How to Crochet a Circle

Have you ever noticed that when crocheting an amigurumi, which usually starts as a circle, the formula is almost always the same: start with 6 single crochets, then increase to 12, then 18, and so on, adding 6 single crochets in each round. Have you ever wondered why that makes a circular shape?

Circle

The answer is math. There is actually quite a bit of math happening in crochet (you didn't know you were a mathematician, did you?), and for a full discussion of it, I highly recommend Daina Taimina's Crocheting Adventures with Hyperbolic Planes. But for, we're going to focus our discussion on making circles.

If you remember back to high school geometry, a relationship exists between the measurement around the outside of the circle (the circumference) and the measurement across the center of the circle (the diameter). When you divide the circumference by the diameter, the answer is always π (pi), which is a famously never-ending number roughly equal to 3.14.

circumference ÷ diameter = π

This means if you want to make a hat that fits around a baby's 16-inch head, you need to make a circle about 5 inches in diameter (16 ÷ 3.14 ≈ 5.09). Awesome! So how does that relate to increasing each round by the same number of stitches?

Well now we need to add your gauge to the equation (I know you're all measuring gauge on all your projects like good little crocheters!). Let's pretend that your gauge is 3 sc and 3 rows = 1 inch (keep in mind that the number of rows worked represents the distance from the center of the circle to the outside, which is its radius; doubling this number equals the full diameter of the circle). With that in mind, let's use π to calculate how many stitches would need to be in each row to make our circle.

# of Rows Radius
(row # ÷ gauge)
Diameter
(radius x 2)
Circumference
(diameter x π)
# of Stitches
(circumference x gauge)
1 0.33" 0.66" 2.07" 6.21
2 0.67" 1.34" 4.21" 12.63
3 1" 2" 6.28" 18.84
4 1.33" 2.66" 8.35" 25.05
5 1.67" 3.34" 10.49" 31.47
6 2" 4" 12.56" 37.68
7 2.33" 4.66" 14.63" 43.89
8 2.67" 5.34" 16.77" 50.31
9 3" 6" 18.84" 56.52

Did you see what happened to the number of stitches needed for each round? In each round, the number of stitches roughly equates to a multiple of six: 6, 12, 18, 24, 30, 36, 42, 48, 54. Granted, it becomes less accurate as the circle becomes larger and for the most perfect circle, extra stitches would need to be added in later rounds.

But for the mathematically challenged, all you really need to know is that adding the same number of stitches to each consecutive round will produce a workable circle, and you don't have to worry about π or making charts to figure out how many stitches should be in that round. How easy is that?