How to use the quarter square triangle calculator
- Choose whether you know the long edge (the outside of a block made of four triangles) or the short edge (the edges that meet at the center) of one finished triangle.
- Enter its finished size, the unit, and how many triangles you need.
- Leave the seam allowance blank for a quarter inch, or change it under More options.
- Cut squares of the size shown, and cut each one on both diagonals to make four triangles.
Formula
cut square = finished long edge + 2 x seam x (1 + sqrt 2)
finished long edge = finished short edge x sqrt 2
squares needed = triangles needed / 4, rounded up
A square cut on both diagonals gives four triangles whose long edges lie on the straight grain of the fabric. Putting a seam allowance on all three sides of the finished triangle gives a larger triangle of the same shape, and its long edge is the side of the square. The result is rounded up to the next eighth of an inch.
Twenty-four triangles with a 6-inch long edge
With a finished long edge of 6 inches and a quarter inch seam, the exact square is 6 + 0.5 x 2.4142 = 7.2071 inches, which rounds up to 7 1/4. Six squares give 24 triangles, and each triangle finishes with short edges of 4.243 inches.
If you know the short edge instead, say 4 inches, the long edge is 4 x 1.4142 = 5.657 and the square is 5.657 + 1.207 = 6.864 inches, rounded up to 6 7/8.
Why quarter square triangles
Cutting a square on both diagonals puts the straight grain on the long edge of each triangle, which is the outside of a block and the edge that needs to stay stable. Half square triangles, cut on one diagonal, put the straight grain on the short edges instead. Choose the type by which edge should not stretch.
Four of these triangles sewn around a point make an hourglass block. Sets of triangles with different fabrics give a pinwheel or a sawtooth pattern. See the Half Square Triangle Calculator for the other cut.
Trimming and rounding
Many quilters cut a little larger than needed and trim the sewn blocks to exact size. The page rounds up to the next eighth inch and shows the exact figure beside it, so you can choose. For whole-block sizes, use the Quilt Block Size Calculator, and for backing and binding, the Quilt Backing and Binding Calculator.
More layout tools
For other layouts and cutting sizes, try the Pillow Cover Size Calculator, Regular Polygon Calculator and Ellipse String Layout Calculator.
Assumptions and limits
- The triangle is an isosceles right triangle, as cut from a square on both diagonals.
- Finished sizes are without seam allowance. All three sides get the same seam allowance.
- The default seam allowance is a quarter inch (0.635 centimeters).
- The number of triangles needed is rounded up to a whole number of squares.
Frequently asked questions
Which edge is the long edge?
The long edge is the side opposite the right angle. In a block made of four triangles around a center point, the long edges form the outside of the block.
Why not use the common rule of adding 1 1/4 inches?
That rule is a rounded form of the same geometry with a little extra for trimming. This page shows the exact figure and rounds it, so you can see how much room you have.
How many triangles come out of one square?
Four, because the square is cut on both diagonals. Half square triangles come two to a square, cut on one diagonal.
Can I use centimeters?
Yes. Choose centimeters and the sizes round up to the next tenth of a centimeter. Keep the seam allowance at 0.635 or enter your own.