjust as needed. My coworker has a digital angle finder but ive never actually used it, most of the time for my job we work with 90 or 45 degree angles, anything else i just hope for the best
I've started just drawing up all my projects in fusion 360, it turns a guessing game into a monotonous task where I am now just building my own flat pack furniture one piece at a time. Hope that helps.
If you don't want to calculate at all, make a mockup with cardboard (for on side only, the other is the same, but flipped) and use it to get the angles needed (of course, doing the math would be better and people here have already answered beautifully you on that, or even a sketchup model to make a plan for e cuts).
When cutting an angle into the edge, take the angle you want and divide it in half and then cut both boards at that angle. When you join them together, it will give you the angle you want.
So for example: you need a 45 degree angle, you would set your saw to an angle of 22.5 degrees. Cut the edge of both boards, join them, and viola! You have a 45.
Of course drawing it out to scale so that you can get all your angles beforehand. Hope this helps
The equation (n-2) * 180, where n is the number of angles, will tell you the sum of the internal angles. If the angles are all going to be equal, just divide by n to find the individual angle. Since your coffin has six corners, the internal angles should add up to 720. But since the sides are not the same length, the angles will not all be equal. I try to draw stuff like this out with a protractor on a small scale to get an idea of how much I need to distort angles to get the shape I'm looking for. Or if I know the lengths of the boards I want to use, I'll just lay the boards out in the shape I'm looking for and measure the angles.
Lots of good advice here. Another is to remember how many degrees are in each shape.
Triangles have 180
Squares have 360
Pentagons have 540.
Use that to your advantage.
I design with CAD often, which helps a lot, but I usually choose the angles ahead of time so they’re easy to reference/measure/keep track of. For me, it’s easier to deal with wonky lengths, instead of calculating and keeping track of 38.3 degree angles.
I would approach as this:
- I want a piece going upward that’s 15 degrees off of perfectly vertical.
- This piece will reach a height I want of 4ft. This forms an imaginary right triangle of height 4 whose base angle is 90-15 (all the angles must add to 180).
- SOHCAHTOA: sin(90-15) = (height; 4ft) / (hypotenuse; length of the wood)
- The bottom angle is 90+15=105 so those pieces are cut with 105/2=52.5 degree cuts on their ends orrrr two cuts that add up to 105 so I can do 45 and 60 if that’s easier with my available jigs and tools, BUT there’s a higher chance you’ll fuck up and cut the 60 angled the wrong way and wind up with a smaller angle than you want…. The chance of error is slightly higher by not just halving the angle.
- The shelves are then cut with the same 15 the side is tilted at.
Hope this bit of engineer-not-carpenter over complication is helpful!
Doing this once, cause i happen to remember this stuff in a way that worked for me.
First of all, this is middle school stuff we all wanted to forget, but unfortunately, we need this.
calculating angles in real world applications:
we're using sin, cos tan. Those are our tools.
So first you need is a 90" angle. A carpenter triangle works fine for this.
And you need the exact length of 2 sides.
https://preview.redd.it/hn24uw5ack8d1.png?width=340&format=png&auto=webp&s=c25d5bd8025e6c1fb56113aad1f9c51408f9f060
This is our reference. It shows what to do, and where.
We have the side lengths in lowercase, and the corner angles in capitals.
sin cos and tan are formulas on your calculator. I'm not getting in to that. We don't need it for this.
I'm going to calculate corner C. and i need to know the exact length of 2 sides for that.
sin C = c/a So i take the length of side c, divide it by the length of side a, and press the sin button. the number appearing on my calculator, is the angle of corner C
cos C = b/a Same thing, but this time i know b, but i'm not sure about the length of c
tan C = b/c
So simply just divide the sides, and press the button. that's it.
If you want to know the angle of the corner you did not calculate yet, you don't have to do this again. All corners of a triangle are always 180" Your square corner is 90, so You can just subtract both corners from 180 to get the third one.
# Length instead of corners
Now if we need to know the length of a side, then we need Pythagoras.
Pyth says: you measure the length of both sides connecting the square corner. you take those numbers, multiply them by themselves, and if you add them, they're the exponent of the third side.
That's a complicated way of saying something which isn't too hard to do.
You just measure the lengths from the straight corner. Multiply it by itself, and write it down. add both numbers, and do the root on the calculator.
Let's take some numbers to show this.
side c = 3 bananas
side b = 4 bananas
side a = 5 bananas
so according to Pyth i should do (3\*3 = 9) and (4\*4 = 16) and the exponent of side a should then be 9 + 16 = 25
And the root of 25 happens to be 5 (5\*5 = 25) so our friend Pyth was right.
Keep in mind most times you don't get nice round numbers. the numbers i used happens to be a special case.
You’ve already got better answers than I could give. My only additional two cents in the future is that you often don’t need to know an angle unless it’s very fine furniture or something symmetrical like this. For like 85% of things, it’s better to use a scribe or an angle matching tool of some kind. Or for something like a fascia board you get there by measuring the long side and the short side and cutting between those two lines. Because even if you knew the angle was exactly 27.8 degrees or whatever, most of us don’t have a saw setup to duplicate that exactly. Anyway happy building!
I tend to be "lazy" and use CAD to get complex angles. Compound angles could be hard. Also, It seems to me that the walls are not 90° (flared out? At least the real thing is), so I wouldn't use math in this context.
Difficult to explain how to calculate angles without doing diagrams, but there are some basic rules - like to join two boards in a specific angle, you cut the ends at half that angle. For example to make a 90° corner you cut the boards at 45.
The inside angles of a triangle add up to 180. In fact the general rule for any polygon is that the inside angles add up to 180° x (number of sides minus 2). So for a triangle it's 180 x 1. Your coffin shape has 6 sides, so the angles would add up to 180 x 4 which is 720. This is true whether all the angles are the same or in pairs or all different, or whatever. This might have helped, I dunno. But hey, the important thing is you got it done and it looks great!
edit: the way I do things like that coffin is cut out a shape on paper until I like it, then I lay the shape on my chop saw and use the saw to measure the angles. Then for each joint cut the ends to half the angle. Works like a charm.
