Sock Math for Machine Knitting Socks

A well fitting pair of socks starts with some sock math and a tension or gauge swatch. If you have a ribber and plan to use it for circular sock knitting, you also need to swatch for balanced tension. These are the settings for your machine that produce the same tension on the ribber bed as the main bed.

Once you have your stitches per inch and rows per inch, you need to measure the circumference of your foot at it’s widest point and the length of your foot. Measure your foot from heel to toe standing. Subtract 3.5″ from that measurement to allow for toe and heel shaping.

You need to figure out how tall you want the leg of your sock too. Keep in mind that if you go very far up the calf, you will probably need to work increases or decreases to accommodate the larger circumference.

Explaining The Sock Math:

For number of stitches to cast on:

Stitches/inch x circumference of foot x negative ease.

Negative ease because you don’t want your sock to exactly fit, you want it to stretch around your foot at least a little:

So with sock yarn I get 9 stitches/inch and my foot is 9.5 inches around.
9 x 9.5 = 85.5, then if I take off 15% negative ease – 85.5 x (1-0.15) I get 72.68 and round down to 72.
If you are using a 2 x 2 Industrial Rib this number must be divisible by 6.
If I am machine knitting the rib flat and seaming later I add 1 or 2 stitches for selvedge.
I divide this number by 2 and 36 stitches is the number of stitches I will rehang on each bed once my ribbing is complete.

Rows to Knit

For the Leg:

First you will need to decide how much of the leg of your sock will be ribbing and how much will be plain knit. So I’ve settled on a 1″ rib followed by a 4″ leg. If I’m getting 12 rows per inch from my yarn and tension then sock math tells me:

I will knit 12 rows of ribbing
followed by 4 x 12 or 48 rows of plain knit.
If I’m knitting this circular on the machine, my carriage makes 2 passes for every row of knit so I will need 2 x 48 or 96 on the row counter before I start shaping my heel.

For the Foot:

My foot measures 9.5″ from heel to toe – standing:

I subtract 1.75″ for the toe shaping and another 1.75″ for the heel shaping. So my sock is 6″ from the end of the heel shaping to the beginning of the toe shaping.
So 12 (my rows per inch) x 6 gives me 72 rows.
If I’m knitting circular on the machine I double that and I’m looking for 144 on the row counter.

Heel and Toe Shaping

For a short row heel and/or toe:

I divide one half of the total number of stitches by 3. So 36/3, I will short row until only 12 needles are still in working position before I start bringing needles back into work.

For a shaped toe:

Generally, the toe decreases are done until you are down to 1/3 of the stitches remaining on each bed. So 72 stitches total, 36 on each bed you would decrease until 12 stitches remaining on each bed.

When knitting 2 x 2 Industrial Rib

To figure out how many needles for a 2 x 2 industrial rib:

Add your selvedge stitches – so 72 + 2, I start with 74
74 total stitches divide by 2 rounded up if necessary – 37.
On my main bed, I will use my 1 x 2 needle pusher to bring out my needles starting with needle L37 and end with R36.
I will reverse this on the ribber – start with L36 and end with R37

On the right of the bed, you will have a single needle grouping on each bed – for zig-zag cast on, cast on then move the stitch from R37 on the ribber to R37 on the main bed.
For e-wrap cast on, go ahead and take R37 out of work on the ribber and pull into work on the main bed before casting on.