Where Knitting and Science Meet: Stitch Gauge and Row Gauge Are Mathematically Related!

Ok, so I'm working on a big new project. In the course of all of the planning, pattern-writing, and yarn-ordering, a question arose.

Why is it that some yarn companies list the stitch gauge on the ball band and omit the row gauge?

And while that question may really be unanswerable, it made me wonder whether there's a formula that I could use to work out the row gauge (or at least a ballpark expectation of row gauge) from the stitch gauge.

One of the patterns that I'm working on will use a chunky yarn with a gauge of 3.5 sts / 5 rows / inch. I'm shopping for yarns online and would like to just make sure that the yarn that I order is perfect for what I want to do. Without having it here to swatch, I'd like to be able to do some quick calculations to double check.

When planning raglan sweaters from the top, the sweater grows in width at the same time as it grows in length. As I'm adding stitches to the chest I'm also adding rows to the armhole, and I need to keep track of both to make sure that when the sweater reaches my goal bust measurement the armholes aren't too long or too short. So, for me, the row gauge is just as important as the stitch gauge.

This is where my science brain kicks in. I know that I'm wrapping a yarn of a given diameter around a needle of a given circumference. We can assume that the yarn is approximately the same diameter along its length, and that the same could be said for the needle. (We're not talking funky fuzzy things or thick-and-thin things, just regular old yarns.) We also assume that we're configuring the yarn in the same manner each time we perform a stitch. (We are working the gauge swatch in stockinette, not in a fancy stitch pattern.) All that being true, it *should* be true that the width of each stitch will always be some proportion of its height AND that that proportion is the same, regardless of diameter of yarn or circumference of needle. (Again, assuming that diameter of yarn and circumference of needle remain consistent over their lengths.)

I decided to look at a few common examples.

Mission Falls puts their stitch and row gauges right in the name of their most popular yarn: 1824. They expect 18 stitches and 24 rows in 4 inches.

If you divide 24 by 18, you get 1.333.

Another common gauge is 20 sts in 28 rows (or 5 sts / 7 rows / inch) Dividing 7 by 5 gets you 1.4.

I did the same calculation for a LOT of stitch and row gauges, and it turns out that they are proportionate!

You get approximately 1.4 rows for every 1 stitch!

My friend Alexandra the Tech Editor sent me a tweet confirming it! We are both officially math geeks, though she is much more proficient than I (she tweeted me with the 1.4 even before I'd come to the end of my testing!)

SO, if you're ever shopping for yarn or patterns and confounded by the lack of row gauge...multiply the stitch gauge by 1.4 and you've got it.

Stefanie Japel is a knitwear designer, author, and instructor. She teaches at live events and also online at http://www.craftsy.com/, where she also writes the Craftsy blog. To learn more about Stefanie, visit http://www.stefaniejapel.com/.

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