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.

Two Color Brioche on the Knitting Machine

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Two color brioche on the knitting machine is basically a two color fisherman’s rib. I will show you how it’s done on the Singer knitting machine.

But it’s important to first think about what you’re asking your machine to do. If you know what the machine is doing or what you want it to do, it won’t matter which brand of machine you’re using. You’ll be able to look in your manual and figure out how to do it.

Consider English Rib

When we knit English Rib, we are asking the machine to tuck on the main bed and knit on the ribber bed for the first pass. Then knit both beds on the second pass.
Our operation table looks like this:

We set the cam lever to tuck, but then set the right side lever to the triangle so the carriage still knits when traveling to the right but tucks when traveling to the left.

For Fisherman’s Rib

On the right to left pass, we knit the ribber and tuck the main bed. Then on the left to right pass, we tuck the ribber and knit the main bed.

Now our operation table looks like this. We set each carriage to tuck in only one direction. The main carriage in the direction the side lever is set to the circle and on the ribber carriage in the direction the set lever is set to ‘0’.

So now we look at Two Color Brioche

Beginning with the carriage on the left this time and using our first color, we want the carriage to tuck the main bed and knit the ribber – in both directions. Then we want our carriage to knit the contrast color on the main bed and tuck the ribber – again in both directions.

Our operation table if there were one, would look something like this.

So in our first step we set the knit carriage to tuck, leave the ribber on knit and run the carriage to the right and back again.

While our carriage is on the left, we change to our second color. With the knit carriage set to stockinette and the ribber to tuck, we knit to the right and back again.

We continue along to our desired length – changing yarn and settings every time the carriages are on the left. The result is ribs in one color and purls in the other and the reverse on the other side.

I have a tutorial up on YouTube as well, if you find it helpful please subscribe while you’re there.

 

Full Fisherman’s Rib on the Knitting Machine

Full fisherman’s rib, also apparently known as full cardigan rib, can be knit on any machine with a ribber.

Full Fisherman’s Rib on a Singer Knitting Machine

We start by casting on as we would for 1×1 ribbing, using either the zig-zag/circular cast on, or eWrap.

There are no instructions for this stitch in my Singer manual, but if there were, the operation table would appear something like the photo above.

Starting with the carriage on the left.
  • We aren’t using the punch card so we set the patterning lever to the circle.
  • On our main bed carriage, we set the left side lever to the circle and the right side lever to the triangle.
  • We set the cam lever to tuck.
  • On the ribber carriage we leave both set the left lever to ‘0’ and leave the right lever on ‘1’.
  • We set the pick knob to the upside down ‘U’.
  • Pitch is ‘P’ and swing set to 5.
  • We set the tension or stitch size appropriate to our yarn and the same on both carriages.

Then we knit

Starting with our carriage on the right, our main bed stitches “tuck” as we knit to the left. The ribber stitches knit, but on the main bed the yarn is just laid in the needles.

Then as we move the carriage back to the right, our main bed knits while our ribber bed just tucks.

The resulting fabric is nice and squishy. The tucks make the fabric thicker and more dense than stockinette or ordinary rib would be, I assume that’s why it’s called fisherman’s rib.

Swung English Rib

Swung English Rib is simply English Rib where we change the swing position of the ribber while knitting.

Swung English Rib on a Singer Knitting Machine

To start we cast on as we would for 1×1 ribbing.

In the Singer manual our operation table looks nearly the same as it did for English Rib. The only change is a line is added and we have information in the swing column.

Starting with the carriage on the left.
  • We aren’t using the punch card so we set the patterning lever to the circle.
  • On our main bed carriage, we set the left side lever to the circle and the right side lever to the triangle.
  • We set the cam lever to tuck.
  • On the ribber carriage we leave both set levers on ‘1’
  • Pitch is ‘P’ and swing set to 5.
  • We set the tension or stitch size appropriate to our yarn and the same on both carriages.

Then we knit

We knit two rows with our swing set to 5. Pitch stays on the ‘P’.

As we knit from left to right both the ribber and main bed knit. On the right to left carriage pass, the ribber knits but the carriage only lays the yarn in the needles on the main bed.

Then we change our swing to ‘7’

This is how our knitting looks before any carriage passes.

We knit left to right and then back to the left.

And then change our swing back to position ‘5’ before knitting 2 more carriage passes and repeating the two instruction rows of the operation table.

We end up with a fabric that looks like rib on one side and a very pretty zig-zaggy effect on the other.

More on Swung English Rib

You can find demonstration of this technique on my YouTube channel – don’t forget to subscribe while you’re there.

 

English Rib for the Machine Knitter

English Rib, also known as Half Fisherman’s Rib or Shaker Knit, is a ribbing variation you can machine knit on any machine with a ribber. Above you can see swatches of English Rib, Swung English Rib and Fisherman’s Rib.

English Rib on a Singer Knitting Machine

To knit English Rib on a Singer machine, we start by casting on as we would for a 1 x 1 rib.

We can see in the above image the Operation Table from the manual for my Singer machine. The first portion deals with the cast on if you use that method, but we see in the second portion our settings for the stitch pattern.

Starting with the carriage on the left.
  • We aren’t using the punch card so we set the patterning lever to the circle.
  • On our main bed carriage, we set the left side lever to the circle and the right side lever to the triangle.
  • We set the cam lever to tuck.
  • On the ribber carriage we leave both set levers on ‘1’
  • Pitch is ‘P’ and swing set to 5.
  • We set the tension or stitch size appropriate to our yarn and the same on both carriages
Then we knit

On the first carriage pass knitting from left to right, both beds knit as usual. I expect as I learn more about using knitting machines this will be proven wrong, but to me it seems as if setting that side lever on the main carriage to triangle allows the carriage to ignore that the cam lever is set to ‘tuck’.

Knitting from right to left, the ribber knits as usual but on the main bed the machine just lays the yarn in the hooks without knitting it. It knits on the next carriage pass when we go from left to right.

We can reverse this and have the machine knit right to left and tuck left to right. We just need to set the left side lever to triangle and the right side lever to the circle.

More on English Rib

You can see a full demonstration of knitting English Rib on the Singer knitting machine on my channel. While you’re there don’t forget to hit the subscribe button!

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