The Knitting Fiend

Introduction: Instead of providing an actual sock pattern, this article discusses how to perform the calculations and make design decisions for a simple footie or "proto-sock" knit in stockinette. Dani asked here, so I thought I'd better explain.

Ok, what's a proto-sock? It's a sock that ends just above the heel turn or flap. I drew a black line across a real sock shown above. Yep, in other words, it's a "footie" or "tennis sock".

Why design a proto sock instead of a full sock? Because all the sock specific calculations occur in the proto sock. To make a real sock, you just add a knit tube above the proto-sock. So, if you understand the footie, you'll soon understand a full sock.

Now to begin!

Compile data.

To design and calculate your sock, you need to collect some data. This data defines the sock size and the stitch and row gauge.

Stitch data
For the purpose of designing a proto sock, pretend to knit a swatch in stockinet. Then, determine the stitch and row gauge, and enter them here:
Stitch gauge: st/in (or cm.)
Row gauge: rows/inch.

While you are at it, unless you have a really, really good memory, write down the needle size you used to knit this swatch. (I'm assuming you use American needle sizes. If you use metric, cross out the "US", and scrawl in "mm" after the number.)

Knitting Needle Size: US .

Now, before proceeding, I want you to calculate something that might prevent you from wasting time later. Divide the row gauge by the stitch gauge and write that down:

Row/Stitch_Ratio = / =

This is called the "row/stitch ratio". For stockinet knit by hand, this ratio usually falls between 1.2 and 1.5. If your ratio falls outside this range, you should remeasure your gauge swatch because you probably made a mistake counting or measuring. You may not have, but it's worth double checking.

Foot data
Next, you need to collect to make the sock fit the wearer's foot the way they like socks to fit. Some data is based on their foot dimensions; some is based on how they like their sock to fit.

Sock_Foot Length.
Have the wearer stand on a piece of paper, hold the pencil vertically and outline their foot. Then, measure from the back to the front. If you can't get the wearer to do this, but know the wearer's shoe size, you can look up their foot length from a chart, like the one I posted here.

Either way, enter the foot length:
Actual_Foot_Length: inches.

Ok. So you might think this is the length you should knit your sock foot, right? Well, maybe.

Some people like their sock foot length to be the same length as their foot; some like them to be a shorter. Guess what? When I knit socks by machine, I reduce the length by 15% to make a snug sock; when I hand knit I make the sock length match my foot length.

Depending on your preferences for sock fit, enter a number between 0 and 15% here: Negative_Length_Ease= %.

Now, calculate the sock foot length using the formula:
Sock Foot Length = Actual_Foot_Length *( 1- Negative_Length_Ease )

Inserting values results in: inches * (1 - ) = inches = Sock_Foot_Length.
If you are familiar with my sockulators, this is sock foot length I request in my sock-u-lators.
Sock circumference

The next thing you need to decide on is the sock circumference.; What is this? Well, if you lay your finished sock flat, and measure across and multiply by 2, that's the sock circumference.
To figure out how large that should be, measure around the widest part of your foot to find your foot circumference. My foot is widest around the instep; some people's feet are widest around the ball of the foot. Don't fret to much, just measure; write that number down here:
Foot circumference:inches.

Once again, you need to account for ease. Most people like their socks a bit tight in circumference. This prevents the sock from rippling and bagging in the shoe. The standard rule is make your sock circumference 10% smaller the foot; that is, have some negative ease.

Enter the Sock_Negative_Ease = %

The formula for the sock foot circumference is:
Sock_Foot_Circumference = (Actual_Foot_Circumference *(1- Sock_Negative_Ease) )

Inserting values, I get:
inches * (1- )= inches= Sock_Foot_Circumference.

You will use this circumference to calculate the number of stitches around the sock footl it's the circumference I request in my sockulators.

We're done collecting data for the "proto-sock" with a short row heel turn. Now, we can calculate the number required to create a sock pattern.

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First a sock is pretty much a constant diameter tube with a heel shape and a toe reduction. To determine the number of stitches to cast on multiply the stitch gauge and the sock circumference, then round to the nearest multiple of 4:

Stitch_Gauge * Sock_Foot_Circumference = stitches= Foot_Stitches.

