Quick answer: how to calculate square in a square
A square in a square block sets one square on point inside another square, so it reads as a diamond floating in a frame. It is made from one center square and four corner triangles, cut from two corner squares, cut once corner to corner.
Center square cut size equals finished block size divided by 1.414, plus 0.5 inch, rounded up to the nearest 1/8 inch. Corner square cut size equals finished block size divided by 2, plus 0.875 inch, rounded up to the nearest 1/8 inch.
For example, an 8 inch finished block needs a 6.25 inch center square and 4.875 inch corner squares. If you need 12 blocks, you need 12 center squares and 24 corner squares, which make 48 corner triangles.
Use the Square in a Square Calculator with your own finished block size and blocks needed, to check center cut size, corner cut size and squares needed before you cut.
How to calculate square in a square
What you need to measure
You need two inputs: finished block size and blocks needed. Finished block size is the size of the block in the finished quilt, after seams are sewn, not the cut size and not the unfinished size. Blocks needed is a whole number, greater than zero. Count blocks by fabric combination, not by quilt, if different blocks use different fabrics.
Formula and calculation rule
Center square cut size equals finished block size divided by 1.414, plus 0.5 inch, 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 the center square is set on point inside the block. Corner square cut size equals finished block size divided by 2, plus 0.875 inch, rounded up to the nearest 1/8 inch. Cut 2 corner squares of this size per block, then cut each once corner to corner, to make 4 corner triangles per block. Each block needs 1 center square and 2 corner squares. Unfinished block size equals finished block size plus 0.5 inch, because seam allowance 0.25 inch on each side is still on the block before it is sewn into a quilt.
Step by step example
Take finished block size 8 inches, blocks needed 12.
Center square cut size: 8 divided by 1.414 equals 5.66, plus 0.5 equals 6.16, rounded up to the nearest 1/8 inch, which is 6.25 inches.
Corner square cut size: 8 divided by 2 equals 4, plus 0.875 equals 4.875 inches. Cut 2 corner squares of this size per block, then cut each once corner to corner, to make 4 corner triangles per block.
Squares needed: center squares 12 times 1 equals 12 squares, corner squares 12 times 2 equals 24 squares, which make 48 corner triangles.
Unfinished block size: 8 plus 0.5 equals 8.5 inches, before the block is sewn into a quilt.
Square in a square cut size chart
| Finished block size | Center square cut size | Corner square cut size |
|---|---|---|
| 2 inches | 2.00 inches | 1.88 inches |
| 3 inches | 2.63 inches | 2.38 inches |
| 4 inches | 3.38 inches | 2.88 inches |
| 5 inches | 4.13 inches | 3.38 inches |
| 6 inches | 4.75 inches | 3.88 inches |
| 8 inches | 6.25 inches | 4.88 inches |
| 12 inches | 9.00 inches | 6.88 inches |
Use this chart for common finished sizes. For other finished sizes, use the calculator above, with the same formulas: center cut size equals finished block size divided by 1.414, plus 0.5 inch, rounded up to the nearest 1/8 inch, and corner cut size equals finished block size divided by 2, plus 0.875 inch, rounded up to the nearest 1/8 inch.
Important variations and exceptions
- Rounding up is expected. 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 the block to unfinished size after sewing. A cut size a little larger than the raw result is not a mistake.
- Trimming to unfinished size is required. After sewing the corner triangles to the center square, trim the block to unfinished size, which is finished block size plus 0.5 inch, before sewing the block into a quilt. Do not sew an untrimmed block into a quilt top and expect it to finish at the right size.
- Corner triangles are on the bias. Corner triangles are cut on the diagonal, so their long edges are on the bias, and they need careful handling so they do not stretch. Sew corner triangles to opposite sides first, press, then sew corner triangles to the remaining two sides, and press again.
- Square in a square versus economy block versus snowball. A square in a square block sets a square on point inside a square, with corner triangles on all four sides. An economy block adds a second round of corner triangles around a square in a square unit, so it needs two rounds of triangle math, not one. A snowball block clips the corners of a plain square with small corner squares, which is the opposite construction, so do not use snowball corner math for square in a square blocks.
- Directional prints. If your center fabric has a directional print and the diamond must run one way, check center square orientation before cutting, because the center square is set on point, not straight. This calculator counts squares, it does not check print direction.
Three blocks share this name, do not mix their math
Square in a square is not one set of cut sizes. Three different blocks share the name, and a 6 inch finished block needs different cuts in each. This guide and calculator use only the first one, the cut-triangle center-on-point block.
| Block, 6 inch finished | Center cut | Corner cuts |
|---|---|---|
| Cut-triangle center-on-point, this guide and calculator | 4.75 inches, 1 square | 3.88 inches, 2 squares cut once diagonally into 4 triangles |
| Stitch-and-flip, center reads as a diamond | 6.50 inches, 1 square | 3.50 inches, 4 squares sewn onto the corners and flipped |
| Economy block, two rounds | First round as above, then a second round of triangles | Two rounds of triangle math, not one, center ends straight again |
The stitch-and-flip numbers are not a contradiction of the cut-triangle numbers. They are a different construction. If a pattern says stitch-and-flip, use its center and corner sizes together, never this calculator's sizes with that method's steps.
