Half-square triangle math, explained

To make a finished half-square triangle, cut your starting squares larger than the finished size and then trim down. The exact amount depends on how many HSTs you want from each pair of squares: add 7/8 inch for the 2 at a time method, 1 1/4 inch for 4 at a time, or double the sum of the finished size plus 7/8 inch for 8 at a time.

An HST, or half-square triangle, is a square block split diagonally into two triangles of different fabrics. The math is all about the diagonal seam and the seam allowance eating into it, so every method builds in a little extra fabric you cut away at the end.

Two at a time: add 7/8 inch

Stack two squares right sides together, draw a line across the diagonal, and sew a quarter inch on each side of that line. Cut on the drawn line and you get two HSTs.

Cut each square 7/8 inch larger than the finished size. For a 4 inch finished HST that means 4 7/8 inch squares. The 7/8 covers the diagonal seam allowance plus a hair for trimming. This is the method most patterns assume, and it is the easiest to keep accurate.

Four at a time: add 1 1/4 inch

Layer two squares right sides together, sew a quarter inch around all four sides, then cut across both diagonals. That gives four HSTs from two squares.

Cut each square 1 1/4 inch larger than the finished size. A 4 inch finished HST needs 5 1/4 inch squares. It is faster than the two at a time method for larger batches, but the outer edges of these HSTs end up on the bias, so handle them gently to avoid stretching.

Eight at a time: double the finished plus 7/8

Draw both diagonals on a large square, sew a quarter inch on each side of both lines, then cut the square into quarters and cut on the drawn lines. You get eight HSTs at once.

Cut each square to double the sum of the finished size and 7/8 inch. For a 4 inch finished HST: (4 + 7/8) times 2 = 9 3/4 inch squares. This is the fastest way to make a pile of matching HSTs, which is why it is popular for scrappy quilts and pinwheels.

Cutting table

Each number below is the size to cut your starting squares for the finished HST size in the left column.

Finished HST	2 at a time	4 at a time	8 at a time
2“	2 7/8“	3 1/4“	5 3/4“
3“	3 7/8“	4 1/4“	7 3/4“
4“	4 7/8“	5 1/4“	9 3/4“
6“	6 7/8“	7 1/4“	13 3/4“

Why trim to size?

Every method here leaves the HSTs a touch oversized on purpose. Pressing pulls the block slightly out of square, and the bias edges want to stretch, so you square up each HST to its unfinished size before piecing. For a 4 inch finished HST, that unfinished size is 4 1/2 inches, which is the finished size plus a half inch for the two seam allowances. A square ruler with a 45 degree line makes this quick: line the diagonal up with the seam and shave the two far sides.

Trimming is the step that keeps points sharp and rows the right length. Skipping it is the most common reason a block of HSTs ends up too small.

Let the app do the math

The half-square triangle calculator gives you the cut size for any finished measurement and any method, so you never have to remember which fraction goes with which. Sashing on iPhone does the same offline and works out how many starting squares you need for the whole quilt.