# Triangle Math {Tutorial}

I was recently contacted via email by someone who saw my Equilateral Triangle Calculator. They were hoping that I could update my spreadsheet to represent the angles of a triangle they would be working with that was not an equilateral triangle. After some thought into the nature of the request, I decided that I want to give tools to be able to figure this out again in the future, should anyone want a different triangle size. (I won’t necessarily always be immediately available to modify a spreadsheet.)

So let’s talk paper templates and accuracy, using triangles as our shape of focus.

I believe there is a lot of beauty in a piece of paper, ruler, and pencil. Maybe that is due to my engineering background and the hand drafting classes I took in college (yup, I took hand drafting and not computer drafting courses). Whatever the reason, I hope this post helps illuminate the power of hand drafting patterns / templates and rubs at least a bit of my excitement off on you. 😉

## Example Parameters

OK, let’s say that you know how big you want your triangle quilt to be when it is complete, and you also know how many triangles you are willing to cut.

## Desired Quilt Size: 64 inches wide by 74 inches long

## Desired number of rows: 16

Desired number of triangles in each row: 29

The easiest measurement to calculate will be the finished height of your pieced triangles. Simply divide the quilt length by the number of rows. In this example, the triangles will finish at 74 / 16 = 4 5/8 inches tall.

When calculating the size of the base of the finished triangle, the first thing to keep in mind is that triangle quilts nest the triangles together in the rows, as the following example top illustrates:

For a row with 29 triangles, that means that the full width of the base of 15 triangles will be used. This is another time when doing a quick sketch on paper with a pencil (it doesn’t have to be exact) can be handy to illustrate your idea. To calculate the finished base width of your triangle, divide the quilt width by the number triangle base widths for a row. In this example, 64 / 15 = 4.26666, which I rounded down to 4 1/4 inches wide. The rounding down to an even measurement results in a finished quilt top of 63 3/4 inches wide, which I thought was close enough to my initial goal of 64 inches.

Now that I know the finished or pieced size of the triangles I need for the quilt top, it is time to figure out the size of the triangles I need to cut in order to achieve the finished size I desire. This is where the hand drafting of a pattern or template comes in.

I started by folding a piece of paper in half. I measured and marked along the folded edge the finished height of the pieced triangle, 4 5/8 inches. On each side of the fold, I measured over half the base width of the finished triangle, half of 4 1/4 inches is 2 1/8 inches. After flattening out the paper, I then used the three measured points to draw out my finished triangle size.

To begin the process of determining the size of the triangles that I need to cut in order to achieve the finished size, I made several measurements 1/4 inch OUTSIDE of the drawn triangle. Note that I marked these quarter inch points perpendicularly to the edge of the triangle as best as I could. After making several quarter inch points, I could connect the points to create the sides of the larger triangle.

Once the larger triangle is drawn, it is then a simple matter of measuring to determine the size of the triangles that need cut. For this example, I would need to cut isosceles triangles that are 5 1/2 inches tall and 5 inches wide at the base.

The pattern itself can then be used to cut your triangles, if you so desire. Note that when I took the final measurements, I rounded to the nearest 1/8 of an inch – the ruler I used was marked in 1/16 inch increments, but I much prefer to work with 1/8 inch measurements as my smallest unit of measure.

And to wrap this all up with why hand drawing templates are awesome, I asked my husband to go through this same exercise using a CAD (computer aided design) program.

The CAD model shows that my measurements were only off by 0.03 inches. Not too shabby! Especially when you consider that quilts tend to shrink 6-9% due to quilting and washing.

This example walked you through how to determine the size triangles you want / need to achieve a particular quilt size. If you have a quilt ruler that cuts triangles a particular size, you can do this in reverse. First, draw the size of the triangles that will be cut. Then measure 1/4 inch INSIDE of the lines and draw the size of the finished triangles. Measure your finished triangle size and then determine how many you will need in a row and how many rows to get your desired quilt size.

I hope this information is helpful, both for having confidence in triangle math calculations and in giving you confidence to create your own hand drafted patterns!

## 19 comments

I like math and have drafted patterns by hand in the past but I had never looked at how to do it if I wanted a quilt with all triangles. Thanks for sharing this. If you eve do another one, I’d love to see how to determine the little things that are cut off so the pieces go together easily when sewing. As I wrote this I thought maybe this wouldn’t need to be done with this type of triangle. Now I may have to draw one and see. Thanks again for your posts. I like that you share your quilts but then approach your blog as a teacher would. Perhaps at a later date, you could teach classes.

The math geek in me loves this.

This is helpful Yvonne. I have a small triangle ruler and this will help me in deterring how many to cut. Thanks!

Thank you, Yvonne. I’m looking forward to using this tutorial soon!

Thank you!

Thank you Yvonne! I have bookmarked this on my laptop and saved it in bloglovin’ for future reference. May I say I went “mmm!” at this: “I believe there is a lot of beauty in a piece of paper, ruler, and pencil. ” Oh me too, me too. Notice I had Brady draw his quilt plan?! Love the math part too, even though sometimes these days it makes my brain ache lol.

Great tip! I know that triangles stump a lot of people.

Well I now know I am not a math geek but like Beth I have a triangle ruler and I could use this to figure out how many to cut.

I’m not very good with many aspects of math but this I can follow (I did better with geometry than algebra). Thanks for this. It’s a great thing to keep handy.

I have yet to make a triangle quilt, but this will be most helpful in the future! Thanks!

I too learnt how to draft on the board … I miss it. Computers are so clinical, but efficient tools so they win speed-wise … but draftibg on a board was art. Great tutorial, very clear 🙂

I’m so glad there are people like you who enjoy this! It makes it so much easier for people like me who get a blank stare when the word math is mentioned!

We did half and half – board and AutoCAD, I loved the computer – we learned technical drawing by building the Eiffel tower – great fun! Lots and lots of triangles!

I will be honest triangles scare me, but I hope someday to overcome that fear, so I’m saving this for future reference.

Only out by 0.03 inches is not too shabby at all!

Thank you so much for this step-by-step tutorial. I find these very helpful and hope you continue to offer this type of tutorial in the future.

Thank you Yvonne! I’m terrible with numbers and this will help a lot! I love triangles – any kind! x Teje

Fascinating! I loved the comparison of pencil and computer. Thanks for sharing.

Maths and quilts go so well together! And loving the beauty of paper, pen and ruler too!