Start from the finished center instead
The same geometry works from the other input. If you know the finished center square, not the finished block, use these rules. Center square cut size equals finished center plus 0.5 inch. Corner square cut size equals finished center divided by 1.414, plus 0.875 inch, rounded up to the nearest 1/8 inch, cut 2 squares and slice each once diagonally. Finished unit size equals finished center times 1.414, because 1.414 is the square root of 2, the diagonal of the center square.
For example, a 5 inch finished center needs a 5.50 inch center cut, corner squares of 4.50 inches after rounding up, and finishes at about 7.07 inches, about 7 and 1/8 inches. That is why square in a square units often land on odd sizes: unless you work backward from the block size you want, the finished size follows the center, not the other way round.
Alignment, grain and trimming
Sew corner triangles to opposite sides first, press, then sew the remaining two sides. Crease the center square and each triangle in half, or pinch a small crease, and match those midpoints, so the center point lands in the middle of each side. Cutting each corner square once diagonally puts straight grain on the two short sides, which become the outer edges of the unit and keep it stable. The long bias edge is sewn to the center first, where the seam controls it, and it must not be stretched while sewing.
Trim to the unfinished size, finished block size plus 0.5 inch, keeping 1/4 inch beyond the center square's points on every side. If a point sits on the trimmed edge, it will be cut off by the next seam. This calculator rounds cut sizes up to the nearest 1/8 inch, which is why its corner size for a 5 inch finished center is 4.50 inches, while a source rounding to the nearest 1/8 inch gives 4.38 inches. Both come from the same formula, the difference is rounding choice only, and the rounded-up size gives room to trim.
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. Using cut size or unfinished size in the formulas gives cut sizes too large.
- Check units. Finished block size, center cut size and corner cut size must be in the same unit, inches or centimetres. In centimetre mode, 1 inch equals 2.54 centimetres, and rounding up is to the nearest 1/8 inch step, which is 0.32 centimetres, not to a whole centimetre.
- Check squares needed by fabric combination. Count blocks by fabric combination, not by quilt, if different blocks use different fabrics. Adding block counts for different fabric combinations into one calculation gives the wrong square count for each combination.
- Check corner triangles against corner squares. Corner triangles made equals corner squares needed times 2, because each corner square cut once corner to corner makes 2 triangles, and each block needs 4 corner triangles from 2 corner squares. If corner triangles made is less than blocks needed times 4, you have too few corner squares.
Try it with the calculator: Use the Square in a Square Calculator with your own finished block size and blocks needed. It uses the same steps as this guide, and it shows center square cut size, corner square cut size, squares needed and unfinished block size, together.
Worked example: 8 inch finished block, 12 blocks needed
This worked example is different from the tool page example, which uses 6 inch finished block and 10 blocks needed.
Center square cut size: 8 divided by 1.414 equals 5.66, plus 0.5 equals 6.16, rounded up to the nearest 1/8 inch, which is 6.25 inches.
Corner square cut size: 8 divided by 2 equals 4, plus 0.875 equals 4.875 inches. Cut 2 corner squares of this size per block, then cut each once corner to corner, to make 4 corner triangles per block.
Squares needed: center squares 12 times 1 equals 12 squares, corner squares 12 times 2 equals 24 squares, which make 48 corner triangles.
Unfinished block size: 8 plus 0.5 equals 8.5 inches, before the block is sewn into a quilt.
Calculate your own square in a square now
Use your finished block size and blocks needed in the calculator, and check the result against the steps in this guide.
Open the Square in a Square CalculatorFrequently asked questions
Center square cut size equals finished block size divided by 1.414, plus 0.5 inch, rounded up to the nearest 1/8 inch. Corner square cut size equals finished block size divided by 2, plus 0.875 inch, rounded up to the nearest 1/8 inch. For example, an 8 inch finished block needs a 6.25 inch center square and 4.875 inch corner squares.
A square in a square block sets one square on point inside another square, so it reads as a diamond floating in a frame. It is made from one center square and four corner triangles, cut from two corner squares, cut once corner to corner.
Each block needs 1 center square and 2 corner squares, which make 4 corner triangles. For example, 12 blocks need 12 center squares and 24 corner squares, which make 48 corner triangles.
Yes. After sewing the corner triangles to the center square, trim the block to unfinished size, which is finished block size plus 0.5 inch, before sewing the block into a quilt. Do not sew an untrimmed block into a quilt top and expect it to finish at the right size.
A square in a square block has one round of corner triangles around a center square. An economy block adds a second round of corner triangles around a square in a square unit, so it needs two rounds of triangle math, not one. Do not use economy block math for a single square in a square block.
Related guides and calculators
Next, read How to Calculate Half-Square Triangles for triangle units, and How to Calculate Quilt Block Size and Layout for block layouts. For square in a square itself, use the Square in a Square Calculator.