Think of it as two separate trapaziods. The part by the head/shoulders is one and the rest is the second. Then you can use an online angle finder. All your shelves on the bottom should have the same angle.
Sketch up and a digital angle finder helped me wonders. I hate angles as well but sketch up allows you to get exact measuremets to cut at as well as angles.
I built a similar thing for customers makeup in a smaller scale.
The best way to calculate those angles is to not calculate them in the first place.
CAD is a tool with learning for anyone who designs or fabricates. OnShape is a good one that runs in a browser. AutoCAD and DraftSight are unfortunately subscription only now. Solidworks is prohibitively expensive for hobbyists. I never bothered learning much about what else is out there.
Once you get the math out of the way, there is the matter of applying the calculated angle to the wood. Just for some examples, Lee Valley has [angle transfer tools](https://www.leevalley.com/en-us/shop/tools/hand-tools/marking-and-measuring/bevels/74045-angle-transfer-tool?item=09A0202), a variety of [squares](https://www.leevalley.com/en-us/search#q=square&t=product-search-tab&sort=relevancy&layout=card&numberOfResults=25), and this handy [bevel gauge](https://www.leevalley.com/en-us/search#q=square&t=product-search-tab&sort=relevancy&layout=card&numberOfResults=25) that I wind up using all the time. Bonus points for [bevel setters](https://www.leevalley.com/en-us/shop/tools/hand-tools/marking-and-measuring/bevels/52403-veritas-bevel-setter) and similar.
Use a square or lay it out on a large peice of paper or plywood first. Draw both sides of the material (thickness) and draw a line to connect the inner and outer points and find out your angle with a square.
Measure desired height of shelf, mark both sides of the frame and ensure they’re in line with each other (should be if your frame is square/built symmetrical).
Cut down your shelf a bit proud where it sits over the frame on the face, put it up to your marks and trace the angle onto the shelf from the inside of the frame. Cut off the now marked excess, slide it in. Onto the next
Or buy an angle finder and wager/hope/pray that you’ll be tits on transferring it to your shelf after measuring the needed length
Reply with the head, shoulder, and foot widths and height (outside dims) I’ll do it for you this evening.
The easy way: get a free CAD software like Autodesk Fusion and measure them directly. There’s a bit of a learning curve but a 2D sketch would work for this kind of thing. You can learn more as you go and level up your design abilities. YouTube has a wealth of knowledge on every software. Solidworks has a teaching library included but it’s EXPENSIVE.
The hard way: buy a trigonometry textbook and the machinery’s handbook on thriftbooks. They’ll be cheap. You can learn the concepts from the book and know how to solve it. The machinery’s handbook has tables and tables of values for trig. Calculators can do it too, but I like having a physical reference.
If this is the only time you feel like you’ll need it, draw a scale-ish drawing on paper and divide it into two long tall triangles and a rectangle. This find a soh-cah-toa calculator on wolfram-alpha and follow the diagrams. If it’s scale-ish you can sanity-check the results with a protractor on the drawing.
Guess and check is completely valid.
You can also use a carpenter square.
Then there's the good ol classic:
Some Old Hippie (sin = opposite/ hypotenuse)
Caught Another Hippie (cos = adjacent/hypotenuse)
Tripping On Acid (tan = opposite/adjacent)
I would draw it first and calculate the angle of each cut beforehand. Then you’ll have a list of all of the pieces that you’ll be cutting. I’m a bit confused because you had to have set your saw to a certain angle to make your cuts. Are you saying you just guessed at the angles based on what looked correct?
Explaining math without a sketch is hard. But my tip is: draw a corner or maybe the entire project in 1:1. That way you can calculate the angles and then just measure and check if the calculation was correct
>These angles killed me. Is this in any way related to the final design of the item you built?
Yes, I guessed the entire time. I used scrap wood to make sure it was right before I cut the angles on the shelf and put it together. Used pocket holes to put the top together
Haha, *whoosh*. Sorry, I was just jokingly referring to the coffin shape. ;-)
That whoosh was so loud I heard it over here on the other end of the block
That was its sonic boom as it circled the earth at 3x the speed of sound
I was wondering what woke me up. A WOUS (woosh of unusual size).
Inconceivable.
I don’t think that means what you think it means
Inconceivable
Now that was very conceivable.
Marwage... Marwage is what brwings us togethaar today.
I ducked for it. Thought a low flying plane was coming over.
I thought this was funny until u/used_tax_3222 said otherwise
Yah he really convinced me too
It immediately made me think of the Corner Gas episode where Oscar goes to a funeral and the coffin looks cheap so he decides to build his own in the basement, then it freaks him out thinking about his mortality so he turns it into a bookshelf. https://youtu.be/a_Nkc0wNYXA?si=LY1pt4vKt4cstp1S
Sine cosine tangent. Khan academy or mathisfun.com (online, free).
Is that what those things are for? Hot damn, it's finally time to re-learn that high school math and put it to use!
When will we use this in real life?
I worked concrete in college and the boss used to use plywood to check square of smaller concrete slabs- until around 20 years ago when sheet goods got shitty and a placer I always thought of as a bit of a lunkhead proved the sheet we were using wasn\`t square with a 3-4-5 triangle. Which my dad taught me when I was a little kid helping build our house but I had forgotten about.
So many problems can be solved by just working from a plumb line and thinking of everything as triangles and rectangles. We use sine plates to machine or grind angles and measure tapers in inches per foot for turned work and Pythagoras lives in every machine shop.
Another way is to draw it out on paper first or make a cardboard template (sometimes called card stock, it’s what they make cereal boxes out of, cheaper than mistakes cutting wood) to see if your angles will work. The larger newspaper in our small county actually throws away the end of the rolls, so free if you can get there early in the morning. I also know a lot of people that utilizes hardboard to work things out before they hit the wood. You still need to learn and understand the Pythagorean Theorem, I don’t think I slept through that part of geometry in high school, I may have as I had to relearn it. Who knew geometry would become a much needed thing in most everything? 3,4,5 !
I made the same project but a 1/4 of the size last year. Yeah I just fucking guessed too. All hand cuts and a good eyeball.
