Setting triangle calculator for on-point quilts

Calculator

How the numbers work

A block turned on point is wider than it is square: corner to corner, it measures the finished size times 1.414 (the square root of 2). A 9-inch block is about 12.73 inches across on point. Everything else follows from that diagonal.

Round both up to the next ⅛ inch. For a layout with A blocks along the top and D down the side, you need 2(A − 1) + 2(D − 1) side triangles, always 4 corners, and A × D + (A − 1)(D − 1) blocks. The quilt center finishes at A × diagonal by D × diagonal.

The opening layout: 9-inch blocks, 4 by 5

These are the numbers the calculator opens with. Count the blocks whose top points touch the top edge (4) and the ones whose side points touch the left edge (5). Those two counts set everything else.

A 9-inch block measures 12.73 inches on point. The side squares are 12.73 + 1¼ = 13.98, rounded up to 14 inches. The corner squares are 6.36 + ⅞ = 7.24, rounded up to 7¼.

The edges need 3 side triangles along the top, 3 along the bottom and 4 down each side: 14 in all. Each 14-inch square gives 4, so cut 4 squares and keep the 2 spare triangles in case one stretches. The corners take 2 squares of 7¼, cut once.

The blocks come in two groups. There are 4 × 5 = 20 in the full grid and 3 × 4 = 12 sitting in the gaps between them, so 32 blocks in total, sewn in 8 diagonal rows (4 + 5 − 1). The center finishes at 4 × 12.73 by 5 × 12.73, which the calculator shows as 50⅞ × 63⅝ inches before borders. Set straight in a 4 × 5 grid, 20 of those blocks would make 36 × 45 inches, so the on-point version is bigger both ways and takes 12 more blocks.

Side and corner cuts for 4- to 16-inch blocks

Widths are rounded to the nearest ⅛ inch and cuts up to the next ⅛, the same as the calculator. For floating blocks, add your 1 to 2 inches to both cuts in this table.

Why the triangles are cut that way

The outside edge of a quilt takes the most handling, and bias edges stretch. Cutting the side triangles from a square cut twice on the diagonal puts the straight grain on their long side, which becomes the edge of the quilt. Corner triangles come from a square cut once, which puts the straight grain on both short sides, again on the outside. Cut them the other way around and the edges wave.

Floating the blocks

Exact triangles bring the block points right to the binding. If you'd rather the points float a little inside the edge, add 1 to 2 inches to both the side and corner cuts, sew the top, then trim it a quarter inch beyond the block points all the way around. See how to square up a quilt for trimming a top straight.

Cutting the triangles from strips

Side squares are big, and it helps to know how they fit across the fabric before you buy. With 40 usable inches across, two side squares fit side by side up to a 13-inch block, where the square is 19¾ inches. At 14 inches the side square is 21⅛ and only one fits per strip.

For the 9-inch example, cut two strips 14 inches deep. Each gives two side squares (28 inches) and leaves a piece 12 × 14, which takes one 7¼ corner square. The two strips cover all four side squares and both corner squares from 28 inches of fabric. Floating the same blocks by 2 inches pushes the side squares to 16 and the corners to 9¼, and the strips get deeper to match.

With a directional print, each square cut twice gives exactly one triangle that sits right way up on each edge of the quilt: the one cut from the square’s top edge goes on the quilt’s top edge, the one from its left edge on the left, and so on. Mark them as you cut. In the 9-inch example, 4 squares give 4 triangles per edge, the sides use 4 each and the top and bottom use 3, so the 2 spares are one top and one bottom.

Sewing an on-point top

1. Lay everything out on the floor first: blocks in diagonal rows, side triangles at the ends of each row, corners last.
2. Sew each diagonal row, adding the side triangles at the ends. Their long edge faces out; line up the right-angle corner with the block so the tips overhang evenly.
3. Join the rows, pinning at every seam, then add the four corner triangles.
4. Handle the top by the straight edges and stay-stitch an eighth of an inch from the edge if it will sit a while before quilting.

Blocks that work well on point include the Ohio star, churn dash and a plain nine-patch. To change a block’s size first, use the block resizer.

You might also like

• Square in a square calculatorCenter and corner triangle cuts for square-in-a-square and two-round economy blocks.
• T-shirt quilt calculatorThe layouts your shirts can fill, with the finished size and the fabric to buy.
• Prairie points calculatorCut square size for any point height, how many points fill each edge, and the fabric to cut them from.
• Half-square triangle calculatorCut sizes for half-square triangles, hourglass units and flying geese, by method.