How to Calculate Half-Rectangle Triangles: A Complete Guide

Quick answer: how to calculate half-rectangle triangles

A half-rectangle triangle, or HRT, is a rectangle divided on the diagonal into two triangles, with two different fabrics. Its finished size is the size in the finished quilt, after seams are sewn, for example 6 by 4 inches.

For the oversize and trim method, cut rectangle width equals finished width plus 1 inch, and cut rectangle height equals finished height plus 1 inch, then trim to the unfinished size, finished size plus 1/2 inch in each direction, after sewing. One pair of rectangles, one of each fabric, makes 2 HRTs.

For example, finished 6 by 4 inch half-rectangles need 7 by 5 inch cut rectangles. If you need 14 HRTs, you need 7 pairs, 7 rectangles per fabric, 14 rectangles total, and you make 14 HRTs exactly.

Use the Half-Rectangle Calculator with your own finished width, finished height and HRT count, to check cut size and pairs needed before you cut.

How to calculate half-rectangle triangles

What you need to measure

You need three inputs: finished half-rectangle width, finished half-rectangle height, and half-rectangles needed. Finished width and finished height are sizes in the finished quilt, after seams are sewn, not cut sizes. Finished width and height can be any rectangle size, unlike flying geese, which must be twice as wide as high. Half-rectangles needed is a whole number, greater than zero. Count half-rectangles by fabric pair, not by quilt, if different fabric pairs use different finished sizes.

Formula and calculation rule

Cut rectangle width equals finished width plus 1 inch, and cut rectangle height equals finished height plus 1 inch, for the oversize and trim method. The extra 1 inch in each direction gives room for the diagonal seam and for trimming to the unfinished size, finished size plus 1/2 inch in each direction, after sewing. Pairs needed equals half-rectangles needed divided by 2, rounded up to a whole number, because each pair of rectangles makes 2 HRTs, and a partial pair cannot be sewn. Rectangles per fabric equals pairs needed times 1, because each pair uses 1 rectangle of each fabric. Total rectangles equals rectangles per fabric times 2, because each pair uses one rectangle of each fabric. HRTs made equals pairs needed times 2, because each pair makes 2 HRTs.

Step by step example

Take finished half-rectangle size 6 by 4 inches, half-rectangles needed 14.

Cut rectangle size: width 6 plus 1 equals 7 inches, height 4 plus 1 equals 5 inches, so cut rectangle size equals 7 by 5 inches, then trim to 6 and 1/2 by 4 and 1/2 inches, the unfinished size, after sewing.

Pairs needed: 14 divided by 2 equals 7 pairs.

Rectangles per fabric: 7 times 1 equals 7 rectangles. Total rectangles: 7 times 2 equals 14 rectangles.

HRTs made: 7 times 2 equals 14 HRTs, exactly the number needed, with no extra HRT.

Half-rectangle cut size chart

Finished half-rectangle size	Cut rectangle size
2 by 1 inches	3 by 2 inches
4 by 2 inches	5 by 3 inches
6 by 3 inches	7 by 4 inches
6 by 4 inches	7 by 5 inches
8 by 4 inches	9 by 5 inches

Use this chart for common finished sizes. For other finished sizes, use the calculator above, with the same formulas: cut width equals finished width plus 1 inch, cut height equals finished height plus 1 inch, then trim to the unfinished size, finished size plus 1/2 inch in each direction, after sewing.

