Quick answer: how to calculate setting triangles
Use the Setting Triangles Calculator with your own finished block size, side triangles needed and corner triangles needed, to check cut sizes and squares needed before you cut. The steps below explain the same formulas, so you can check the calculator result by hand.
Setting triangles fill the edges of an on-point quilt top, so the top becomes a straight sided rectangle. Side setting triangles sit along the four sides of the top. Corner setting triangles sit at the four corners of the top.
Side setting triangle square cut equals finished block size times 1.414, plus 1.25 inches, rounded up to the nearest 1/8 inch. Cut each side square twice on the diagonal to make 4 side triangles per square.
Corner setting triangle square cut equals finished block size divided by 1.414, plus 0.875 inch, rounded up to the nearest 1/8 inch. Cut each corner square once on the diagonal to make 2 corner triangles per square.
For example, an 8 inch finished block with 16 side triangles needed and 4 corner triangles needed needs a 12.625 inch side square cut and a 6.625 inch corner square cut, with 4 side squares and 2 corner squares, which make 16 side triangles and 4 corner triangles exactly.
How to calculate setting triangles
What you need to measure
You need three inputs: finished block size, side triangles needed and corner triangles needed. Finished block size is the size of one square block in the finished quilt, after seams are sewn, not the cut size and not the unfinished size. Side triangles needed is the number of side setting triangles in your on-point layout, counted from your layout diagram along all four sides. Corner triangles needed is normally 4, one for each corner of a rectangular on-point top. Count triangles from your own layout, do not guess the count, because the square counts follow directly from the triangle counts.
Formula and calculation rule
Side setting triangle square cut equals finished block size times 1.414, plus 1.25 inches, rounded up to the nearest 1/8 inch. The number 1.414 is the square root of 2, which comes from the diagonal of a square, because on-point blocks are set at 45 degrees. Cut each side square twice on the diagonal to make 4 side triangles per square, so the straight grain sits on the outer edge of each side triangle, not the bias.
Corner setting triangle square cut equals finished block size divided by 1.414, plus 0.875 inch, rounded up to the nearest 1/8 inch. Cut each corner square once on the diagonal to make 2 corner triangles per square.
Side squares needed equals side triangles needed divided by 4, rounded up to a whole number, because each side square makes 4 side triangles, and a partial square cannot be cut. Corner squares needed equals corner triangles needed divided by 2, rounded up to a whole number, because each corner square makes 2 corner triangles. Side triangles made equals side squares needed times 4. Corner triangles made equals corner squares needed times 2. If triangles needed is not an exact multiple of triangles per square, triangles made will be more than triangles needed, which is extra triangles, not a mistake.
Step by step example
Take finished block size 6 inches, side triangles needed 12, corner triangles needed 4.
Side square cut: 6 times 1.414 equals 8.48, plus 1.25 equals 9.73, rounded up to the nearest 1/8 inch, which is 9.75 inches. Cut each side square twice on the diagonal to make 4 side triangles per square.
Corner square cut: 6 divided by 1.414 equals 4.24, plus 0.875 equals 5.12, rounded up to the nearest 1/8 inch, which is 5.125 inches. Cut each corner square once on the diagonal to make 2 corner triangles per square.
Side squares: 12 divided by 4 equals 3 squares, which make 12 side triangles exactly. Corner squares: 4 divided by 2 equals 2 squares, which make 4 corner triangles exactly.
Setting triangle cut size chart
| Finished block size | Side square cut size | Corner square cut size |
|---|---|---|
| 4 inches | 7.00 inches | 3.75 inches |
| 5 inches | 8.38 inches | 4.50 inches |
| 6 inches | 9.75 inches | 5.13 inches |
| 7 inches | 11.25 inches | 5.88 inches |
| 8 inches | 12.63 inches | 6.63 inches |
| 9 inches | 14.00 inches | 7.25 inches |
| 10 inches | 15.50 inches | 8.00 inches |
| 12 inches | 18.25 inches | 9.38 inches |
Use this chart for common finished block sizes. Chart values are rounded to 2 decimal places. The calculator rounds cut sizes up to the nearest 1/8 inch, so the chart matches the calculator at 2 decimal places, except that the 12 inch corner cut is 9.375 inches at full precision, shown as 9.38 inches in the chart. For other finished block sizes, use the calculator above, with the same formulas: side square cut equals finished block size times 1.414, plus 1.25 inches, rounded up to the nearest 1/8 inch, and corner square cut equals finished block size divided by 1.414, plus 0.875 inch, rounded up to the nearest 1/8 inch.
Important variations and exceptions
- On-point, block to block, without sashings only. These formulas assume an on-point layout, block to block, without sashings. If sashing is used, these formulas do not apply, because sashing changes the edge geometry and the triangle sizes. Work a sashed on-point layout separately, do not use these cut sizes for it.