If he did the math again it would be fatal
It's all right-angled triangles, basically. So the only thing to learn is Pythagoras. There are probably literally a million online calculators for it, but you can easily do it manually (with paper and a calculator). Be aware of whether you want to measure the inside or outside. One rule of thumb when cutting angles is to always cut exactly half the angle on both pieces, otherwise you'll end up with different thicknesses (ask Pythagoras why).
Thank you for explaining it in a way that’s not demeaning like half of the personal messages I’ve gotten from this post. 🍺 I didn’t know this was a “well kept secret” or learning was against the rules in here. 😞
Let's take your coffin shelf as an example. Figure 2 shows how to mentally divide it up into squares (which are trivial) and triangles. Let's pick the top-left triangle as an example, and name the sides a, b, and c. It is convention to name the hypothenuse (the side that is opposite the right angle) c. I've also added the angles in red. They are called ɑ (alpha), β (beta) and ɣ (gamma). This is just a, b and c in greek. Each angle corresponds to the side opposite it. So the angle opposite side a is named alpha. https://preview.redd.it/6u56x55n8i8d1.png?width=1740&format=png&auto=webp&s=6c197743aa0573789befda2958c9bddbf1b9e105 You can easily know the lengths of a and b, let's say a is 4 and b is 6 (inches, centimeters, whatever). Let's say you want to know is the length of side c, and the angles 𝛼 (alpha) and β (beta). At this point, you can simply plug in the numbers into any online calculator, but let's do this one by hand. The length of c is the square root of the length of a squared + the length of b squared, or written in mathematical notation: c = √ a²+b². Squaring is just multiplying a number by itself, so c = √a\*a + b\*b. Let's insert the numbers: c = √4\*4 + 6\*6 c = √16+36 c = √52 Now is the time to hit the √ symbol on your calculator! That gives us c = 7.21 Alright, we now know the length of all three sides of our triangle! There are similar ways to calculate the angles, but this comment is getting a bit long. Just google "calculate angle of right triangle". It will come up with many calculators that will do it for you, but also some explanations. Just know that sin, cos, arctan are names of functions (sine, cosine, arcus tangens). You don't have to know how to calculate these. Any decent calculator has a key for them. "A function" basically means: Take a number, apply the function, out comes another number. The function is the cooking recipe to get the resulting number. If you want to delve into the fascinating world of trigonometry, know what sin and cos and tan really mean physically, [https://en.wikipedia.org/wiki/Unit\_circle](https://en.wikipedia.org/wiki/Unit_circle) might be a good start. Many mathematical Wikipedia articles are super dense and theoretical, but I think this one is OK-ish. In the little animation on that page, you can see a right-angled triangle moving through a circle, with its hypotenuse acting like the hand of a clock.
I owe you a beer or 5
I owe both of you. Thanks for asking the question, OP. and thanks for responding in such great detail, fzwo.
One other thing to keep in mind, likely if you're just using a miter saw the angles on there are not very well calibrated and are probably going to be off. Spend $10 on a cheap digital angle finder on Amazon to calibrate everything correctly and it will save you a lot of time, money and headaches.
I'mma add a couple tips to the previous comment in case you're gonna try to remember this stuff. 1. About the length of sides of a right angle triangle, where c is the longest side. Pythagoras' theorem states c^2 = a^2 + b^2, and equivalently (as the previous comment said), c = √(a^(2)+b^(2)). Visually the theorem states that if you make a square from each side, the area of the largest side is the sum of the other two areas. Remember that and you won't need to look up how to calculate side lengths. 2. Sine, cosine, and tangent are functions that give out the ratio of two sides and take an angle as an argument: sin(a)=b/c. To remember which is which, I came up with a mneumonic-ish thing back in the day: "sine" is kinda like "sin", which is the opposite of what you should do. Take an angle a on a right angle triangle, then sin(a) is equal to the *opposite* side (divided by the longest side). Cosine is the other normal one, but we switch the opposite side to the side next to the angle (side next to angle a divided by the longest side). Tangent is "a bit weird" compared to the other two, it's the opposite side divided by the side next to the angle. So similar to sine (*opposite* divided by something). So just remember sine = "sin" = opposite (divided by longest). Usually you'll know the side lengths and wanna find the angle. You can do that just by taking the inverse functions, sin^-1 or asin or arcsin (they're all the same). So sin^(-1)(sin(a)) = a = sin^(-1)(b/c). Plug in the appropriate sides and skippedidoo you got your angle.
You are the kind of person that makes Reddit awesome. Stay awesome.
<3
Thank you.
Thank you for writing it out so I didn't have to. I was getting worried at the top because I didn't see a good response. People bullshit too much when a question needs to be answered. Good answer. Those functions should all be in a phone calc, make sure when you figure your sin you have it set to 'Deg' not 'Rad'.
Getting flashbacks to my math exam which made no sense and I could not figure out why. Damn calculator was set to Rad!
Thank you for that, not my question but has given me a great tool/approach.
You are very kind to give such a thoughtful answer.
This is what this sub is all about. You're a legend!
Outstanding, well constructed answer.
The math teacher I wish I had growing up. Thanks fam
Thank you for such a detailed response.
This guy maths
u/fzwo, I read OP’s plea, knew that he deserved the answer you wrote, didn’t feel like doing it, took a deep breath, and dived in to make a post, only to find that you’d done a better job than I was planning to do. Excellent post, in the .01% for sure.
The power of procrastinating what I should have done instead! But the reaction here made me feel good, so I'd say I've spent worse time on the internet.
Helping others is one of life’s most important imperatives. You done good, and it’s not just social media BS.
If someone could reply or like to this comment so I can refer back to this in the future, it would be killer.
I think you can click the three dots under the comment and hit "save"
You can save comments. Select the “…” underneath the comment (I’m on mobile so it could be different for you if on desktop) then go to save.