Why round to the nearest multiple of 4? Here are 4 reasons:

1. An even number of stitches is required when grafting the toe. You want the top and bottom of the foot to have the same number of stitches. Of course, you could get away with rounding to 2, but 4 is ok.
2. Rounding to 4 lets you use  either 2 x 2 ribbing or 1 x 1 ribbing without adjusting the number of stitches between the stockinet and the ribbing.
3. Rounding to four simplifies directions for distributing stitches on DPNs and
4. Rounding to four it simplifies calculation of the heel turn because the heel has even numbers.

For these reasons you will find most commercial sock patterns round are based on multiples of 4 stitches. Later on, if you design a funky sock and have good reason to round to some other number, go ahead.

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Now that I have this value, I can start writing directions.

• Using appropriate size needles, cast on stitches. Join. Work 4 rounds in rib of your choice.; Work 1 round stockinet. (This makes a small trim that prevent curling then leaves you with a round in stockinet. That's all. When you knit a real sock replace this with a tube to make the sock top. )

• Begin heel turn. (There are a bunch of ways to organize the heel turn. Because I want to focus on calculating, I'm not going to discuss a persnickety details to prevent. )

• Place 1/2 stitches just worked on a stitch holder; these will be the instep stitches.; Work short rows over the heel stitches as follows:

• Row 1: Knit side facing. Knit until 1 stitch remains on left hand needle. Wrap next stitch and turn work.
• Row 2: Purl side facing. Purl until 1 stitch remains on left hand needle. Wrap next stitch and turn work.
• Row 3: Knit until 2 stitches remain on left needle. Wrap next stitch and turn work.
• Row 4: Purl side facing. Purl until 2 stitches remains on left hand needle. Wrap next stitch and turn work.

• Continue working in pattern established until __??__ stitches remain on left hand needle ending by working a purl row.

Opps! I need to calculate how many stitches remain on the left hand needle! How do I do that?

When knitting a sock with a short row heel, most people like to work short rows over 1/2 the total number of foot stitches. Why 1/2? Mostly, it's that you want the widest deepest heel turn possible with this method, but you don't want the heel turn to creep around the instep or top of foot. So, half is the ideal fraction.

Also, when working short rows, you need to work until you are just working a "small number of stitches" number of stitches in some purl row? How many? Well, here are the two factors: 1) You'd like the small number of stitches to hug the back of your heel 2) you'd like to make the turn as deep as possible. Many people find working until 1/3 the number of stitches involved in short rows feels comfy; this translates to 1/6 the total stitches in the foot.  Some people prefer to work until 1/2 the number of stitches in the short rows; this translates to 1/4 the total stitches in the foot and give a shallower heel turn. (I usually like 33%)

So, enter a number between 33% (for 1/3) and 50% (for 1/2) and enter that here: Heel_fraction = % of Heel_stitches.

Calculate the number of stitches left on the left hand needle as follows:

[Half_foot_stitches * (1- Heel_fraction) ] / 2 =
      [stitches * (1- )] / 2 = Number_left = stitches.

That's the number we need to fill in the instruction!

• Continue working in pattern established until  stitches remain on left hand needle when you finish a purl row.
• Hang a row marker to measure foot length.

• Work increasing short rows.
• Row 1: Knit side facing. Knit up to first wrapped stitch. Knit wrapped stitch with its wrap. Wrap next stitch and turn.
• Row 2: Purl side facing: Purl up to the first wrapped stitch. Purl wrapped stitch with its wrap. Wrap the next stitch and turn.
• Rows 3: Repeat row 1 but knit stitch with both its wraps.
• Row 4: Repeat row 2 but purl stitch with both its wraps.
• Continue in pattern established until you have are working all stitches.
• You are done with the heel.
• Pick up the instep stitches, and distribute stitches on four needles.

• Work until foot measures __??__ inches. . .

Oops! Another blank to fill in. Worse, calculating the correct length is going to take a while. Luckily, we'll be calculating other values we need along the way.

But maybe we don't need to calculate this? Many patterns just suggest you work until the toe reaches the bottom of big toe, or until it's 1-2" shorter than you want the foot to be or something like that. You can write your patterns that way too; it works kinda-sorta ok.

