The Maths of Knitting a Circle

This post is a response to Episode 130 of the Knit Knit Café, a knitting podcast of which I have become a regular listener.

‘Guest Barista’ Susan is trying to work out the maths of knitting a flat-topped hat, where the top is circular. Listen to the podcast section from 31:30 onwards and you can hear the original discussion, where Abby and Susan between them describe the problem much better than I can! But basically the question is this – what is the decrease formula for working out how to knit a flat circle from the outside in?

It’s just maths, of course*. I am a relatively new knitter and I have never actually tried this, but I am very mathematically inclined and I see no reason why the following wouldn’t work. Bear in mind that we are knitting in the round here, so each ’round’ is actually part of a long spiral.

Before you start you need three numbers:

  • S = the number of stitches that you are starting with around the outside edge of your circle (the circumference)
  • C = the length in inches of your circumference
  • G = your row gauge – that is, how many rows you knit for a vertical inch of knitting.

Step 1 is to calculate r = the radius of your eventual circle.

r = C ÷ 2 ÷ pi

circle

Step 2 is to times r by G, your row gauge. So let’s say you’ve worked our your radius to be 3 inches and your row gauge is 6 rows/inch, then you do 3 x 6 = 18 . The number that you end up with is the number of rounds that you need to work to get to the middle of your circle – let’s call is N.

Step 3 is to take S, the number of stitches around the outside of your circle, and to take away 3. Call this number D. D is the number of stitches that you need to decrease in total in order to end up with 3 stitches left at the middle of the hat.

So we now have the following: (if you are nervous of doing algebra then I suggest that you write these out in a separate list with the calculated number next to each letter so that you have an easy reference)

  • S = the number of stitches that you are starting with around the outside edge of your circle (the circumference)
  • C = the length in inches of your circumference
  • G = your row gauge – that is, how many rows you knit for a vertical inch of knitting.
  • r = the radius of your circle
  • N = the number of rounds that you’re going to need to work, and
  • D = the total number of decrease stitches

Step 4 (nearly there!): do D ÷ N. This will tell you how many stitches you need to decrease on each round, using your favourite decrease. In order to get a nice even circle, you should try and spread the decreases out around the circle as much as possible, and try not to decrease at the same point on next-door rounds.

At the end of this, you’ll end up with 3 stitches left. Break the yarn, and pull the tail through the stitches to secure them.

One important thing to note is that you will very rarely end up with nice whole numbers to work with, so you may have to do a bit of ‘fudging’ to end up with something sensible – it’s obviously not possible to decrease exactly 5.4 stitches per round, for example! Just bear in mind that you want to keep everything as symmetrical and even as possible in order to get a nice smooth circular shape. This will be easier in lighter weight yarns where a single stitch corresponds to a smaller measurement in inches.

If anyone tries these instructions, by the way, I’d love to hear about it and to see your results!

x

*This is one of the things that I love about knitting, incidentally – so much is “just maths”! Geek, me?

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