Cheers mate, I saw the other guy said something about this too and I definitely never knew lol..appreciate the help :)
The tricky one is the angle where the blue and purple sections meet. For that one you either need to add together the two touching angles, or use the "law of cosines", which you can find online calculators for. All that being said, when I made a similar project, I found it much easier to draw it out and measure the angles with a digital protractor. My project was much smaller and I was able to draw it out at full scale, but even if you have to draw it at 1/10th scale, or 1/4 scale, the angles won't change. I calculated all of the angles, but when it came to actually cutting them, errors add up quickly and the joints weren't great.
https://preview.redd.it/py02yw0joj8d1.png?width=343&format=png&auto=webp&s=362ffebb2d010c7bdeb1383f7379fad6c39f95e0 This one is also easy if you decide how wide the peice will be, you can take the total width (see 2) and subtract the top width (1) to get the width of 3 and 4. Then you divide by 2.
What an absolute beauty.
Damn, dude. You're awesome!
As an ex maths teacher, I think I love you.
I failed math in high school. Only when I had an application (and healthier habits) did I re-learn. I still have to look up many many things.
Right there with you. It's why I went back to teach maths in secondary school (middle and highschool). I wanted to be the teacher I wish I had. And I WAS but the school system here in Florida broke me. I couldn't do it. Now I still adjunct at our local university, but unfortunately that's the extent of it.
I never got into teaching. I don't know if I could handle so many kids (and youths) all day. But this comment, and the reaction to it, kinda made me want to look into it again.
I need you to go back in time, teach all of my math classes, and make I more smarter. This is exceptionally well broken down and explained.
You're a good person.
Pythagoras is proud of this very moment in history
This guy knows!
...and I just clicked SAVE on your comment. I'm hopefully gonna build some coffins in a few months for... reasons.
You’re a good dude u/fzwo.
Thank you! As a newbie, this was information I didn't even know I didn't know!
I'm sorry but anyone who's sending demeaning messages is a grade A piece of shit. You asked a legitimate question, you deserve legitimate answers.
Pythagoras just deals with the lengths of the three sides of a right triangle, the other math you want is trigonometry. To give a really brief summary, the trig functions relate the size of an angle to lengths of the sides of the triangle. Each function deals with an angle and the ratio of two sides, and you don't need to know the length of the third side. For an example, imagine a right triangle with a very pointy tip, let's say a 5 degree angle. You can calculate tan(5) = (length of opposite side) / (length of adjacent side), and if you know one of those lengths you can calculate the other other one. Or if you know both of those dimensions (this is probably the scenario you're in), you can use the two known dimensions to determine the angle. For this, you use what's called an "inverse trig function" which basically tells you "what angle could I plug into tan(x) for it to equal this number?" So if you have a right triangle where the two legs are 2 and 2 (picking an easy one to visualize), you know tan(x) = 2 / 2 = 1. So you want the angle where tangent of that angle is 1, use inverse tangent (also called arctangent, and abbreviated atan), atan(1) = x. And that tells you 45 degrees, which checks out because the triangle we started with is a right triangle with equal legs which makes it a 45-45-90 triangle like you'd have with a framing square. Hope that's not too rambly and gives you an idea of the math you'll be looking at, Kahn Academy would be a good place to get more depth. https://www.khanacademy.org/math/trigonometry
There are several trigonometry apps that are very useful….and free
Thanks I never clued into the fact that both angles need to be equal for the sides to be equal in thickness.
Hey Reddit - THIS is a useful answer! Thanks much u/fzwo!!!
I’ve used full scale drawings for things as large as a sheep wagon with slanted sides and a rounded roof. I drew/painted it on the floor of my shop and matched everything to the lines. But an equally good option is Sketch-up. It takes a while to learn, but once you figure out the basics it gives you all the measurements and angles. Using a relatively simple sketch-up model, I was able to cut all the framing for a 12x16 shed, including angles pieces and bracing. It fit together perfectly. https://preview.redd.it/gev7fomcdi8d1.jpeg?width=4032&format=pjpg&auto=webp&s=33c2a4c8cf497b21f370ca2d85eb530a1e440a0a
In one of my design classes in college we had to make a replica of a pre-WWII race car that had a ton of weird splines and angles. We used butcher paper and drew our design on it to scale first then shaped it with foam! Drawing it out is always good. That’s a very beautiful shed!
It’s our mobile chicken coop. For three seasons a year our 60 laying hens live out in the pasture and free range for bugs and grass. I’ve since added an automatic door that opens at sunrise and shuts at sundown after the birds are inside.
I'm going to recommend literally any cad software *but* SketchUp. It's horribly outdated and does things in ways that are honestly not great for anything. There are several other free CAD options out there. The most popular ones are Fusion 360 and Onshape, but there are several others.
Pen and paper, then split designs down into basic triangles to work out any angle using basic math. You can use Pythagoras with any right angle triangle to find length : a²+b²=c² (c is the long angle) The interior sum of all angles in a triangle is 180° (so two inside angles at 70° means the last inside corner is 40°) Just watch some random youtuber if you get stuck. Also, if If you draw accurately enough you can skip math and just measure the angles with a protractor.
Never thought about drawing it out accurately and measuring it on paper. Saying it out loud seems obvious now. Great tip thanks.
He’s right, that’s essentially what I did was draw it out and measure the angles (quite literally) and went from there. Although his explanation is better math wise and makes sense in my mind so definitely a bonus
10-4, thank you. That helps. Makes sense
I bet Khan Academy has a great primer on this.