But what if the sock isn't for you? How are you going to figure out the length has reached the bottom of the wearer's toe? Or what if your toes are ultra long or short? Well, we can calculate the length of the as yet unshaped toe and subtract it from the total sock length.

To figure out the toe length, we first need to need to decide how you are going to decrease for the toes decide how many stitches you want to graftt for the toe. Then you need to decide how many stitches will remain when you stop shaping the toe.

For the purpose of this tutorial, we will decrease by alternating plain rounds and reduction rounds. To work a reduction round, identify the "top" and "bottom" of the foot. Divide the stitches so half are for the top and half for the bottom. Remember, the heel turn stitches were on the bottom of the foot, so you can trace a line from the heel turn edges to the sides of the toe. You'll find it convenient to distrubute stitches so the needle tips fall at the sides of the toe, so do that. (Remember all this. I'm not going to describe it again. Unless you ask. Then I'll repeat in comments.)

To actually work a reduction round, decrease 1 stitch on the right and 1 stitch on the left of the top of the sock and do the same on the bottom. You'll end up reducing 4 stitches on each reduction round.

Now, how many stitches do you want left when you finish shaping the toe. Many people, including me, like to reduce down to 1/2 the total number of stitches for the toe. Some like fewer; some like more; this depends on whether you have pointy toes or flat ones.

If you don't like 50%, change the number below to match the percentage of you'd like to have left when you finish the toe:
Toe_fraction = % of foot stitches.

Based on the number you entered, you will work this many reductions rounds:
[ (1- Toe_fraction)* Foot_stitches] / 4 = = Reductions.

How many will remain after shaping the toe?
Toe_stitches = Foot_stitches - 4 * Reduction = toe stitches.

Because you work reduction rounds every other round, the number of rounds you knit will be
Toe_rounds = 2 * Reduction =.

You can determine the toe length by dividing the number of toe rounds by the row gauge, like this:
Toe_Length = Toe_rounds / Row_Gauge = inches. (Notice, this is the only time we've used the row gauge!)

We've almost calculated the number I needed to fill in the incomplete instruction! To make the sock measure the length you want, you need to subtract the Toe_Length from the Sock_Foot_Length and insert that number in the instruction, which becomes:

• Work even until foot measures inches
• Now work 1 reduction round every 2 rows until a total of stitches remain. (Notice, I filled in the value for "toe stitches".)
• Break yarn; graft toe.
• Tidy up, block sock, make another one, wear.

That's it. You've calculated everything you need to create a footie pattern. You probably also understand why we round to a multiple of four stitches, and can make some decisions about the sock dimensions based on your personal preferences.

I know you still may not know how to deal sock issues you might care about like:

Can I make the ankle wider or narrower than the foot. (Yes, but there are two basic different ways. Either use a different type of heel or knit the top of the sock with larger needles.)

What if I want to knit a fancy stitch pattern? Well, then you will need to think about the stitch pattern, and some of the decisions about rounding. But, you shouldn't try to design a fancy stitch pattern until you understand the decisions involved in designing a stockinette sock.

I could think of more questions, but I think it would be better if you just ask them, then I can answer the ones you actually have! Good luck with your own sock designs.

Stumble it (and place in Knitting/crochet!)

4 Comments »

1. Awesome tutorial! I’ve been wanting to make a pair of footies and this is most helpful. Thank you!

   Comment by Jennifer — 3/24/2006 @ 8:46 am

2. This is EXACTLY what I was after! Thank you Thank you Thank you! Now all I need your address to live up to my promise of chocolate =)

   And hey, did I mention THANK YOU?

   Comment by Dani — 3/24/2006 @ 6:02 pm

3. [...] Posted Under: Knitting, Socks Dani 7:09 pm Have you seen what Lucia did for lil ol’ me? [...]

   Pingback by Yea, I Knit… » Worthy of a 2nd post — 10/29/2006 @ 6:55 am

4. [...] My own but I used this calculator to help me with the heel and toe Yarn: Grignasco Strong Print Recipient: [...]

   Pingback by Ankle Socks « The Trouble with Sbubble — 7/3/2009 @ 10:32 pm

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