Quilt math · Calculator
Half-rectangle triangles: what size to cut
The rectangles to cut for half-rectangle triangles of any size, exactly or a little large to trim, and how to sew them so they lean the right way.
The short answer
For a 2″ × 4″ finished half-rectangle triangle, cut 3¼″ × 5⅞″ rectangles of each fabric, sew, and trim to 2½″ × 4½″. To sew them with no trimming, cut 2¾″ × 5⅜″ instead. Cut both rectangles face up, on the same diagonal.
Work out yours
Free · no accountFinished 2″ × 4″, trimmed to 2½″ × 4½″
For 8 units
Sew, press, then trim to 2½″ × 4½″ with the seam running exactly corner to corner.
The triangles’ points overhang: line up the seam lines, not the points, ¼″ in from each edge.
Both face up, cut on the same diagonal, so every unit leans the same way. Cut the other diagonal for the mirror image.
Designing a quilt? Quarter Inch draws your blocks to scale and works out the yardage for every fabric as you go.
Start designing freeThe same seams as the app’s half-square triangles: each side grown by the ¼″ seam about the triangle’s incenter, up to the next ⅛″
Half-rectangle triangle size chart
For units twice as tall as they are wide. Cut one rectangle of each fabric; together they make two units. “To trim” adds ½″ each way to the exact size.
| Finished | Exact rectangle | Rectangle to trim | Trim to |
|---|---|---|---|
| 1″ × 2″ | 1¾″ × 3⅜″ | 2¼″ × 3⅞″ | 1½″ × 2½″ |
| 1½″ × 3″ | 2¼″ × 4⅜″ | 2¾″ × 4⅞″ | 2″ × 3½″ |
| 2″ × 4″ | 2¾″ × 5⅜″ | 3¼″ × 5⅞″ | 2½″ × 4½″ |
| 2½″ × 5″ | 3¼″ × 6⅜″ | 3¾″ × 6⅞″ | 3″ × 5½″ |
| 3″ × 6″ | 3¾″ × 7⅜″ | 4¼″ × 7⅞″ | 3½″ × 6½″ |
| 3½″ × 7″ | 4¼″ × 8⅜″ | 4¾″ × 8⅞″ | 4″ × 7½″ |
| 4″ × 8″ | 4¾″ × 9⅜″ | 5¼″ × 9⅞″ | 4½″ × 8½″ |
| 4½″ × 9″ | 5¼″ × 10⅜″ | 5¾″ × 10⅞″ | 5″ × 9½″ |
| 5″ × 10″ | 5¾″ × 11⅜″ | 6¼″ × 11⅞″ | 5½″ × 10½″ |
| 5½″ × 11″ | 6¼″ × 12⅜″ | 6¾″ × 12⅞″ | 6″ × 11½″ |
| 6″ × 12″ | 6¾″ × 13⅜″ | 7¼″ × 13⅞″ | 6½″ × 12½″ |
How it’s worked out
A half-rectangle triangle (HRT) is a rectangle of two long, thin right triangles. A half-square triangle adds the same amount to both sides, because its corners are 45°. An HRT’s corners aren’t, so the seam allowance adds more to the long side than the short one, and there’s no simple “add ⅞″” rule.
Here’s the exact way. A triangle with ¼″ added on every side is the same shape, just bigger, grown from the center of the circle that fits inside it. Each side grows in the ratio (r + ¼″) ÷ r, where r is that circle’s radius: for a right triangle, half of (short side + long side − diagonal).
| The finished unit | 2″ × 4″ |
|---|---|
| Its diagonal: √(2² + 4²) | 4.472″ |
| The inner circle’s radius: (2 + 4 − diagonal) ÷ 2 | 0.764″ |
| Each side grows by (radius + ¼″) ÷ radius | × 1.327 |
| The rectangle exactly | 2.655″ × 5.309″ |
| Up to the next ⅛″ | 2¾″ × 5⅜″ |
Check it on a square: the same sum for a 3″ half-square triangle gives 3⅞″ × 3⅞″, the familiar finished size and ⅞″ (3⅞″). See half-square triangles.
Cutting and sewing them
- Cut one rectangle of each fabric, both right side up.
- Cut both on the same diagonal, bottom left to top right. Each gives two triangles.
- Pair a triangle of each fabric, right sides together, long edges matched. The points overhang: slide them until the seam lines cross ¼″ in from each edge.
- Sew ¼″ from the long edge, press, and trim the unit to 2½″ × 4½″, with the seam running exactly corner to corner.
Why cut large? The points of an HRT’s triangles are long and thin, so lining them up exactly is hard. Cutting ½″ larger each way (3¼″ × 5⅞″ for 2″ × 4″) and trimming makes every unit come out the same.
What changes the answer
- The lean. HRTs come in two mirror images. Count how many of each your block needs before you cut.
- Trimming with a ruler. A 45° line doesn’t help here. Mark the corner-to-corner line on your ruler with tape, or use a ruler made for HRTs.
- Flying geese. A goose is a different unit: one triangle with a small one each side, at 45°. See flying geese.
Questions
Short answers.
Something else? A real person replies.
hello@quarterinch.app
What is the formula for half-rectangle triangles?
Each side grows by (r + ¼″) ÷ r, where r is half of (width + height − diagonal). Round each up to the next ⅛″, or cut a little larger and trim. The calculator above does the sum.
What size rectangle for a 2″ × 4″ HRT?
2¾″ × 5⅜″ exactly, or 3¼″ × 5⅞″ to trim to 2½″ × 4½″.
Why don’t my HRTs make a rectangle?
The two triangles lean opposite ways. That happens when the rectangles are stacked right sides together to cut. Cut them both face up, on the same diagonal.