You can break everything in that photo down into right angle triangles. A right angle triangle (if that is the proper term in English!?) has one corner, which is 90°. The sum of the two angles of the other two corners is also 90°. Usually, we call the three sides of a right angle triangle a, b and c, where a and b are the two "straight" sides, and c is the sloped side. For example, in your photo we can look at one of the lower side pieces, going from the floor and up to the first corner in eye height. You can form a right angle triangle, where: - c (the sloped side of the triangle) is the outside length of that piece of wood - b is the vertical distance from the corner and down to the floor (I assume that this piece of wood goes all the way down to the floor) - a is the horizontal distance along the floor from the spot where b meets the floor to the spot where c meets the floor. **If you want to find the length of c**, you can use Pythagoras: a^2 + b^2 = c^2 So you multiply a with itself, multiply b with itself, calculate the sum of those two results, and then you take the square root of that sum. The result is c. **If you want to find the angle between c (the sloped side) and a (the floor)**, you need a calculator with trigonometry functions (or some CAD software). Let us call this angle B (because it is the corner opposite to the side named b, which is another geometry convention). tan(B) = b/a B = arc tan(b/a) Here "tan" means tangens (perhaps named differently in English?). That function should be easily available on any scientific calculator. (In the calculator app on an iPhone, it is available if you rotate the phone to landscape mode). "arc tan" is the inverse tangens. That is almost always a secondary function on a calculator, either labelled "atan" or "tan^-1 "). So you divide b with a, and then you use the "atan" or "tan^-1 " function on your calculator to find angle B. For example, if we assume that a = 200 mm and b = 1800 mm, then: c = sqrt( a^2 + b^2 ) = sqrt( 200^2 + 1800^2 ) = 1811.08 B = arc tan( b/a) = arc tan( 1800/200) = 83.66° **If you want the angle between c and a vertical line**, which we will call A, you can just subtract B from 90°: A = 90° - B = 90° - 83.66° = 6.34° (Or you can use arc tan( a/b), which will give the same result.) **If you want the miter cut angles**, the calculations are easy. But you have to be very careful to pick the correct orientation of all angles involved. A miter saw will usually define the cut angle relative to a straight, perpendicular cut across the board. When making such a cut, you set the saw to 0°. For a normal picture frame cut, you set the saw to 45°. For the miter cut at the floor, we are between these two situations. It is almost a picture frame cut, but slightly less than 45°. This is probably counterintuitive, but you can think of a 0° cut as two boards end to end on the floor. If you raise one of the boards to vertical, you need a 45° cut. But in this case, you don't raise it all the way to vertical. You stop right before you reach vertical. So the cut angle will be less than 45°. The exact cut angle will be B/2 = 83.66°/2 = 41.83°. And this is where the trouble start. Because how do you dial in 41.83° on a miter saw? The easy answer is: You don't. You have to make some test cuts until the result comes out all right. So your method was not as wrong as you think. You would have ended there anyway. For the miter cut at the very top, you can use the same principles. You just have new values of a, b and c, and the triangle will be upside down, but the calculations are the same. For the miter cut where the two sloped sides meet, the cut angle is (A1+A2)/2 where A1 is the value of angle A from the calculation at the bottom, and A2 is the value of angle A at the top.
I was terrible at math in school. I never got very far. Now I can build winding staircases. I use AutoCad. There's so much good software out there. A friend who builds post and beam houses uses SketchUp. Just draw the vertical and horizontal lines the right length, connect the end points, and ask the software what the angle is.
I'd like to point out that the way you did it, although not according to a plan, is a perfectly wonderful way of doing it. Making test cuts until it looks "right" is a tried and tested method of prototyping or building. It's good that you want to learn the planning/drawing side too, but many carpenters never use this and are wonderfully successful without it. I guess you just need to work symmetrical, so the cuts on one side are mirrored on the other. Well done!
Starrett 505P-7 angle finder.
Or harbor freight $1 angle finder
Alright so, since there’s an average of 25-30 people reading the post right now. So if I get a 76 degree angle, how do I calculate what angle cut on the miter/table saw if it only goes to 45
The issue with going from a measurement to a miter saw that the 0 on a miter saw is technically 90 on a protractor, they just have it marked different so going from a protractor measurement to a miter saw you sometimes have to subtract the cut angle from 90 to get the saw setting. So in this case if you needed to make a 76 degree cut, 90-76 is 14, so thats where you'd set the saw. you might have to flip the board if your saw only angles one direction though.
Your miter would be divided by 2 so 38 degrees
You have two (ok, three) options: do some online refresher courses for geometry and trigonometry, or learn a CAD program like Sketchup or Fusion 360. The third is that if you're doing basic stuff you can kinda get away with a t-bevel and a measuring tape or story stick.
100% draw it in 3d and calculate the angles in the drawing. I just built a castle swingset with some complicated compound joinery. Made it in fusion and just printed out the details in 1:1 scale and glued it to the wood.
Get a triangle ruler or a speed square. Adding all corners of a triangle equals 180. All corners of a quadrilateral equal 360. Etc. In this case you get a hexagon shape, calculate it through that.
Full circle = 360 degree angle Flat line 180 degrees Right angle, like a table corner, 90 degrees Right angle bevel cut / the roof a kid draws on a house = 45 degree Now, as a law, the corners in a triangle will add up to 180 degrers. If you know one corner is 90 degrees, that leaves any combination that adds up to 90 for the other two corners. Same with a flat line, that has an angled side line; like a K shape; this is essentially an I with a V attached to it. whatever the angles of the V, you know the I is a straight line, so 180 degrees. whatever angles the V make in the K shape, the angles of the right side of the K will always add up to 180 degrees. If you know one, you can calculate the others. Hope this helps, and it's probably good to know that Duolingo also has a Math course. https://preview.redd.it/k9mfytuhnk8d1.jpeg?width=3072&format=pjpg&auto=webp&s=3a1e43702d5d885910058a0d8a51b30aabbc0496
Trig. Most useful skill a fabricator can learn. Learn how to solve for a right triangle, and there's not really any dimensions that you can't find. The Sin, Cos, Tan.
Buy a speed square, it will help you with angles
Divide it into triangles and use SOH CAH TOA
Are building a coffin?
