How to Cut Equilateral Triangles

Equilateral triangles can be a little intimidating at first, but once you get the hang of them they really aren’t too hard.

Math

One thing that really drives me nuts about quilting tutorials is how often the math gets ignored. It is arguably the most important step in planning your quilt! It was especially hard to find the formulas for equilateral triangles – perhaps because the math involved is slightly more complicated – but then how does anybody figure out how many triangles they need to cut for their quilt? No worries – I’ve got you covered here!

Let’s say you’re looking to make an equilateral triangle baby quilt that is approximately 40″ x 50″.

Start by deciding how tall you want your finished triangles. This number can be anything you decide! What size triangle do you feel like working with? For easy math, pick something in intervals of ¼”. For our example let’s make the finished triangles 4¼” tall. To figure out how rows many triangles you’d need along the length of the quilt you simply divide the quilt length by the triangle height:

50 ÷ 4.25 = 11.77

Obviously you can’t have partial triangles, so round up or down, whichever makes more sense. I’d round up here and use 12 rows of triangles, making the quilt 51″ long.

To determine how tall of a strip you should cut for your triangles, simply add ¾” to your finished triangle height. This adds the extra needed for seam allowance. For our example you would need to cut strips of fabric 5″ tall.

To figure out how many triangles are needed in each row, we first need to figure out the measurement of the triangle side using the formula

triangle side = (2 ÷ √3) × height

With a little help from a calculator this time (because I’ve never been good at math in my head)

(2 ÷ √3) × 4.25 = 4.91

Then we divide the quilt width by the length of the triangle side

40 ÷ 4.91 = 8.15

Again round to a whole number. Let’s round down this time, using 8 triangles across, making the quilt about 39¼” wide. Now we can’t just stop there – because the triangles are sewn together alternating up and down, that’s actually only half of the triangles needed. You need to double that to get the full number, keeping in mind that two half triangles go on the ends.

So our example quilt would have 12 rows with 15 full triangles and 2 half triangles in each row.

That’s how you figure out how many triangles you need when you know the size you want to make your quilt. Not too hard, right?

Cutting

Now that you know how many triangles you need you can get to cutting!

To cut your equilateral triangles using this method you’ll need a ruler with a 60° mark. There’s lots of different rulers, so yours might look slightly different than mine. I have a long rectangle ruler, so that’s what I’ll be using in this tutorial.

In case you skipped the math part above, you’ll need to cut your fabric strip ¾” taller than your finished triangle height × the length of the fabric. The triangles I’m cutting in this example are 9½” × the width of fabric.

Since you’ll be sewing along so many bias edges, starch can be helpful. If you’re careful handling your pieces it’s not necessary, but it can make the triangles easier to work with.

Trim off the selvages. Line up the 60° angle on the ruler with the top of the fabric, leaving ¼” along the top of the triangle. This gives you a half triangle with seam allowance that you can use on the ends of your rows.

Cut.

Line up the 60° angle with the bottom of the fabric, making sure the ruler forms a point with the fabric. This makes your first equilateral triangle.

Continue rotating the ruler from top to bottom in order to keep cutting triangles along your strip.

As you cut stack all your equilateral triangles matching the straight of grain together and mark the straight of grain side. You’ll thank yourself later! (It’s important to know which side is which when you sew.) I use a pin on the bottom triangle to mark mine.