How to crochet an ideally flat circle?
It’s pure math, which translates to stitches of any height.
Below, you’ll find detailed explanations, but you can always skip the hassle of manual calculations and use this Flat Circle Calculator.
The relative sizes of common stitches
For our purposes, the relative sizes matter, not the absolute ones. Let’s look at the sizes of common stitches this way:
- a single crochet (sc) is a tiny square: 1 x 1
- a half double crochet (hdc) is about 1 x 1.5
- a double crochet (dc) is 1 x 2
- …
The formula
Each new round adds to the radius of our circle.
The formula for calculating the circumference is
C = 2 * π * r, where r is the radius.
Using this formula, we can calculate how many stitches there must be in each round of the circle.
Example: single crochet circle
For example, let’s say we’re using only single crochet (sc) stitches, which are 1 x 1.
On the first round, the radius is 1. Let’s use the formula:
C = 2 * π * r = 2 * 3.14 * 1 = 6.28
This result can be rounded to 6. That means, for the first round, we need to make 6 stitches
(ever wondered why all circles start with 6 stitches?).
For the second round:
C = 2 * π * r = 2 * 3.14 * 2 = 12.56
So, for Round 2, we need 12 or 13 stitches. In many cases, 12 is the better choice, it’s divisible by 2, 3, 4, and 6, while 13 is a prime number. Divisibility helps in future rounds and makes calculations easier.
However, in this case, we’re exploring an ideal, mathematically correct circle, so we round it to 13.
Round 3:
C = 2 * π * r = 2 * 3.14 * 3 = 18.84
Eventually, using mathematical rounding, you’ll get:
Round 1: 6 stitches
Round 2: 13 stitches
Round 3: 19 stitches
Round 4: 25 stitches
Round 5: 31 stitches
Round 6: 38 stitches
Round 7: 44 stitches
Round 8: 50 stitches
Where to place increases?
We know how many stitches we need to work in total on each round, but how do we choose exactly where to place those increases?
First, you need to find how many stitches are added in this round. Say we’re on round 8, and we need to make 50 stitches. In the previous round, we made 44. That means we need to add 6 stitches this round.
Let’s divide the length of previous round by this number:
44 / 6 = 7.33333\
Note the two integers this value falls between: 7.333 falls between numbers 7 and 8:
low = 7
high = 8
Next step: calculate the number of high-count increases:
high-count increases = stitches in the last round - (low * total increases) = 44 - (7 * 6) = 2
After that, calculate the number of low-count increases:
low-count increases = total increases - low rate increases = 6 - 2 = 4
When you start stitching the round, work all low-count increases first, then finish with the high-count ones.
In this example, we will stitch first high:
4 increases every 7 stitches
and then low:
2 increases every 8 stitches.
So, you’ll place increases at stitches:
7, 14, 21, 28, 36, 44.
Too many increases?
You might have noticed that on Round 2, there are 7 stitches to be added, which is 1 more than the total number of stitches in Round 1. This means that, with single increases (i.e., 2 stitches in each stitch), you can add a maximum of 6 stitches. The remaining stitch must be added as a double increase: 3 single crochets in a single stitch.
In our example, that’s just 1 double increase.
Let’s formulate a general rule for the case when the amount of stitches to be added is greater than the number of stitches in the previous round.
Let:
a = stitches to be added
p= stitches in the previous round
% = symbol to denote the remainder from division: x % y = remainder of x / y.
Then:
a % p → the number of increases to be done on each stitch;
a / p → the frequency of an extra increase, rounded mathematically.
Using taller stitches
For taller stitches, the math works the same way.
For double crochet (dc) stitches, each round adds 2 to the radius, instead of 1, as it does with sc stitches.
Based on the same formula C = 2 * π * r, we can calculate the number of dc stitches on each round:
Using the same formula:
C = 2 × π × r
we can calculate the number of dc stitches needed on each round.
Round 1: 2 * 3.14 * 2 = 13 stitches
Round 2: 2 * 3.14 * 4 = 25 stitches (+ 12);
13 / 12 = 1.08
low = 1
high = 2
high-count = 13 - (1 * 12) = 1
low-count = 13 - 1 = 12
result: first 12 increases every 1 stitch, and then 1 increase every 2 stitches
Round 3: 2 * 3.14 * 6 = 38 stitches (+ 13);
25 / 13 = 1.9
low = 1
high = 2
high-count = 25 - (1 * 13) = 12
low-count = 13 - 12 = 1
result: 1 increase every 1 stitch, and then 12 increases every 2 stitches
Round 4: 2 * 3.14 * 8 = 50 stitches (+ 12);
38 / 12 = 3.16
low = 3
high = 4
high-count = 38 - (3 * 12) = 2
low-count = 12 - 2 = 10
result: 10 increases every 3 stitches, and then 2 increases every 4 stitches
Let’s try a mix?
Let’s do the same, but alternate rounds with sc and dc:
Round 1 (sc):
r = 1;
2 * 3.14 * 1 = 6 stitches
Round 2 (dc):
r = 3 (1 sc + 1 dc);
2 * 3.14 * 3 = 19 stitches (+ 13);
13 - 6 = 7; 7 > 6;
13 / 6 = 2 increases on each stitch,
13 % 6 = 1 extra increase
calculation where to place an extra increase (redundant, but good for the sake of math):
6 / 1 = 6
low = high = 6
result: 1 extra increase every 6 stitches
Round 3 (sc):
r = 4 (2 sc + 1 dc);
2 * 3.14 * 4 = 25 stitches (+ 6);
19 / 6 = 3.16
low = 3
high = 4
high-count = 19 - (3 * 6) = 1
low-count = 6 - 1 = 5
result: first 5 increases every 3rd stitch, and then 1 increase every 4 stitches
Round 4 (dc):
r = 6 (2 sc + 2 dc);
2 * 3.14 * 6 = 38 stitches (+ 13);
25 / 13 = 1.9
low = 1
high = 2
high-count = 25 - (1 * 13) = 12
low-count = 13 - 12 = 1
result: 1 increase every 1 stitch, and then 12 increases every 2 stitches
Round 5 (sc):
r = 7 (3 sc + 2 dc);
2 * 3.14 * 7 = 44 stitches (+ 6);
38 / 6 = 6.3
low = 6
high = 7
high-count = 38 - (6 * 6) = 2
low-count = 6 - 2 = 4
result: 4 increases every 6 stitch, and then 2 increases every 7 stitches
Round 6 (dc):
r = 9 (3 sc + 3 dc);
2 * 3.14 * 9 = 57 stitches (+ 13);
44 / 13 = 3.38
low = 3
high = 4
high-count = 44 - (3 * 13) = 5
low-count = 13 - 5 = 8
result: 8 increases every 3 stitch, and then 5 increases every 4 stitches
Conclusion
In this article, we’ve gone through the key calculations needed to crochet a flat circle using different stitches. We’ve learned how to determine the number of stitches for each round based on stitch height, and how to evenly space the increases across the round, all driven by pure math!
To skip the complex manual calculations, you can use the Crochet Flat Circle Calculator.
Enjoy!