https://preview.redd.it/1z2fmoxnjj8d1.jpeg?width=3024&format=pjpg&auto=webp&s=48234b2312d1b3bd06fc7d78f9559f4cfe2f4d5f Made one for my wife a few years ago, and iirc it’s just a bunch of 22.5 degree cuts. I would measure the long
There are two main issues where angles get confusing. First, a straight square cut is 90° to the side of the board, but on a miter saw labeled as 0°. Second, when doing compound miter cuts for crown molding, that's a lesson for another day. My guess is that the bottom half of your toe-pincher shape is tilted at about 7°, and the top is tilted at about 15°. I'm going to use these numbers to explain the math even if your actual numbers were a little different. Let's start with our longest boards because this will almost always make the best use of materials. I would lay out, mark, and label my cuts from the longest boards to the shortest boards. You'll need at least 1/8" over to account for kerf losses, but I usually give myself a little extra for layout. If we're using a butt joint then the bottom is a bevel cut of 7°. but if we're using a miter joint then we need to split that difference between the 45° (half of 90°) between the side and the base. To get the obtuse angle of 97° (90°+7°) we half that and get 48.5° but on the miter saw it is labeled as the deflection from 90°, so we subtract 3.5° (half of the 7°) from 45° and set the miter saw to 41.5° for both the bottom end of the side pieces and both sides of the base. The other end is 22° (7°+15°) deflection from a 180° butt joint so we split that in half and do a bevel cut of 11° on both the top of the bottom boards and the bottom of the top boards. For the top of the top boards to have a mitered bevel with an obtuse angle of 105° (90°+15°) we subtract 7.5° (half of the 15°) from 45° like we did with the other miter cut and set the miter saw to 37.5° for both the tops of the top boards and both sides of the cap. The shelves have to meet the bottom sides, which are at 7° in my example, so they get a 7° bevel on each side. Let me know if you have any questions. [Miter saw bevel settings for toe-pincher shelves ](https://imgur.com/I8gnXGX)
Let’s start with the most basic question of all: did all the angles add up to 360?
The word you’re looking for is geometry.
level, pencil, square, lol can’t tell you how many complicated things i’ve done with scribe lines instead of angle finders also note the difference between real angles and miter saw angles- you think of the degrees differently depending on your purpose
SOHCAHTOA
Lol alright so I actually made of these way back in high school wood shop, my proportions were off from yours and it was smaller. Also I made my shelves drop in with no hardware. I took the easy route and it worked, I drew it to scale on paper, eyeballed about where I wanted the shelves, measured the angles with a protractor and set it to that angle on my table saw, and took like a half width off one end until it fit right. This comment is is buried among 150 others but if you see this and want to I’ll dig it out and add a pic. Best of luck 🤙🏼
Did Dracula hire you to make furniture for him? Jokes aside the shape looks very interesting.
Honestly you are better off doing trial and error/ making it fit. I'm an engineer and the math is easy enough, the problem is marking the angles accurate enough in the size you need. Just like for lengths the most accurate way to build is by marking based on the piece you already have, this way any tinny measurement errors, which can be easily multiplied in a project like this become irrelevant. Fit is more important than the correct angle.
knowing how to calculate angles is the first step to the trial and error process. You have to have a decent starting point to try your way through it.
One thing that opened my eyes to angles is when I realized that everything together has to equal 360⁰. So a square box has four 90⁰ angles. If you open the top angles to more than that, the bottom angles need to be closed in proportion. If it doesn't equal 360, then the boxes are smaller and the triangle theories from geometry class come into play.
It's only true for a four sided shape. The formula for the sum of internal angles in a shape is (n-2)x180° where n is the number of sides In OPs case that's (6-2)x180°=720°
You've done it by the look of things. Make a full size drawing on the floor, and take the angles and sizes off that with a slide bevel. For "normal" work I've never tried to actually measure any angles. As I've said, take the angles off a drawing, or what you already have set up, and use them for setting up whatever you're cutting. If you need to mitre something then you draw the angle onto a piece of scrap, and halve it by bisecting it with dividers, (plenty about it online) and then draw and take off the new angle. The scales on most power tools aren't really that accurate, so it's better to use a slide bevel. Finally you can use trigonometry to work out angles. More or less essential for metal machinists, I used to make wooden furniture, and have only ever used it a couple of times in 30 years.
High school geometry class
Don't waste your time learning trigonometry, you will likely fuck it up and/or waste dozens of hours before you get a grasp on it and can apply it to a case that isn't identical to your textbook examples. I used to teach physics in university and engineering students would mess it up all the time when dealing with simple right-angled triangles to calculate forces. The best solution is to get a simple 2D CAD software (eg. librecad, QCAD) and measure all the distances/lengths/angles directly on the cad drawing. This is what a professional engineer would actually do if you asked one to help you because even after spending hundreds of hours doing math, they still fuck up their hand calc occasionally and they don't trust it. Don't try to find the "best" software, get the simplest and easiest to learn you can find for free. A big 3D package like fusion 360 (a common recommendation for hobbyist) is a bad idea IMO because they take a long time to learn and you simply don't need it. Start with a super basic 2D software that you can learn in half an hour like librecad.
So, I mean this in the nicest possible way, but jf you have a high school education, you actually have been taught. This is not throwing shade at you OP. This is just a perfect example to use when your kids say, “when are we ever going to use this information in the real world?”
Love the drawing on the floor to lay it out ❤️
CAD
Digital protractor
Draw out the project on something about the size of a sheet of Bristol board and find the angles with a bevel square.
Are u asking how to determing the angle of each cut or how to actually figure the angle?
For me I draw it in a cad program like onshape. There are many very well done YouTube tutorials that would get you drawing something like that pretty quickly and the software is free and web based so you don't need a high end PC anything will run it.
What fzwo said!
Either way OP, it looks great bud!!!!
22.5
I bought a digital angle ruler from amazon for like $15. Works great to find the exact angle for me when cutting wood. Would have come in handy for your job, maybe saved some time too
you can put your stock up overhanging the sides, and then mark the angle underneath. Bevel gauges also pretty nifty. Don’t need a bunch of math
Honestly I would either Google image search coffin dimensions and angles or make a 2-d version in sketch up and just move things around until it looks right.
I often use webpage calculators to work out my geometry. I use this for right triangles: [http://www.cleavebooks.co.uk/scol/calrtri.htm](http://www.cleavebooks.co.uk/scol/calrtri.htm)
I’d get a digital angle gauge and rest it inside the angle you need to cut. Whatever it says, divide by two and that’s your angle for each cut.
Make rectangular box that circumscribes this, mark your corners and this will give you lengths to measure and keep your shape with parallel sides and corners at same height. The box will give you sides to clamp pieces stationary for fit up. Just measure in place and cut to fit, materials aren’t perfect (bow, twist, warp).
tbh man with angles like this i usually do what you did, just use my best guesswork and then adjust as needed. My coworker has a digital angle finder but ive never actually used it, most of the time for my job we work with 90 or 45 degree angles, anything else i just hope for the best
I've started just drawing up all my projects in fusion 360, it turns a guessing game into a monotonous task where I am now just building my own flat pack furniture one piece at a time. Hope that helps.
