Monday, February 20, 2012

On Gauge Math: Even a Quarter of a Stitch Matters

I was teaching a knitting class the other day when much to the surprise of my students, a math class broke out.

A student who will shall call G. is working on a sweater. Because G. is a sensible sort (who has known me long enough to know I would tell her off if she didn't...) she swatched.

The gauge required is 8 sts/4 inches.  Before she measured, G. did something we all would do: she divided. 8 sts for 4 inches - that's 2 sts an inch.

So G. measured her swatch and saw 2 stitches per inch. She was good to go! She had needles, yarn, and a plan for a fabulous quick knit jacket for early spring!

Now, being a sensible sort, G. decided to consult me to see if I agreed with her results. And it was a big horrible no.

I measured 4 inches, carefully counted the stitches, and got 9 stitches in 4 inches. 9 stitches in 4 inches is definitely not 8 stitches. 9 stitches in 4 inches is 2.25 stitches an inch; 8 stitches in 4 inches is 2 stitches an inch. Now, the difference is only a measly quarter of a stitch. G. had measured 1 inch, and in the fuzzy, fluffy yarn G is using, that quarter of a stitch over an inch was pretty hard to see.... it's a mistake we might all make, I don't blame her one bit.

G. is a lovely person, and she would never say so, but I had the distinct sense that she felt I was making a mountain out of a molehill: she really couldn't see why I was so worried about that quarter of a stitch.

But here's the problem: what seems like a rounding error - a tiny little fraction of a stitch - can make a HUGE difference. Enormous. Ludicrous, even.

The finished size of the garment is 44 inches, and you cast on 88 stitches for the full body circumference. 88 sts at 2 sts per inch = 88/2=44.  Perfect.

But at 9 stitches per 4 inches... 88 sts at 2.25 sts per inch =88/2.25 = 39.1 inches around.

Yes, that's right. A quarter of a stitch difference makes for a nearly 5 inch difference in the finish garment.

It turns out that your parents were right - math does matter!


cari said...

So... Did G. change needle size and re-swatch, or do more math and change the pattern to suit her tension???

kiwicanuck said...

I'm searching a sweater right now - going to go back and double check my math! Timely read!

May said...

Thanks for the reminder. Well timed as I'm starting a new project!

Guilty Party said...

I think I am the guilty party and no I didn't re-swatch. I just put the giant needles aside and went back to safely knitting socks...but I always, always appreciate Kate's insight, direction and support. It saves me from many a knitting disappointment.

Wendy Thomas said...

I can never get the gauge correct it seems. I'm working on a baby's dress and had worked two swatches and as a result gone down a needle size or two. But when I had the front half done I measured the width of the bodice (the only width measurement given) and it was way too wide for the length. In addition, often, my swatches end up longer than they're supposed to be so I don't have a square. It was all very puzzling. So I decided just to keep knitting swatches with different sized needles (all very small -- in the region of 2.25 and 2.5 mm -- pattern called for 3 and 3.25) and lo and behold I got the correct size *and* a square swatch. Well worth the time!