Quilt math · Calculator
Quarter-square triangles (hourglass units)
The square to cut for any finished hourglass unit, exact or a little large to trim, and the two ways to sew them.
The short answer
Cut squares 1¼″ bigger than the finished size, then cut them twice on the diagonals. For a 4″ finished hourglass unit, cut 5¼″ squares, or 5½″ and trim to 4½″. One square of each of two fabrics makes two units.
Work out yours
Free · no accountFinished 4″, trimmed to 4½″
For 4 units
Exact. Cut twice on the diagonals: four triangles a square, their long sides on the straight grain. 2 squares of each fabric.
Exact. Make two half-square triangles, layer them with the colors opposite, sew ¼″ each side of the diagonal and cut: two units. 2 squares of each fabric.
Make the units, then trim each to 4½″, the ruler’s center on the point where the seams cross. 2 squares of each fabric.
Designing a quilt? Quarter Inch finds every quarter-square triangle in your blocks and gives the cut, the count and the method for each fabric.
Start designing freeSame sums as the app: @quarterinch/cutting QST.exact and QST.trim · cut twice on the diagonals
Quarter-square triangle size chart
The square to cut for each finished hourglass unit, exact or a little large to trim. Worked out by the same code as Quarter Inch’s cutting charts.
| Finished | Exact square | Square to trim | Trim to |
|---|---|---|---|
| 1″ | 2¼″ | 2½″ | 1½″ |
| 1½″ | 2¾″ | 3″ | 2″ |
| 2″ | 3¼″ | 3½″ | 2½″ |
| 2½″ | 3¾″ | 4″ | 3″ |
| 3″ | 4¼″ | 4½″ | 3½″ |
| 3½″ | 4¾″ | 5″ | 4″ |
| 4″ | 5¼″ | 5½″ | 4½″ |
| 4½″ | 5¾″ | 6″ | 5″ |
| 5″ | 6¼″ | 6½″ | 5½″ |
| 5½″ | 6¾″ | 7″ | 6″ |
| 6″ | 7¼″ | 7½″ | 6½″ |
| 7″ | 8¼″ | 8½″ | 7½″ |
| 8″ | 9¼″ | 9½″ | 8½″ |
| 9″ | 10¼″ | 10½″ | 9½″ |
| 10″ | 11¼″ | 11½″ | 10½″ |
| 11″ | 12¼″ | 12½″ | 11½″ |
| 12″ | 13¼″ | 13½″ | 12½″ |
How it’s worked out
A quarter-square triangle (QST) is a quarter of a square, cut corner to corner both ways. Four of them sew into an hourglass unit, the star points of an Ohio Star. Each triangle’s long side is the outside edge of the unit, on the straight grain, and its short sides are the seams inside it.
So the square’s side has to be the triangle’s long side with its seams. At each end of the long side, a ¼″ seam on the short side meets it at 45°, and that end grows by ¼″ × (1 + √2). Both ends together add 1.207″, and the next ⅛″ up is 1¼″. So cut a square the finished size and 1¼″.
| The finished size | 4″ |
|---|---|
| Its size before it’s sewn in | 4½″ |
| The square to cut: the finished size and 1¼″ | 5¼″ |
| Or the finished size and 1½″, then trim | 5½″ → 4½″ |
| One square of each of two fabrics makes | 2 units |
Two ways to sew them
Half-square triangles first
Pair a light and a dark square, right sides together. Sew ¼″ each side of one diagonal, cut and press: two half-square triangles. Lay them right sides together with the colors opposite and the seams nested. Draw the other diagonal across the seam, sew ¼″ each side, cut on the line and press. You have two hourglass units, each 4½″ square. The square is the same 5¼″: the two steps use the seams of a square cut twice.
Triangles cut first
Cut each square twice on the diagonals and sew the four triangles in pairs, then the pairs together. Use this when the four triangles of a unit aren’t two fabrics: an Ohio Star’s star points are two background and two star triangles, from two different squares.
In a 12″ Ohio Star the hourglass units are 4″ finished, so Quarter Inch’s cutting chart gives: 2 squares 5¼″ of Background and 2 squares 5¼″ of Dark, cut twice on the diagonals.
Points that match. The middle of an hourglass, where four points meet, shows every error. Cut 5½″ and trim to 4½″, with the ruler’s center on the crossing: each point then ends ¼″ from the edge, ready for the next seam.
What changes the answer
- Bias edges. The seams inside the unit are on the bias, and stretch. Press, don’t iron back and forth.
- Not the same as half-square triangles. A half-square triangle’s square is the finished size and ⅞″, because its straight sides are on the outside. See half-square triangles.
- Your seam. Four seams meet in the middle, so a seam a thread too wide shows four times. Sew one test unit first.
Questions
Short answers.
Something else? A real person replies.
hello@quarterinch.app
What is the formula for quarter-square triangles?
Finished size plus 1¼″, cut twice on the diagonals. Or finished plus 1½″, and trim each unit to the finished size and ½″.
What size square for a 4″ hourglass block?
5¼″ exact, or 5½″ to trim to 4½″.
What’s the difference between a half-square and a quarter-square triangle?
A half-square triangle is half a square, cut once: its short sides are on the outside of the unit. A quarter-square triangle is a quarter, cut twice: its long side is on the outside. That’s why they add different amounts.
How many hourglass units from two squares?
Two. One square of each fabric makes two half-square triangles, and those two make two hourglass units.