The math of crochet

Stitches for a width

Gauge is the number of stitches, and of rows, that fit a set measure, usually 4 in (10 cm). Divide to get stitches to the inch. Then multiply by the width you want.

An example. Your swatch has 14 stitches to 4 in. That is 14 ÷ 4 = 3.5 stitches to the inch. For a blanket 36 in (91 cm) wide you need 3.5 × 36 = 126 stitches.

Crochet gauge shows how to make and measure the swatch.

Rows for a length

The sum is the same, with rows in place of stitches.

An example. The same swatch has 16 rows to 4 in, which is 16 ÷ 4 = 4 rows to the inch. For a length of 48 in (122 cm) you need 4 × 48 = 192 rows. If the stitch pattern repeats over 2 rows, 192 is 96 whole repeats, so it fits. If it did not, you would round to the nearest whole repeat.

A starting chain from a multiple

Most stitch patterns repeat across the row. The multiple is the number of stitches in one repeat. The "plus" is the few extra that finish the row and keep the edges straight. A pattern states both, as in "chain a multiple of 4 plus 3".

To find the chain, pick the number of repeats, multiply, and add the plus once.

An example. You want about 126 stitches. With a multiple of 4 plus 3, 30 repeats give 30 × 4 + 3 = 123 and 31 repeats give 31 × 4 + 3 = 127. The nearer is 127.

Check what the multiple counts. Some patterns include the turning chain in it and some do not. The starting chain calculator does this sum from a swatch and a multiple.

Why a flat circle adds the same number every round

The distance round a circle is its width across times pi, about 3.14. Every round of crochet makes the circle wider by the same amount: the height of one stitch on each side. So the distance round grows by the same amount each time, and the same number of new stitches fills it.

How many depends on the shape of the stitch. A stitch about as tall as it is wide needs 2 × 3.14 = 6.28 more stitches a round, which in whole stitches is 6. That is the usual figure for single crochet (double crochet in United Kingdom terms). Double crochet (treble in United Kingdom terms) is about twice as tall, and its usual figure is twice as many: 12.

An example. A single crochet circle that starts with 6 stitches has 6 × 10 = 60 stitches in round 10. See flat circle for the rounds themselves.

Scaling by a ratio

If you follow a pattern stitch for stitch at a different gauge, every width changes by the same ratio: the pattern's stitch gauge divided by yours. Every length changes in the same way, by the ratio of the row gauges.

An example. A pattern is written for 16 stitches to 4 in. You get 14. The ratio is 16 ÷ 14 = 1.143, so every width comes out about 14 percent larger. A piece meant to be 40 in (102 cm) wide comes out at 40 × 1.143 = 45.7 in (116 cm).

To keep the size, change the hook until your gauge matches, or change the stitch count as above. How to make a crochet pattern bigger or smaller sets out the ways.

Yarn for a larger size

Yarn goes by area. Work out the area of each size, divide one by the other, and multiply the yarn by that ratio. The answer is an estimate.

An example. A pattern for a blanket 30 in (76 cm) by 36 in (91 cm) asks for an estimated 1,000 yd (914 m). You want one 50 in (127 cm) by 60 in (152 cm). The areas are 30 × 36 = 1,080 and 50 × 60 = 3,000 square inches. The ratio is 3,000 ÷ 1,080 = 2.78, so the estimate for the larger blanket is 1,000 × 2.78 = 2,780 yd (2,540 m).

For a closer estimate, weigh a swatch: the yarn calculator works from its weight and size.

Crochet in mathematics

The borrowing goes both ways. Crochet has been used in mathematics to make models of the hyperbolic plane, a curved surface whose geometry is hard to picture.

Where to go next

• For the shapes these sums make, see how to crochet shapes.
• For common blanket sizes to aim for, see the blanket size chart.