- Side triangles and corner triangles are not interchangeable. Side triangles are larger, are cut twice on the diagonal, and sit along the sides. Corner triangles are smaller, are cut once on the diagonal, and sit at the corners. Do not use a side square cut size for corner triangles, or a corner square cut size for side triangles, or the edges and corners will not fit.
- Cutting direction controls the grain. Side triangles must be cut twice on the diagonal so straight grain sits on the outer edge, not bias. If a side square is cut only once on the diagonal, the outer edge will be on the bias, and it can stretch out of shape while you sew and press. Corner triangles are cut once on the diagonal, and their outer edges are straight grain by that cut.
- Extra triangles are expected when counts do not divide evenly. Side squares make 4 triangles each, and corner squares make 2 triangles each. If side triangles needed is not a multiple of 4, side squares are rounded up, and side triangles made will be more than side triangles needed. If corner triangles needed is not a multiple of 2, corner squares are rounded up, and corner triangles made will be more than corner triangles needed. Extra triangles are not a mistake.
- Rounding up is expected, rounding down is not safe. Cut sizes are rounded up to the nearest 1/8 inch, so cut sizes may be a little larger than the raw formula result, which gives a little room for trimming. Do not round cut sizes down, because a smaller square will leave the quilt top short at the edges or corners.
- Square blocks only. These formulas assume square finished blocks. Rectangular blocks set on point need different math, because the side and corner triangles are not the same shape on all sides. Do not use these formulas for rectangular on-point blocks.
First, the names: side, set-in, end and corner mean the same two pieces
Different pages call the same two pieces by different names, and that is where most cutting mistakes start. A side setting triangle is also called a set-in triangle and a quarter-square triangle. A corner setting triangle is also called an end triangle and a half-square triangle. Learn the piece by its cut, not by its name alone. The side piece comes from a square cut twice on the diagonal, so it makes 4 triangles and its long edge sits on the straight grain. The corner piece comes from a square cut once on the diagonal, so it makes 2 triangles. Never cut both pieces the same way. If every setting triangle is cut the same way, one of the two pieces will put a bias edge on the outside of the quilt, and that edge can stretch while you sew, press and quilt, and the border can ripple.
This guide and its calculator cover an on-point layout, block to block, without sashings only. If your layout has sashing, stop here and work that layout separately, because sashing changes the size the triangles have to fill. No sashed setting triangle formula is published in this guide, because the pages read for this guide give no sashed formula in readable text.
Count triangles from your grid, not from a guess
The tool asks for triangle counts, not for rows and columns, so count first from your own layout diagram. Corner triangles are always 4, from 2 corner squares, on a rectangular on-point top. A single block set on point needs only those 4 corners. Side triangles depend on the grid: side triangles equal 2 times rows plus columns, minus 4. Side squares equal side triangles divided by 4, rounded up to a whole square. Count the points along the top edge when you count across, because on an on-point top the top edge is points, not whole blocks. Count before you cut, and check triangles made against triangles needed afterwards.
| On-point grid, rows by columns | Side triangles needed | Side squares to cut | Side triangles made | Extra side triangles |
|---|---|---|---|---|
| 2 by 2 | 4 | 1 | 4 | 0 |
| 3 by 3 | 8 | 2 | 8 | 0 |
| 3 by 4 | 10 | 3 | 12 | 2 |
| 4 by 4 | 12 | 3 | 12 | 0 |
| 4 by 5 | 14 | 4 | 16 | 2 |
| 5 by 5 | 16 | 4 | 16 | 0 |
Corner triangles stay the same in every row of this table: 4 triangles from 2 corner squares. The cut sizes for those squares still depend on the finished block size, from the chart above. Extra side triangles in the 3 by 4 and 4 by 5 rows are spares from rounding squares up, not a mistake.
How an on-point top goes together
An on-point top is not sewn in straight rows across. It is assembled in diagonal rows, ends first. Start at the top left and work down, one diagonal row at a time, then join the rows and line up the block seams when the rows meet. The end units at the top left and bottom right are one block with two side triangles and one end, or corner, triangle around it.
For a side triangle, line up its 90 degree angle with the corner of the block and pin it in place, then sew with a 1/4 inch seam and repeat on the opposite side of the block. For a corner triangle, line up its point with the centre of the unit you have just made, using a ruler to check the point sits in the centre, then pin and sew. Expect a small tail of triangle fabric overlapping the block at each step. That tail is normal, and it can be trimmed after the seam is sewn. Once the rows are joined, the top is ready for borders and quilting.
Pressing is a choice, not a settled rule on this page. One approach presses toward the setting triangles so the block seams sit flat under them. The other presses seams open so the top lies flat, and then the key check is that every unit still measures correctly, with locking backstitching at the start and stop of each seam so an open seam does not come apart. Pick one way for the whole top and check measurements as you go, rather than switching halfway.