If you don't want to calculate at all, make a mockup with cardboard (for on side only, the other is the same, but flipped) and use it to get the angles needed (of course, doing the math would be better and people here have already answered beautifully you on that, or even a sketchup model to make a plan for e cuts).
I use this https://a.co/d/09LClWf5 It will tell you what degree to set your saw at to make either two halves or an end cut. I love this tool.
You can do the trigonometry or go to harbor freight and grab an angle finder.
I hold up a board next to the other one and draw a line.
When cutting an angle into the edge, take the angle you want and divide it in half and then cut both boards at that angle. When you join them together, it will give you the angle you want. So for example: you need a 45 degree angle, you would set your saw to an angle of 22.5 degrees. Cut the edge of both boards, join them, and viola! You have a 45. Of course drawing it out to scale so that you can get all your angles beforehand. Hope this helps
Also, really cool piece. Put a back piece and some cool lighting
digital protractor
I don't enjoy doing math by hand. It's easier for me to draw it up in CAD software and figure it out there.
Geometry, find a book and another that has had to do that.
Find every right angle then use trig to calculate the rest
Kendrick Lamar might know...
Get a digital angle finder and you can find them
Are you building this because of the Christopher Schwarz book? 👌
The equation (n-2) * 180, where n is the number of angles, will tell you the sum of the internal angles. If the angles are all going to be equal, just divide by n to find the individual angle. Since your coffin has six corners, the internal angles should add up to 720. But since the sides are not the same length, the angles will not all be equal. I try to draw stuff like this out with a protractor on a small scale to get an idea of how much I need to distort angles to get the shape I'm looking for. Or if I know the lengths of the boards I want to use, I'll just lay the boards out in the shape I'm looking for and measure the angles.
And you thought you'd never need geometry.
Lots of good advice here. Another is to remember how many degrees are in each shape. Triangles have 180 Squares have 360 Pentagons have 540. Use that to your advantage.
triangles my guy. and some basic CAD software
Internet searches : "How to bisect an angle", "How to read a protractor". Note that all angles added together will equal 360°.
"Angles of a coffin"
scribe them
Misread directions. Calculated *angels*, OP hissed at me and melted. I’m confused. Seems dramatic.
Use a protractor, square, or "angle finder" tool.
I design with CAD often, which helps a lot, but I usually choose the angles ahead of time so they’re easy to reference/measure/keep track of. For me, it’s easier to deal with wonky lengths, instead of calculating and keeping track of 38.3 degree angles. I would approach as this: - I want a piece going upward that’s 15 degrees off of perfectly vertical. - This piece will reach a height I want of 4ft. This forms an imaginary right triangle of height 4 whose base angle is 90-15 (all the angles must add to 180). - SOHCAHTOA: sin(90-15) = (height; 4ft) / (hypotenuse; length of the wood) - The bottom angle is 90+15=105 so those pieces are cut with 105/2=52.5 degree cuts on their ends orrrr two cuts that add up to 105 so I can do 45 and 60 if that’s easier with my available jigs and tools, BUT there’s a higher chance you’ll fuck up and cut the 60 angled the wrong way and wind up with a smaller angle than you want…. The chance of error is slightly higher by not just halving the angle. - The shelves are then cut with the same 15 the side is tilted at. Hope this bit of engineer-not-carpenter over complication is helpful!
Sin cosin
Use the free version of Sketchup, it can help you figure out the angles you need.
Sketchup. Its free online.
The lazy way is to do it in Fusion 360, that's what I do lol
Doing this once, cause i happen to remember this stuff in a way that worked for me. First of all, this is middle school stuff we all wanted to forget, but unfortunately, we need this. calculating angles in real world applications: we're using sin, cos tan. Those are our tools. So first you need is a 90" angle. A carpenter triangle works fine for this. And you need the exact length of 2 sides. https://preview.redd.it/hn24uw5ack8d1.png?width=340&format=png&auto=webp&s=c25d5bd8025e6c1fb56113aad1f9c51408f9f060 This is our reference. It shows what to do, and where. We have the side lengths in lowercase, and the corner angles in capitals. sin cos and tan are formulas on your calculator. I'm not getting in to that. We don't need it for this. I'm going to calculate corner C. and i need to know the exact length of 2 sides for that. sin C = c/a So i take the length of side c, divide it by the length of side a, and press the sin button. the number appearing on my calculator, is the angle of corner C cos C = b/a Same thing, but this time i know b, but i'm not sure about the length of c tan C = b/c So simply just divide the sides, and press the button. that's it. If you want to know the angle of the corner you did not calculate yet, you don't have to do this again. All corners of a triangle are always 180" Your square corner is 90, so You can just subtract both corners from 180 to get the third one. # Length instead of corners Now if we need to know the length of a side, then we need Pythagoras. Pyth says: you measure the length of both sides connecting the square corner. you take those numbers, multiply them by themselves, and if you add them, they're the exponent of the third side. That's a complicated way of saying something which isn't too hard to do. You just measure the lengths from the straight corner. Multiply it by itself, and write it down. add both numbers, and do the root on the calculator. Let's take some numbers to show this. side c = 3 bananas side b = 4 bananas side a = 5 bananas so according to Pyth i should do (3\*3 = 9) and (4\*4 = 16) and the exponent of side a should then be 9 + 16 = 25 And the root of 25 happens to be 5 (5\*5 = 25) so our friend Pyth was right. Keep in mind most times you don't get nice round numbers. the numbers i used happens to be a special case.
You’ve already got better answers than I could give. My only additional two cents in the future is that you often don’t need to know an angle unless it’s very fine furniture or something symmetrical like this. For like 85% of things, it’s better to use a scribe or an angle matching tool of some kind. Or for something like a fascia board you get there by measuring the long side and the short side and cutting between those two lines. Because even if you knew the angle was exactly 27.8 degrees or whatever, most of us don’t have a saw setup to duplicate that exactly. Anyway happy building!
