Math…please don’t be scared

There I sat, admiring my swatch.  Loving it really.  The drape, the gauge, the yarn, the color, all was well.  Look at that red thing (details of said swatch intentionally and shamelessly obscured in the interest of secrecy preservation).

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It’s Blue Sky Alpacas’ Alpaca Silk in Crabapple and it’s filling me with glee.  The other thing it was filling me was doubt.  Had I let my swatching fever take too strong a hold?  Was I going to run out of yarn because I’d knit such a nice big swatch?  I’m a swatch keeper.  I’ll rip them out if I have to, but especially for book projects (where the full project is usually knit by someone else), I really like to keep them if I can.

So I did what seemed reasonable…I did math.

As I was doing this, I realized this was the single most useful bit of math I do, and I do it often.  I wondered if I could write it up in a way that might help someone who shies away from math.  I know math aversion runs deep in some folks, but this is so useful it might be worth trying.  Let’s see, shall we?

First, the set up.  I had a swatch.  It had 1,470 stitches in it (we can talk about estimating stitch counts later if folks are interested, for now just take my word for it), and it weighed 10.2 grams.  I had 90 grams of yarn leftover to use for the project.  I wanted to know how big a project I could make.  So if you write that out in numbers instead of words, it looks like this:

1,470 stitches / 10.2 grams = X stitches / 90 grams

So to say that in words again, I made 1,470 stitches with 10.2 grams of yarn, so I can make X stitches with 90 grams of yarn…what’s X?

Now, if you recall your first algebra class, you’ll remember that you can generally do the same thing to both sides of an equation and it stays the same.  So for this question, you can multiply both sides by 90 grams, and something neat happens.  See how X had been divided by 90 grams to start with?  Well if you then multiply it by 90 grams, X (our mystery answer) gets left there all alone (which is what we want).

(1,470 stitches / 10.2 grams) * 90 grams = X stitches
X = 12,970 stitches

So now I know my project can have up to 12,970 stitches.  Now, to be safe (because maybe my tension will change or maybe my scale was off or maybe the bind off will be a yarn hog), I’ll round that down a bit to give myself a safety factor, but this is hugely useful.  It tells me (thanks to a bit more math used to see how many stitches would be in the size I want the finished piece to be) that I’ve got plenty of yarn for my plan for this project.

But, here’s the useful thing, you don’t just do this for stitch counts, you can do it any time you have a known relationship and you want to know about a specific example.  So if you know that your ball of yarn weighs 50 grams and is 200 yards long (there’s your known relationship), and you know your hat weighs 43 grams (there’s your specific example), you can figure out how much yarn it used. For that, you’d set it up like this:

200 yards / 50 grams = X yards / 43 grams
(200 yards / 50 grams) * 43 grams = X yards
X = 172 yards

So you multiplied each side by 43 grams and found out your hat took 172 yards.

It’s always the same approach, the only thing you have to do is pay attention to the units.

So you’ve got three parts: your known relationship  (that can be yards per gram from the ball band, or stitches per gram from a calculation like we did above, or most any other thing you want), your mystery answer, and your specific example.  Write it down so that your known relationship is on one side, and be sure that the thing that has the same units as your mystery answer is on top.  So see how we were interested in stitches in the first example, and we put stitches first?  And see how we were interested in yards in the second example and we put yards first?  Be sure you write it that way.  That’s equal to your mystery answer divided by your specific example.  All you have to do then is that one little bit of multiplication, and you’ve got your answer.

Try working through a few examples yourself and see if you can get the hang of it.  It’s how you do things like figure out ‘I have part of a ball left, how many yards is that?’ or ‘how many yards did this pair of socks actually need’ and it really will make your knitting life much easier.

Popping back in later in the day to add that I have this scale, and I love it. It is cheap and accurate (and, you know, tiny and cute, which is always good), and it comes in handy for measuring yarn on at least a weekly basis.