How the On-Point Quilt Setting Triangle Calculator works
Enter the finished block size and the layout to get the squares to cut for the side and corner triangles, how many of each, and how big the quilt comes out.
How this is calculated
A square block turned on point is as wide as its diagonal, which is the side of the block times the square root of 2 (1.414). Blocks set this way leave triangular gaps all round the edge of the quilt, and two different triangles fill them.
- Side triangles fill the gap between two neighbouring blocks along an edge. The two short sides are sewn to the blocks, so each is as long as a block. The long side lies on the edge of the quilt and is as long as the block's diagonal.
- Corner triangles fill the four corners. The long side is sewn to one block, so it is as long as a block. The two short sides lie on the edges of the quilt.
side square = finished block × √2 + 1 1/4" cut on both diagonals → 4 triangles
corner square = finished block ÷ √2 + 7/8" cut on one diagonal → 2 triangles
then round each square up to the next 1/8"For 12" blocks that gives 18 1/4" and 9 3/8" squares. The sources below that give a formula print the same one, with small differences in the constant (1.41, 1.414 or √2) and in whether the result is rounded up or to the nearest 1/8".
Why the two triangles are cut differently
Fabric stretches along the bias and much less along the straight grain. The sources cut these triangles so that the straight grain ends up on the outside edge of the quilt and the bias edges are sewn to the blocks, and several of them say that is the reason.
- Cutting a square on both diagonals gives four triangles whose long side was an edge of the square. That is the side of a side triangle that lies on the quilt edge.
- Cutting a square on one diagonal gives two triangles whose two short sides were edges of the square. Those are the two sides of a corner triangle that lie on the quilt edges.
Cutting both kinds the same way would work for size, but it would leave a bias edge on the outside of the quilt for one of them.
Where 1 1/4" and 7/8" come from
They are the seam allowance. Adding 1/4" outside all three sides of a right-angled triangle makes its long side longer by 1.207" and each short side longer by 0.854". Rounded up to the next 1/8" on a ruler those become 1 1/4" and 7/8", which are the figures the sources print. This tool works the two figures out from the geometry and gets the same ones.
So the sizes here are the exact size plus seam allowance, rounded up. At 1/8" rounding a square is never smaller than the triangle needs and is less than 3/16" larger. They are not oversized for trimming. Several of the sources suggest cutting larger than the chart if you like to trim the finished top square, and one describes its chart as the minimum size.
One small difference from the sources: most of them multiply by 1.414 and this tool uses the full square root of 2. Between 1" and 20" in half-inch steps that moves two results by 1/8" compared with the same formula worked with 1.414: the side square for 16" blocks is 24" here, and the corner square for 17 1/2" blocks is 13 1/4" here.
How many of each
Count the blocks whose points touch the top edge (across) and the blocks whose points touch one side (down). One more block sits in each space between four of those, so the quilt has across × down blocks plus (across − 1) × (down − 1). A side triangle fills every gap between two blocks on an edge: across − 1 on the top and on the bottom, down − 1 on each side. There are always four corner triangles, from two squares. These counts are worked out from the layout rather than taken from a source; the tests add up the area of every piece and check that together they fill the quilt exactly.
With no sashing the quilt, before borders, measures across × the block diagonal by down × the block diagonal.
Sashing
With sashing round every block and whole cornerstones, a side triangle's short side runs along one sashing strip and one cornerstone, so the side squares are worked out as if the block were one sashing width larger. A corner triangle's long side runs along a sashing strip and the cornerstone at each end of it, so the corner squares are worked out as if the block were two sashing widths larger. The quilt then measures (across × (block + sashing) + sashing) × 1.414 wide, and the same with down for the height.
Two sources cover sashing. Quiltville's page treats the block and its sashing as one unit, one sashing width larger, for both triangles. The Quilting Nook's handout adds one sashing width for the side triangles and two for the corners, so that the outside cornerstones stay whole. This tool draws that second layout, with whole cornerstones on the outside, and for it the corner triangles need two. If your pattern trims the outside cornerstones in half, it is a different layout and these sizes do not apply to it.
Why a published chart may not match this tool
Published charts do not all round the same way. Going by what each page itself says: Quiltville and Generations Quilt Patterns round up to the ruler mark, Shadywood Quilts rounds to the nearest 1/8", and Quiltville's author adds that she likes to round the squares for side triangles up a little further, from an odd eighth to the next quarter inch. So two charts can give different cut sizes for the same block, and either may differ from this tool by a ruler mark. This tool always rounds up to the increment you choose, and shows the figure before rounding so you can see what each size was rounded from.
What this does not cover
Square blocks only, 1/4" seam allowances, inches. It does not work out yardage, borders, or rectangular blocks, and it assumes every block in the quilt is the same size.