Important variations and exceptions

• Odd HRT count. If half-rectangles needed is an odd number, pairs needed is rounded up, and HRTs made will be one more than half-rectangles needed, which is one extra HRT, not a mistake. For example, 15 HRTs need 8 pairs, and make 16 HRTs, with one extra HRT.
• Trimming is required. Cut rectangles in this method are oversized by 1 inch in each direction, and they are not finished size before trimming. Trimming to the unfinished size, finished size plus 1/2 inch in each direction, after sewing is required, not optional, and it is not a correction for a wrong cut size. Do not trim to the finished size itself, or the unit will finish 1/2 inch too small once sewn into the quilt.
• HRT versus HST versus flying geese. An HRT is a rectangle divided on the diagonal, with any rectangle size. An HST is a square divided on the diagonal, with cut size finished size plus 7/8 inch, by the two-at-a-time method. A flying geese block is a rectangle with finished width twice finished height, with no-waste cut sizes. Do not use HST or flying geese cut sizes for HRTs, or your HRTs will be the wrong size.
• Directional prints. If your fabric has a directional print and triangles must all run one way, check triangle orientation before cutting, because diagonal cutting turns print direction. This calculator counts rectangles, it does not check print direction.
• A pair makes a mirror pair, not two identical units. The 2 HRTs from one pair slope in opposite directions. If a pattern needs all HRTs sloping the same way, a pair does not give you 2 usable units. Cut for the direction you need, and count by direction, not just by pair.

Warning: the cut size depends on the method, not just the finished size

There is no single HRT cut size for a finished size. Different methods start from different oversized rectangles and trim differently, so a cut size taken from one method must not be used with the trimming steps of another. The calculator and this guide use one method only: oversize and trim, finished size plus 1 inch in each direction.

Method	Finished 2 by 4 inches	Cut rectangles
QuiltPilot oversize and trim (this guide and calculator)	2 by 4 inches	3 by 5 inches
1:2 oversize method (Bonjour Quilts, 3rd Story Workshop)	2 by 4 inches	3 by 6 inches
Two-rectangle method (Jacquelynne Steves)	2 by 4 inches	3 and 1/2 by 5 and 3/4 inches
Two-rectangle method (Wild Plum Lane, for 2 by 4 inches)	2 by 4 inches	3 and 1/2 by 5 and 1/2 inches
Paper piecing patches (Generations Quilt Patterns)	2 by 4 inches	3 and 7/8 by 5 and 1/4 inches

The paper piecing row is not an oversize and trim size. It is the patch size for that paper piecing pattern, so do not use it as a cut size for the oversize and trim method. If a pattern gives you a cut size, use that pattern's cut size and its trimming steps together, and do not replace either one with the calculator's size.

For a finished size far from the common 1:2 ratio, make one test unit from scrap fabric first, before cutting good fabric. The diagonal angle is sharper, trimming is harder, and a test unit shows whether the trim lands where the points need to be.

Trimming: the diagonal does not meet the corner

This is the step where HRTs most often go wrong, and it is different from HST trimming. After sewing, trim to the unfinished size, which is finished size plus 1/2 inch in each direction. For a 2 by 4 inch finished HRT, trim to 2 and 1/2 by 4 and 1/2 inches.

Do not line the diagonal seam up with the corners of the trimmed unit. The diagonal must sit 1/4 inch from the edge at both ends, so that when the unit is sewn into the quilt with a 1/4 inch seam, the point lands exactly on the corner. If you trim with the seam on the corner, the point will be cut off in the next seam. Mark the 1/4 inch alignment points on your ruler, line those points up with the seam, trim two sides, then turn the unit and trim the other two sides. The longer and skinnier the HRT, the harder this is, so centre the unit and check both ends before cutting.

Direction first: Set A and Set B

An HRT cannot be rotated like an HST to change its diagonal. Rotating an HST 90 degrees still gives the same shape with the diagonal reversed. Rotating an HRT 90 degrees gives a short, wide unit instead of a long, tall one, so the diagonal direction must be planned before cutting, not fixed afterwards.

Count by direction, not just by pair. One pair of rectangles makes 2 HRTs, but they slope in opposite directions, a mirror pair. Makers call the two directions Set A and Set B, or right-sided and left-sided. If a pattern needs all HRTs sloping the same way, a pair does not give 2 usable units. For directional prints this is irreversible, so check the diagonal direction on scrap fabric first, before cutting good fabric.

