How to use the on-point calculator
- Enter the finished block size. That is the size it shows in the quilt, ½ inch smaller than the block before you sew it in.
- Count the full blocks along the top edge and down one side, with the blocks turned so they stand on a point.
- Leave oversize at 0 for exact cuts, or add an amount if you like to trim the edges after sewing.
- Add a border width if you want one.
How on-point math works
Turning a square block 45 degrees makes it as wide as its diagonal. The diagonal of a square is its side times the square root of 2, about 1.414, so an 8 inch block takes up about 11.31 inches. That is why on-point quilts come out bigger than the same blocks set straight.
Half-square shapes called side setting triangles fill the gaps along the edges, and the four corners get smaller triangles that each fill a quarter of a block. The cut sizes come from the same diagonal plus seam allowances. A square cut twice on the diagonal has its long edge on the straight grain, which is what you want on the outside of a quilt. That needs 1¼ inches added. A square cut once has its short edges on the straight grain, which suits the corners, and needs ⅞ inch added.
The blocks form two grids: the across by down grid, and a second grid between those blocks that is one smaller each way.
Formulas
- Block diagonal = finished block × 1.414.
- Quilt center = blocks across × diagonal by blocks down × diagonal.
- Full blocks = across × down + (across − 1) × (down − 1).
- Side triangles = 2 × (across − 1) + 2 × (down − 1); squares = triangles ÷ 4, rounded up.
- Side square = finished × 1.414 + 1¼", cut twice diagonally.
- Corner square = finished ÷ 1.414 + ⅞", cut once diagonally; always 2 squares for 4 corners.
Worked example: 8 inch blocks
The blocks are 8 inches finished, set 4 across and 5 down. The diagonal is 8 × 1.414 = 11.31 inches, so the center is 4 × 11.31 = 45.25 inches wide and 5 × 11.31 = 56.57 inches long.
Full blocks: 4 × 5 = 20 in the main grid plus 3 × 4 = 12 between them, so 32. Side triangles: 2 × 3 + 2 × 4 = 14, which takes 4 squares with 2 triangles left over.
The side squares are 11.31 + 1.25 = 12.56, rounded up to 12⅝ inches. The corner squares are 8 ÷ 1.414 = 5.66, plus 0.875 = 6.53, rounded up to 6⅝ inches.
Setting triangle sizes by block size
Exact cuts, rounded up to the next ⅛ inch.
| Finished block | Diagonal | Side square, cut twice | Corner square, cut once |
|---|---|---|---|
| 4" | 5.66" | 7" | 3¾" |
| 5" | 7.07" | 8⅜" | 4½" |
| 6" | 8.49" | 9¾" | 5⅛" |
| 8" | 11.31" | 12⅝" | 6⅝" |
| 9" | 12.73" | 14" | 7¼" |
| 10" | 14.14" | 15½" | 8" |
| 12" | 16.97" | 18¼" | 9⅜" |
These sizes match published examples. Snuggles Quilts cuts 9¾ inch side squares and 5⅛ inch corner squares for 6 inch blocks. Designed to Quilt works the 8 inch corner square as (8 ÷ 1.414) + ⅞ = 6.533 and rounds it up to 6⅝ inches, the same as the table.
On point or straight set: blocks for common quilt sizes
A block set on point covers its diagonal, so the same blocks spread further. The table picks the whole number of blocks across and down that comes closest to each standard size. It then compares that layout with a straight set of the same blocks from our quilt layout calculator. Neither has sashing or borders.
| Block, size | On point layout | On point blocks | On point center | Straight blocks | Straight top |
|---|---|---|---|---|---|
| 8", throw | 4 × 6 | 39 | 45.3" × 67.9" | 48 | 48" × 64" |
| 8", twin | 6 × 8 | 83 | 67.9" × 90.5" | 99 | 72" × 88" |
| 8", queen | 8 × 8 | 113 | 90.5" × 90.5" | 132 | 88" × 96" |
| 10", throw | 4 × 5 | 32 | 56.6" × 70.7" | 35 | 50" × 70" |
| 10", twin | 5 × 6 | 50 | 70.7" × 84.9" | 63 | 70" × 90" |
| 10", queen | 6 × 7 | 72 | 84.9" × 99.0" | 90 | 90" × 100" |
| 12", throw | 3 × 4 | 18 | 50.9" × 67.9" | 20 | 48" × 60" |
| 12", twin | 4 × 5 | 32 | 67.9" × 84.9" | 42 | 72" × 84" |
| 12", queen | 5 × 6 | 50 | 84.9" × 101.8" | 64 | 96" × 96" |
The on-point layouts use fewer pieced blocks for a top of about the same size. They do add setting triangles, and some sizes come out a few inches larger or smaller. Add a border to bring the center to the size you want.
Fabric for setting triangles
Side and corner triangles are often cut from one background fabric. For the 4 by 5 layout above, here is how many squares to cut and the fabric for all of them, from 42" fabric with 10 percent extra.
| Finished block | Side squares | Corner squares | Fabric for both |
|---|---|---|---|
| 4" | 4 at 7" | 2 at 3¾" | ⅜ yd |
| 5" | 4 at 8⅜" | 2 at 4½" | ½ yd |
| 6" | 4 at 9¾" | 2 at 5⅛" | ½ yd |
| 8" | 4 at 12⅝" | 2 at 6⅝" | 1 yd |
| 9" | 4 at 14" | 2 at 7¼" | 1⅛ yd |
| 10" | 4 at 15½" | 2 at 8" | 1¼ yd |
| 12" | 4 at 18¼" | 2 at 9⅜" | 1½ yd |
With 8 inch blocks, the 4 side squares and 2 corner squares take 1 yard. The calculator does not plan on-point quilts with sashing between the blocks, which changes both the triangle sizes and the count.
Setting a single block on point
To turn one block into a larger square, sew a corner triangle to each side. Phoebe Moon uses the corner triangle formula for this: cut two squares of the finished block size ÷ 1.414 + ⅞ inch, and cut each once on the diagonal. An 8 inch block takes two 6⅝ inch squares and finishes about 11.31 inches square. For more on sewing the rows, read the guide to setting blocks on point.
Tips for on-point quilts
- Sew the quilt in diagonal rows, with a side triangle at each end of a row, then join the rows.
- Handle the cut triangles gently. Their inner edges are on the bias and stretch if pulled.
- You cut setting triangles slightly large, so their points stick out past the block edges. Line up the square corner and let the tip hang over.