What this calculator is tested against
This tool cannot be published unless it reproduces every example below. 13 are copied from a published source. 6 were worked by hand from the cited rule.
| Example | Expected | Basis |
|---|---|---|
| 12" finished blocks (worked example on the page) | side squares 18 1/4", corner squares 9 3/8" | Published Quiltville, "On Point Quilts!" (Bonnie K. Hunter) |
| 6" finished blocks (worked example on the page) | side squares 9 3/4", corner squares 5 1/8" | Published Quiltville, "On Point Quilts!" (Bonnie K. Hunter) |
| 3" finished blocks (chart row) | side squares 5 1/2", corner squares 3" | Published Quiltville, "On Point Quilts!" (Bonnie K. Hunter) |
| 4 1/2" finished blocks (chart row) | side squares 7 5/8", corner squares 4 1/8" | Published Generations Quilt Patterns, setting triangles chart |
| 8" finished blocks (chart row) | side squares 12 5/8", corner squares 6 5/8" | Published Generations Quilt Patterns, setting triangles chart |
| 9" finished blocks (chart row) | side squares 14", corner squares 7 1/4" | Published Generations Quilt Patterns, setting triangles chart |
| 10" finished blocks (chart row) | side squares 15 1/2", corner squares 8" | Published Generations Quilt Patterns, setting triangles chart |
| 20" finished blocks (chart row) | side squares 29 5/8", corner squares 15 1/8" | Published Generations Quilt Patterns, setting triangles chart |
| 7" finished blocks (chart row) | side squares 11 1/4", corner squares 5 7/8" | Published APQS, "Reference charts for squares on point" (PDF) |
| 7 1/2" finished blocks (chart row) | side squares 11 7/8", corner squares 6 1/4" | Published APQS, "Reference charts for squares on point" (PDF) |
| 18" finished blocks (chart row) | side squares 26 3/4", corner squares 13 5/8" | Published Shadywood Quilts, side and corner triangle cutting chart |
| Point-to-point measurement of a 12" block (diagonal chart, decimal column) | 16.97" | Published APQS, "Reference charts for squares on point" (PDF) |
| Four 6 3/4" blocks on point across, no borders | 38.2" wide | Published APQS, "Reference chart for squares on point" |
| 12" blocks, 3 across by 4 down | 18 blocks (12 + 6), 10 side triangles from 3 squares, 4 corner triangles from 2 squares | By hand Geometry of the layout (derivation in core.js; pieces checked to fill the quilt exactly) |
| 12" blocks, 3 across by 4 down: size before borders | 50.91" × 67.88" (3 and 4 times the 16.97" diagonal) | By hand Geometry of the layout (derivation in core.js; pieces checked to fill the quilt exactly) |
| 5" blocks, 6 across by 8 down | 83 blocks (48 + 35), 24 side triangles from 6 squares | By hand Geometry of the layout (derivation in core.js; pieces checked to fill the quilt exactly) |
| 8" blocks cut with a ruler read to 1/4" | side squares 12 3/4", corner squares 6 3/4" | By hand Same formula as the charts, rounded up to the next 1/4" instead of the next 1/8" |
| 6" blocks with 3/4" sashing and whole cornerstones | side squares from 6 3/4" (10 7/8"), corner squares from 7 1/2" (6 1/4"); 6 side triangles from 2 squares | By hand The Quilting Nook, on-point setting with sashing and cornerstones (PDF) |
| 8" blocks with 2" sashing | side squares 15 1/2", corner squares 9 3/8" | By hand Side triangles as for a 10" block (Quiltville sashing rule); corner triangles as for a 12" block (geometry, The Quilting Nook) |
Sources
- Quiltville: "On Point Quilts!" (Bonnie K. Hunter)The formulas (multiply by 1.414 and add 1-1/4"; divide by 1.414 and add 7/8"), four worked examples, a chart of common sizes, how the rows go together, and the rule for sashing. Read from the page itself.
- Generations Quilt Patterns: setting triangles for on-point quilt layoutsThe same two formulas, the reason each triangle is cut the way it is (which edges are on the straight grain), and a chart from 1-1/2" to 20". Read from the page itself.
- APQS: reference charts for squares on point (PDF)A chart of block diagonals and a chart of corner and side triangle squares from 3" to 15", from a longarm machine maker. Read from the text of the PDF.
- Shadywood Quilts: side triangle and corner triangle cutting chartThe formulas written with 1.41 and with 1.414, rounded to the nearest 1/8", grain direction for both cuts, and a chart from 3" to 18". Read from the page itself.
- Thimbles and Needles: setting and corner triangles cutting chart for on-point quiltsThe formulas written with the square root of 2 and worked with 1.414, examples for 6" and 8" blocks, and which edge of each triangle faces the outside of the quilt. Its chart is an image, so it is not used for the tests in this tool.
- The Quilting Nook: calculating setting triangles for an on-point setting with sashing and cornerstones (PDF)With sashing and whole cornerstones: side triangles from block plus one sashing width, corner triangles from block plus two. Read from the text of the PDF.