Half-Square Triangle Calculator (Plus QSTs and Flying Geese)

Calculator

Turn on JavaScript to use the calculator, or use the rules below.

The rules behind it

Every cut size comes from the finished size of the unit, written f below. Exact sizes come out right only if your quarter-inch seam is accurate; the “to trim” sizes leave a sliver you square up afterward, which most quilters find faster in the end.

Unit and method	Exact cut	Cut to trim	Units from one pair
Half-square triangle, two at a time	f + ⅞ in	f + 1 in	2
Half-square triangle, four at a time	(f + ½) × 1.414 + ½ in, rounded up to the next ¼ in		4
Half-square triangle, eight at a time	2f + 1¾ in	2f + 2 in	8
Quarter-square triangle (hourglass)	f + 1¼ in	f + 1½ in	2
Flying geese, no-waste (large square)	w + 1¼ in	w + 1½ in	4
Flying geese, no-waste (four small squares)	h + ⅞ in	h + 1 in	4

A pair means one square of each fabric, right sides together. For flying geese, w is the finished width and h the finished height, which is half the width.

Eight 3-inch units, method by method

The calculator opens on 8 units at 3 inches finished, and the result table puts the three methods side by side. Read across a row: the square to cut, how many units one pair makes, and how many pairs you need for the count you typed.

Two at a time: squares of 3⅞ inches exact or 4 inches to trim, 4 pairs.
Four at a time: 5½-inch squares, 2 pairs.
Eight at a time: 7¾ inches exact or 8 to trim, 1 pair.

Every unit gets trimmed to 3½ inches, the finished size plus a half inch, and the note under the table says so. The calculator gives only a to-trim size for four at a time: the formula, (3 + ½) × 1.414 + ½, comes to 5.45 inches, and it rounds up to the next quarter. The extra goes into the trim.

When the count doesn’t divide evenly, the pairs round up. Ask for 10 units and two at a time says 5 pairs, four at a time 3 pairs (12 units, 2 spare) and eight at a time 2 pairs (16 units, 6 spare). Only two at a time lands on exactly 10, which suits small counts.

Cut sizes for 1- to 6-inch units

Finished	Two at a time, exact / trim	Four at a time	Eight at a time, exact / trim	Trim unit to
1 in	1⅞ / 2 in	2¾ in	3¾ / 4 in	1½ in
1½ in	2⅜ / 2½ in	3½ in	4¾ / 5 in	2 in
2 in	2⅞ / 3 in	4¼ in	5¾ / 6 in	2½ in
2½ in	3⅜ / 3½ in	4¾ in	6¾ / 7 in	3 in
3 in	3⅞ / 4 in	5½ in	7¾ / 8 in	3½ in
4 in	4⅞ / 5 in	7 in	9¾ / 10 in	4½ in
5 in	5⅞ / 6 in	8½ in	11¾ / 12 in	5½ in
6 in	6⅞ / 7 in	9¾ in	13¾ / 14 in	6½ in

Which method to use

Two at a time is the one to learn first: draw a diagonal, sew a quarter inch on each side, cut on the line. It gives the most control over the points and wastes little when you need a handful of units.

Eight at a time is the fastest way to make a lot of matching units, like the 80 in a charm-pack zigzag. You draw both diagonals, sew on both sides of each, and cut the square into eight. Because the units come out a fraction off, cut to trim and square each one up.

Four at a time has a catch: you sew all the way around the outside of the pair, then cut on both diagonals, so every unit ends up with bias on its outer edges. Press with an up-and-down motion instead of sliding the iron, and starch the squares first if your fabric is soft.

What one pair of precut squares makes

Precuts are the usual reason to work backward from the square to the unit. Using the trim sizes, so each unit can be squared up:

Pair of	Two at a time	Four at a time	Eight at a time
5-in charm squares	2 units, 4 in finished	4 units, 2½ in finished (cut is 4¾, so ¼ in to spare)	8 units, 1½ in finished
10-in layer cake squares	2 units, 9 in finished	4 units, 6 in finished (cut is 9¾, so ¼ in to spare)	8 units, 4 in finished

Precuts have pinked edges, so line the ruler up with the points, not the valleys, when you check a square against these numbers.

Reading the hourglass and flying geese results

Switch the unit to quarter-square triangle and the table shows one method: two squares sewn into half-square triangles, which are then paired and cut a second time. For 8 hourglass units at 3 inches, it asks for 4 pairs of squares at 4¼ inches exact or 4½ to trim, and units trimmed to 3½.

For flying geese, the size you enter is the width, and the unit is half as tall. At 4 inches and 8 geese, the stitch-and-flip method needs 8 rectangles of 4½ × 2½ and 16 sky squares of 2½. The no-waste method needs 2 large goose squares of 5¼ and 8 small sky squares of 2⅞, and the calculator suggests 5½ and 3 if you want room to trim. Either way the finished unit should measure 4½ × 2½ before it goes into a block. The calculator always makes geese twice as wide as they are tall. For long, skinny star points, the half-rectangle triangle calculator covers a different unit that does that job.

Common mistakes

Trimming off center. Line up the ruler’s 45-degree line with the seam before you trim, not the edge of the fabric.
Pressing too early. Set the seam with the iron first, then open the unit and press toward the darker fabric.
Mixing methods in one quilt. Units from different methods can differ by a thread or two, which shows where points meet. Pick one method per quilt.

The steps for each method, with diagrams, are on how to make half-square triangles, the hourglass block and flying geese. To work out cuts for a whole block at a new size, use the block resizer.

Half-square triangle calculator