Oversize and trim: one policy for this guide
Other pages disagree on how much oversize to allow, so this guide states one policy plainly. The calculator rounds both cut sizes up to the nearest 1/8 inch and gives no separate oversize input. Use those rounded up sizes as your cut sizes, and trim the quilt edge after the top is together if you need to. Never cut smaller than the rounded up size. If you want a float and trim allowance beyond that, add a stated amount of your own before you cut and keep it the same for every square, and do not mix a thread larger on one square with a full inch larger on another. The tool itself adds nothing beyond the round up, so any extra you choose is yours to track, not a number the calculator will show.
How to make sure your result is correct
- Check finished size, not cut size and not unfinished size. Measure finished block size in the finished quilt, after seams are sewn, not cut sizes before seams are sewn and not unfinished size before the block is sewn into a quilt top. Using cut size or unfinished size in the formulas gives cut sizes too large.
- Check units. Finished block size, side square cut size and corner square cut size must be in the same unit, inches or centimetres. In centimetre mode, 1 inch equals 2.54 centimetres, so the side addition of 1.25 inches equals 3.18 centimetres, and the corner addition of 0.875 inch equals 2.22 centimetres. Rounding up is to the nearest 1/8 inch step, which is 0.32 centimetres, not to a whole centimetre.
- Check the cutting direction before you cut. Side squares are cut twice on the diagonal, for 4 triangles per square. Corner squares are cut once on the diagonal, for 2 triangles per square. If the cutting direction is swapped, the triangle counts and the grain direction will both be wrong, even if the square sizes are right.
- Check triangles made against triangles needed. Side triangles made equals side squares needed times 4. Corner triangles made equals corner squares needed times 2. If triangles made is less than triangles needed, you have too few squares. If triangles made is more than triangles needed, and triangles needed is not an exact multiple of triangles per square, that is expected, not a mistake.
- Check the sashing assumption. Confirm your layout is on-point, block to block, without sashings, before you use these cut sizes. If your layout has sashing, stop and work a sashed on-point layout separately, because these formulas do not apply.
Try it with the calculator: Use the Setting Triangles Calculator with your own finished block size, side triangles needed and corner triangles needed. It uses the same steps as this guide, and it shows side square cut size, corner square cut size, squares needed and triangles made, together.
Worked example: 8 inch finished block, 16 side triangles, 4 corner triangles
This worked example is different from the tool page example, which uses a 12 inch finished block, 20 side triangles and 4 corner triangles.
Side square cut: 8 times 1.414 equals 11.31, plus 1.25 equals 12.56, rounded up to the nearest 1/8 inch, which is 12.625 inches. Cut each side square twice on the diagonal to make 4 side triangles per square.
Corner square cut: 8 divided by 1.414 equals 5.66, plus 0.875 equals 6.53, rounded up to the nearest 1/8 inch, which is 6.625 inches. Cut each corner square once on the diagonal to make 2 corner triangles per square.
Side squares: 16 divided by 4 equals 4 squares, which make 16 side triangles, exactly the number needed, with no extra side triangles.
Corner squares: 4 divided by 2 equals 2 squares, which make 4 corner triangles, exactly the number needed, with no extra corner triangles.
Calculate your own setting triangles now
Use your finished block size, side triangles needed and corner triangles needed in the calculator, and check the result against the steps in this guide.
Open the Setting Triangles CalculatorFrequently asked questions
Side setting triangle square cut equals finished block size times 1.414, plus 1.25 inches, rounded up to the nearest 1/8 inch, cut twice on the diagonal to make 4 side triangles per square. Corner setting triangle square cut equals finished block size divided by 1.414, plus 0.875 inch, rounded up to the nearest 1/8 inch, cut once on the diagonal to make 2 corner triangles per square. For example, an 8 inch finished block needs a 12.625 inch side square cut and a 6.625 inch corner square cut.
Side setting triangles sit along the four sides of an on-point quilt top. They are larger, are cut twice on the diagonal, and 4 side triangles come from one side square. Corner setting triangles sit at the four corners of an on-point quilt top. They are smaller, are cut once on the diagonal, and 2 corner triangles come from one corner square. Side and corner triangles are not interchangeable.
Side squares needed equals side triangles needed divided by 4, rounded up to a whole number. Corner squares needed equals corner triangles needed divided by 2, rounded up to a whole number. For example, 16 side triangles need 4 side squares, which make 16 side triangles exactly, and 4 corner triangles need 2 corner squares, which make 4 corner triangles exactly.
No. These formulas assume an on-point layout, block to block, without sashings. If sashing is used, these formulas do not apply, because sashing changes the edge geometry and the triangle sizes. Work a sashed on-point layout separately, do not use these cut sizes for it.
Side triangles are cut twice on the diagonal so straight grain sits on the outer edge, not bias. If a side square is cut only once on the diagonal, the outer edge will be on the bias, and it can stretch out of shape while you sew and press. Corner triangles are cut once on the diagonal, and their outer edges are straight grain by that cut.
Related guides and calculators
Next, read How to Calculate Sashing for sashing between straight set blocks, and How to Calculate Square in a Square for a square set on point inside a block. Use the Setting Triangles Calculator for your own measurements, and for block layout, see the Block Size Calculator.