The Mathematics of Knitting

Do you knit? Can you explain gauge? And how the heck are we supposed to know how many stitches we need to cast on to achieve a specific target width?  Looking at my frequently asked questions there are a lot of open questions related to calculations, so let’s talk about the mathematics of knitting this month!

Today, I’m going to share my thoughts on the first big topic of mathematics in knitting with you: Knitting gauge and aspect ratio. (Don’t run away now! It’s going to be interesting for non-nerds, too. Promise!)

For everybody (or at least, most of us) math classes were not the most popular in school. Mathematics is a subject most people just cannot make friends with, and usually this has two reasons: It’s an abstract concept, and most teachers don’t do a good job explaining.

But …

Knitting Needs Mathematics.

If you’re a knitter who loves to follow patterns created by others you don’t need to be involved in the underlying math problems. All calculations have been done already, all you need is to follow the pattern and you’ll be okay. Don’t you?

Well, there are a lot of things that can go wrong – even then. Ever knitted a sweater supposed to fit you but ended up fitting your teddy bear?

My first attempt to knit a sweater without checking gauge first ended up in something my husband could wear instead. When I tried it on it would have made a great dress if my hips were double as wide as they are. (Nice knee length, though!)

What went wrong?

I didn’t check gauge first. Didn’t work a gauge swatch neither. Just took the needle size the pattern called for and the same yarn and started to knit right away – a huge mistake.

Knitting Gauge and Aspect Ratio

The most important concept in knitting is gauge. How many stitches do you need to achieve a width of 4 in (10 cm)? How many rows do you need to work to achieve the same height? These numbers are called your knitting gauge. Patterns state these numbers like “20 stitches and 26 rows equal 4 x 4 in (10 x 10 cm)”, or something similar.

What does this mean?

Simple: If you imagine a knitted 4 x 4 in (10 x 10 cm) square using this gauge you would count 20 stitches in width and 26 rows in height. Or put it this way: to achieve a target width and height of 4 x 4 in (10 x 10 cm) you need to work 20 stitches and 20 rows.

The mathematics of knitting: gauge
20 stitches and 26 rows equal 4 x 4 in (10 x 10 cm): a hypothetical swatch.

The aspect ratio of your stitches is the ratio of the width and height of them.

If you need 20 stitches and 20 rows to get 4 x 4 inches you have an aspect ratio of 20:20 = 1:1.

If you need 20 stitches and 21 rows to get 4 x 4 inches you have an aspect ratio of 20:22 = 1:1.1.

And so on:

  • 20 stitches / 24 rows in 4 x 4 in = 1:1.2
  • 20 stitches / 26 rows in 4 x 4 in = 1:1.3
  • 20 stitches / 28 rows in 4 x 4 in = 1:1.4
  • 20 stitches / 30 rows in 4 x 4 in = 1:1.5
  • 20 stitches / 32 rows in 4 x 4 in = 1:1.6

Changes in gauge and your aspect ratio directly affect how your knitted fabric looks like. Examples of aspect ratios 1:1, 1:1.2, 1:1.4 and 1:1.6 (left to right, top to bottom) are shown in the picture below.

Mathematics of knitting: various aspect ratios

The thinner your yarn and your needles, the more stitches and rows per inch you will need to achieve a certain width and height. But one thing is very important:

Your aspect ratio depends on YOU and how YOU KNIT only.

And it might even depend on your state of mind, if you had a beer or two, if you’re excited or sad or agitated; and eventually a gazillion of other factors.

Three more things.

First, I’m working on swatches using the very same yarn and a set of different needle size to determine my personal personal gauge interval using a giving yarn. Research question: Is my gauge affected by booze? Hypothesis: yes, it is.

Second, I’m curious to start a study with a decent number of participants to research the boundaries of aspect ratios in knitting. Seriously. Are you in? If yes, please comment below or shoot me an email.

Third: I’m continuing the mathematics of knitting tomorrow with deeper insights about the influence of knitting gauge on increase angles in triangles (link will be added as soon as its available).

I’m off to conduct some gauge research now. Sweet dreams everybody. 🙂

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4 thoughts on “The Mathematics of Knitting

  • April 7, 2017 at 6:43 am
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    I’d be happy to participate in that aspect ratio study. I almost always get gauge on my first try in stitches per inch, but it generally takes me a few more rows than called for to get there. I’d like to get really good at figuring sweater modifications for a custom fit. Understanding my row gauge better would help me to fudge where I place increases and decreases to get the right silhouette. Long story short: count me in!

    Reply
    • April 9, 2017 at 8:00 pm
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      Thanks for your interest! I’ll let you know as soon as I am finished setting it up!

      Reply
  • April 15, 2017 at 11:08 pm
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    I would be interested to participate in your study of aspect ratio. I am currently looking at Gauge and Tension to try to deepen my understanding of this all important part of knitting.

    Reply
  • May 11, 2017 at 1:38 am
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    Hopefully, if I’m selected to participate it will get me knitting items other than afghans. Elderly hands seem to impact my gauge these days but I’m determined to overcome and stop using this excuse.

    Reply

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