Pi Socks (free)

Interesting stripes using the number Pi

Interesting stripes using the number Pi

This pattern has been first published as a regular blog post. Now it’s part of the pattern section and has been slightly reformatted, reworded and checked for spelling and other errors.


Dieses kleine kostenlose Strickrezept (ich zögere, es Anleitung zu nennen) erschien erstmal als ein Blogartikel, ist nun jedoch fest hier hier in der Pattern-Sektion zu finden. Ich habe ein paar Umformatierungen vorgenommen, einiges umformuliert und ein paar Rechtschreibfehler ausgebessert. Die Anleitung ist nur in Englisch verfügbar, aber wer Socken stricken kann, für den ist hauptsächlich das Prinzip der Streifen wichtig.


Use any fingering weight sock yarn of your liking, about 200 meters per color. It can even be a heavier 6-ply sock yarn if you want something that knits up faster. Gauge doesn’t really matter here as long as you know how to re-calculate things to get a sock that actually fits.

The pictured socks are worked in Schachenmayr nomotta Regia Uni/Solid 4-ply/4-fädig in chocolate brown and green.


Sample was knitted on 2.5 mm needles as I prefer a dense fabric for my socks for durability. And 2.5 mm works good for me. Others use 2.25 or 2.75 mm needles.


These socks were knit to fit the best husband of all. He sports shoe size EUR 42 with feet slightly on the wide side therefore I cast on 68 stitches.

Regia provides extensive tables on sizes and gauges for their numerous yarns on their German website.

Choose your number of stitches and off it goes!

Stripe Pattern

The stripes are based on Pi’’s numerical value truncated to 50 decimal places: 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510. Pretty cool number, eh?! You could start out knitting as the digits appear above: 3 rounds color A, 1 round color B, 4 rounds color A, 1 round color B and so on. Alas, what to do when we hit the first zero? „Zero rounds of color A/B“?! You’d get one wide stripe and couldn’t decode it back into the two digits it was composed of.

To compensate for that problem we go with a simple rule:

Add 1 to each of Pi’s digits so that even 0 ist represented accordingly.

Color A: 4 rounds
Color B: 2 rounds
Color A: 5 rounds
Color B: 2 rounds
Color A: 6 rounds
and so on

Pi stripe sequence chart

Pi stripe sequence chart

Sock Pattern

While working the stripes knit your socks following your favorite basic sock pattern. You can either do them toe-up or cuff-down or whichever way suits you. I usually work mine top-down with a cuff in 1×1-ribbing for 15 to 20 rounds, switch to plain stockinette stitch until the sock measures about 15 to 20 cm (6 to 8“) and work a flap-heel. For the heel I stopped working stripes but chose to knit it in the brown yarn instead. As soon as the heel was turned and stitches for the instep were picked up I started working the stripes again. The toes I also did in plain brown and closed them using kitchener stitch.

My second sock continues where the first one left off. This way my socks represent Pi as 3.14159 26535 89793 23846 26433 83 (1st sock) 279 50288 41971 69399 37510 582 (2nd sock). Of course the stripes will not necessarily work out evenly so should you decide to follow my example you might have to live with socks where one leg is a couple of rows longer or shorter than the other. Same goes for the foot. I don’t mind but if you’re a stickler for such things you might want to just work two socks with the same stripe sequence. Or you could probably do some counting in advance to figure out which sequences of digits give you the same checksum.

While working the stripes I didn’t cut the yarn not in use but carried it up on the inside making sure it didn’t pull too tight or wasn’t hanging too loosely. That way you can spare yourself a hell of a lot of sewing in ends later. Where the colors change a little jog appears that seems to drive some people nuts. Again, I don’t mind. I did nothing to avoid it. There are all kinds of tips out there on how to minimize „The Jog“ if you actually care about it.

Fun socks with interesting stripes

Fun socks with interesting stripes

Happy knitting!

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