Two ways to sew HRTs

Cut diagonally first. Cut both rectangles on the diagonal, then sew a triangle pair right sides together with the tips offset by about 1/4 inch, with a 1/4 inch seam. This is the direct route, and it handles bias edges while sewing.

Twist whole rectangles, then cut apart. Layer the two rectangles, twist the top one so the corners line up, draw the diagonal, sew 1/4 inch on each side of the drawn line, then cut along the line. This also makes 2 HRTs, and it avoids handling bias edges while sewing, but the twist setup is finicky, and twisting the wrong way gives the opposite direction. Whichever route you use, trim afterwards to the unfinished size, finished size plus 1/2 inch in each direction, with the diagonal 1/4 inch from the edge at both ends.

The 1:2 sizes other sources use, kept separate from this calculator

For the common 1:2 ratio, where finished length is twice finished width, several sources agree on a different oversize rule from this calculator: cut width equals finished width plus 1 inch, cut length equals finished length plus 2 inches, then trim to finished size plus 1/2 inch in each direction. Use this table only with that method, never mix its cut sizes with this calculator's trimming steps.

Finished HRT size	Cut rectangles, 1:2 method	Trim to, unfinished
1 by 2 inches	2 by 4 inches	1 and 1/2 by 2 and 1/2 inches
2 by 4 inches	3 by 6 inches	2 and 1/2 by 4 and 1/2 inches
3 by 6 inches	4 by 8 inches	3 and 1/2 by 6 and 1/2 inches
4 by 8 inches	5 by 10 inches	4 and 1/2 by 8 and 1/2 inches
5 by 10 inches	6 by 12 inches	5 and 1/2 by 10 and 1/2 inches

For a ratio other than 1:2, do not treat the plus 1 inch and plus 2 inch rule as guaranteed. Use it only as a starting guess, make one test unit from scrap fabric, and adjust, especially the length, before cutting good fabric.

How to make sure your result is correct

• Check finished size, not cut size. Measure finished width and finished height in the finished quilt, after seams are sewn and after trimming, not cut sizes before seams are sewn. Using cut sizes in the formulas gives cut sizes too large by 1 inch in each direction.
• Check units. Finished width, finished height and cut sizes must be in the same unit, inches or centimetres. In centimetre mode, 1 inch equals 2.54 centimetres, so cut width equals finished width plus 2.54 centimetres, and cut height equals finished height plus 2.54 centimetres.
• Check HRT count by fabric pair. Count half-rectangles by fabric pair, not by quilt, if different fabric pairs use different finished sizes. Adding HRT counts for different fabric pairs into one calculation gives the wrong rectangle count for each fabric pair.
• Check HRTs made against HRTs needed. HRTs made equals pairs needed times 2. If HRTs made is less than HRTs needed, you have too few pairs. If HRTs made is one more than HRTs needed, and HRTs needed is odd, that is expected, not a mistake.

Worked example: 6 by 4 inch finished HRT, 14 HRTs needed

This worked example is different from the tool page example, which uses 4 by 2 inch finished HRT and 20 HRTs needed.

Cut rectangle size: width 6 plus 1 equals 7 inches, height 4 plus 1 equals 5 inches, so cut rectangle size equals 7 by 5 inches, then trim to 6 and 1/2 by 4 and 1/2 inches, the unfinished size, after sewing.

Pairs needed: 14 divided by 2 equals 7 pairs.

Rectangles per fabric: 7 times 1 equals 7 rectangles. Total rectangles: 7 times 2 equals 14 rectangles.

HRTs made: 7 times 2 equals 14 HRTs, exactly the number needed, with no extra HRT.

Frequently asked questions

Related guides and calculators

Next, read How to Calculate Flying Geese for the rectangle unit that must be twice as wide as high, and How to Calculate Half-Square Triangles for square triangle units. For half-rectangles themselves, use the Half-Rectangle Calculator.