Stoichiometry and Knitting

calculator[1]I don’t get to use my college degrees very often (they’re in a couple fairly impressive-sounding branches of biology and chemistry), but sometimes I get to use a technique I learned in school.  It always makes me happy to use to use things my professors never would have expected.

For example:  Stoichiometry.

Never heard of it?  Not a problem.  Stoichiometry is a fancy chemistry word for a really useful way to do conversions.

If you’ve ever figured out how many stitches there are an inch of sweater or how many rows you need to knit to make a  foot of scarf, you’ve probably done stoichiometry without even knowing it.

Here’s the idea:

You know how if you divide a number by itself, it equals 1?  (Like:  2/2=1)  Stoichiometry tells you that you can do the same thing with words, units, and variables (remember x from high school algebra?).

So what does that mean?  Let’s take a really simple example:

1We can cancel out the “sts” from the top and bottom, so the answer (1) doesn’t have any units.

Now, that example is kind of useless to us, right?  So let’s use stoichiometry to do something that really is useful.  Figuring out how many rows we need to knit to get a 7 inch-tall sock.

Start by making a list of everything you know:

  • Our gauge is 12 rows/inch.
  • We want a 7 inch sock.

You could probably figure this one out in your head (or just on a calculator), but let’s do it the long way for example’s sake.

Start with the number that has a single unit (in this case the “7 inch” finished length) then, build your equation, multiplying across, and making sure that you cancel out your units as you go:

4 We can cross out the units that appear on the top and on the bottom (in this case, the “inches”).

Then we just multiply across, and the answer to the problem gets whatever unit is left (in this case, “rows”)3

So, in this example, if you have a 12 row/inch gauge and you want to knit a 7 inch sock, you have to work 84 rows.

Does that make sense?  Want to do one more (slightly complicated) example?

OK:  Imagine you’re designing a sweater pattern.  You want the front to be covered with fair-isle patterned stripes that are 8 rows tall.  You want to calculate how many stripes you will need to work to cover the front.

Here’s what we know about your sweater:

  • Gauge: 6 rows/inch
  • Sweater length from hem to shoulder: 22 inches
  • Stripe width: 8 rows/stripe

So, let’s set up the formula (starting with the sweater length- remember, begin your calculation with the number with the single unit.)

5(See how I flipped the 8 rows/stripe upside down, so it’s 1 stripe/8 rows?  That’s totally OK!  And, actually really important.  Flip any/all of your numbers, if it makes the units cancel out correctly.  Just remember, if you flip your the number, make sure you flip your units, too.)

Once everything is lined up correctly, start crossing out units that cancel:

6Then multiply across:7And then divide the top by the bottom.8So, in this example, you’d need to work 16.5 Fair Isle stripes to cover the entire front of your sweater.

Cool right?  (Or maybe that’s just me being a math nerd.)

Of course, you don’t have to use stoichiometry to work these things out, but it’s a great tool to have in your pocket- you never know when it will come in handy.

Do you think you’d ever use this technique to calculate bits of your pattern?  Do you have a different technique for calculating things?  Or do you avoid math completely?

6 thoughts on “Stoichiometry and Knitting

  1. Maggienesium

    Nope, not just you 🙂 I find myself using this for everything, knitting, soap making, cooking, carpintery etc. Dead useful in ways I never imagined – and to be honest, kinda fun!

  2. Talya

    And I thought that was just algebra. 33 rows/7 rows = x/140 stitches. Solve for x, and you find out how much you’ve knitted at the end of 33 rows. Or you can use the same equation to find out how many stitches you need to cast on for a large hat, if you only have instructions for a medium, and you know your gauge.

    1. onemilljellybeans Post author

      Totally! There are a bunch of ways to do it. I like using stoichiometry because it lets me convert through a whole bunch of intermediate steps without having to write out a bunch of new equations, but the algebraic method you mention totally works too!

  3. Claudia

    Hehe. So nice to see someone else geeking out over the math in their knitting. After all, getting to crunch numbers is half the fun, right? Love reading your blog!


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