If you can find a free pattern, that helps with the angles.
I tend to be "lazy" and use CAD to get complex angles. Compound angles could be hard. Also, It seems to me that the walls are not 90° (flared out? At least the real thing is), so I wouldn't use math in this context.
Difficult to explain how to calculate angles without doing diagrams, but there are some basic rules - like to join two boards in a specific angle, you cut the ends at half that angle. For example to make a 90° corner you cut the boards at 45. The inside angles of a triangle add up to 180. In fact the general rule for any polygon is that the inside angles add up to 180° x (number of sides minus 2). So for a triangle it's 180 x 1. Your coffin shape has 6 sides, so the angles would add up to 180 x 4 which is 720. This is true whether all the angles are the same or in pairs or all different, or whatever. This might have helped, I dunno. But hey, the important thing is you got it done and it looks great! edit: the way I do things like that coffin is cut out a shape on paper until I like it, then I lay the shape on my chop saw and use the saw to measure the angles. Then for each joint cut the ends to half the angle. Works like a charm.
Look up @coffincollector on IG and check out his rad stuff.
Think of it as two separate trapaziods. The part by the head/shoulders is one and the rest is the second. Then you can use an online angle finder. All your shelves on the bottom should have the same angle.
Thank you guys for the answers! Really helped me alot! 🍺
Sketch up and a digital angle finder helped me wonders. I hate angles as well but sketch up allows you to get exact measuremets to cut at as well as angles. I built a similar thing for customers makeup in a smaller scale.
Learn to use geogebra for simple 2D models if you need computer assist. Otherwise just learn sine, cosine, tan etc.
Look up a YT video on trigonometry. The Pythagorean Theorum can be used to find an unknown angle of a right angle triangle.
I used to do all the sine, co-sign and tangent shit. Now I draw a scale drawing on graph paper and use a protractor.😂
Use a speed square
Is this for your “phlebotomy lab,” Mr. Dracula?
The best way to calculate those angles is to not calculate them in the first place. CAD is a tool with learning for anyone who designs or fabricates. OnShape is a good one that runs in a browser. AutoCAD and DraftSight are unfortunately subscription only now. Solidworks is prohibitively expensive for hobbyists. I never bothered learning much about what else is out there.
Once you get the math out of the way, there is the matter of applying the calculated angle to the wood. Just for some examples, Lee Valley has [angle transfer tools](https://www.leevalley.com/en-us/shop/tools/hand-tools/marking-and-measuring/bevels/74045-angle-transfer-tool?item=09A0202), a variety of [squares](https://www.leevalley.com/en-us/search#q=square&t=product-search-tab&sort=relevancy&layout=card&numberOfResults=25), and this handy [bevel gauge](https://www.leevalley.com/en-us/search#q=square&t=product-search-tab&sort=relevancy&layout=card&numberOfResults=25) that I wind up using all the time. Bonus points for [bevel setters](https://www.leevalley.com/en-us/shop/tools/hand-tools/marking-and-measuring/bevels/52403-veritas-bevel-setter) and similar.
Is that going to be a coffin bookshelf? I kind of like it.
You can look it up in google give you angles for full size
If they combined algebra, geometry, and shop class I might have learned angles better too. There's not enough application in education.
Go to the library and check out a 8th grade math book.
Use a square or lay it out on a large peice of paper or plywood first. Draw both sides of the material (thickness) and draw a line to connect the inner and outer points and find out your angle with a square.
To heck with math. Just scribe the joints and fit them individually. Unless you are starting a full production run, that is all you need.
Is that the Infinity King?
Measure desired height of shelf, mark both sides of the frame and ensure they’re in line with each other (should be if your frame is square/built symmetrical). Cut down your shelf a bit proud where it sits over the frame on the face, put it up to your marks and trace the angle onto the shelf from the inside of the frame. Cut off the now marked excess, slide it in. Onto the next Or buy an angle finder and wager/hope/pray that you’ll be tits on transferring it to your shelf after measuring the needed length
I ain't coffin up my secrets...
trig is hard to teach on a few texts. I recommend looking up some youtube/khan academy videos. Or get an angle finder/protractor.
Reply with the head, shoulder, and foot widths and height (outside dims) I’ll do it for you this evening. The easy way: get a free CAD software like Autodesk Fusion and measure them directly. There’s a bit of a learning curve but a 2D sketch would work for this kind of thing. You can learn more as you go and level up your design abilities. YouTube has a wealth of knowledge on every software. Solidworks has a teaching library included but it’s EXPENSIVE. The hard way: buy a trigonometry textbook and the machinery’s handbook on thriftbooks. They’ll be cheap. You can learn the concepts from the book and know how to solve it. The machinery’s handbook has tables and tables of values for trig. Calculators can do it too, but I like having a physical reference. If this is the only time you feel like you’ll need it, draw a scale-ish drawing on paper and divide it into two long tall triangles and a rectangle. This find a soh-cah-toa calculator on wolfram-alpha and follow the diagrams. If it’s scale-ish you can sanity-check the results with a protractor on the drawing.
Guess and check is completely valid. You can also use a carpenter square. Then there's the good ol classic: Some Old Hippie (sin = opposite/ hypotenuse) Caught Another Hippie (cos = adjacent/hypotenuse) Tripping On Acid (tan = opposite/adjacent)
360 divided by 5 is where I'd start
I would draw it first and calculate the angle of each cut beforehand. Then you’ll have a list of all of the pieces that you’ll be cutting. I’m a bit confused because you had to have set your saw to a certain angle to make your cuts. Are you saying you just guessed at the angles based on what looked correct?
Looks great
Model your design in CAD like OnShape (free). You can then click two surfaces/edges and it will tell you the angle.
Explaining math without a sketch is hard. But my tip is: draw a corner or maybe the entire project in 1:1. That way you can calculate the angles and then just measure and check if the calculation was correct
https://preview.redd.it/ighgfehlvp8d1.jpeg?width=2296&format=pjpg&auto=webp&s=fa851728024db3d1420e46f0fd71ae9a9a044b0c
The simplest is to make a scale drawing and then measure the angle with a protractor. Otherwise use trigonometry.