Quilt Math

Half square triangles and flying geese from squares

Both units are sewn from squares before any triangle is cut, so no stretchy bias edge is handled. The cost is that the square has to be bigger than the unit by a fixed amount, and the amount depends on the method.

For half square triangles made two at a time, two squares are sewn a quarter inch either side of one diagonal and cut apart. The square is the finished size plus seven eighths of an inch. Eight at a time, the squares are sewn either side of both diagonals and cut four ways; the square is twice that. The sewn unit is the finished size plus half an inch.

Flying geese four at a time, the no-waste method, use one large square of the goose fabric, the finished width plus an inch and a quarter, and four small sky squares, the finished height plus seven eighths. Stitch and flip uses a rectangle and two squares, each the finished size plus half an inch, and cuts the corners away.

These sizes are exact: they assume a seam of exactly a quarter inch. Many quilters prefer to cut a little bigger and trim every unit to size. One source adds a quarter inch to the half square triangle square; another gives no-waste geese as the width plus an inch and a half and the height plus an inch. Charts rarely say which kind of size they list, which is why two charts for the same unit can disagree. The calculators offer both and say which is which.

Chart: square to cut for half square triangles, by finished size and method

Each cell is the exact starting square for the finished size in its row, two at a time or eight at a time. Add a quarter inch if you like to trim.

Method
Finished size of the unitTwo at a timeEight at a time
1 in1.875 in3.750 in
1.5 in2.375 in4.750 in
2 in2.875 in5.750 in
2.5 in3.375 in6.750 in
3 in3.875 in7.750 in
3.5 in4.375 in8.750 in
4 in4.875 in9.750 in
4.5 in5.375 in10.750 in
5 in5.875 in11.750 in
6 in6.875 in13.750 in
8 in8.875 in17.750 in

Work out your own numbers: Half square triangle calculator

Chart: goose fabric to cut for flying geese, by finished width and method

Each cell is the side of the large square for the two no-waste methods, or the width of the rectangle for stitch and flip, for the finished width in its row. The rectangle's height is the sky square in the next chart.

Method
Finished width of the unitNo-waste, four at a timeNo-waste with room to trimStitch and flip, one at a time
2 in3.250 in3.500 in2.500 in
3 in4.250 in4.500 in3.500 in
4 in5.250 in5.500 in4.500 in
5 in6.250 in6.500 in5.500 in
6 in7.250 in7.500 in6.500 in
7 in8.250 in8.500 in7.500 in
8 in9.250 in9.500 in8.500 in
10 in11.250 in11.500 in10.500 in
12 in13.250 in13.500 in12.500 in

Work out your own numbers: Flying geese calculator

Chart: sky squares to cut for flying geese, by finished width and method

Each cell is the side of the small sky squares for the finished width in its row. The finished height of the unit is half its width.

Method
Finished width of the unitNo-waste, four at a timeNo-waste with room to trimStitch and flip, one at a time
2 in1.875 in2.000 in1.500 in
3 in2.375 in2.500 in2.000 in
4 in2.875 in3.000 in2.500 in
5 in3.375 in3.500 in3.000 in
6 in3.875 in4.000 in3.500 in
7 in4.375 in4.500 in4.000 in
8 in4.875 in5.000 in4.500 in
10 in5.875 in6.000 in5.500 in
12 in6.875 in7.000 in6.500 in

Work out your own numbers: Flying geese calculator

Used by

Sources