## Tuesday, July 12, 2011

### Math for Knitters: Part 1 (the math)

One of the most common questions I see on Ravelry is something to this extent: "I have/need yarn.  How much do I have/need?"  Another frequent question that has the same answer is "Should I buy a scale or a yardage counter?" Either way, the solution to your problem comes from converting between mass and meterage.  **NOTE: I use the term "mass" to talk about how heavy a yarn is (i.e. what I read on the scale in oz or g).  "Weight" refers to the fibre weight or density, such as laceweight or worsted.

I'm Canadian so for the purposes of this entry, I will be using the metric system.  It's not scary and it makes a lot more sense than the imperial system.  However, not all manufacturers use the metric system, so that's OK.  If, everywhere you see "g" (grams) you substitute oz (ounces), and for "m" (meters) you substitute yards, everything will work out fine.  If you need to change units, you can either use a converter tool (I usually just Google something like "50m to yards" and it gives me the answer I'm looking for).

Anyway, I'm going to cut to the chase.  Read the introduction if you want to know why on earth you would want to do this.  You'll need a scale, a ruler or meter stick, and a calculator.

Step 1: Find out the weight of your yarn.  You can do this by:
a) Looking at the ball band or the yarn page on Ravelry
a.1) My yarn has a mass of 70g and each ball should have 110m of yarn.  I want to find out how much one meter of yarn will weigh.  We do this by dividing meters by grams.
$x=\frac{\textup{m}}{\textup{g}}=\frac{110\textup{m}}{70\textup{g}}=1.571\textup{m/g}$

b) Finding out your grams per meter using a scale and ruler
b.1) You find this out by measuring some yarn out using a ruler or meter stick (I would go with 3m of yarn at least, maybe more for laceweight or lighter).  The more yarn you measure out, the more accurate your reading will be.  Home scales may be sensitive to air currents and are not always sensitive to the last decimal point.  Unfortunately this may mean that your final number could be off by a bit, so that's why it's important to invest in a good scale (or work in a deli or post office!).  You use the exact same formula as above, substituting the numbers for the ones you measured.

Step 2: Find out the mass of your yarn.  Put the yarn on the scale and weigh it.  I have 55g of yarn.  I know some of this ball has been used but I don't know how much, and I'd like to make something that calls for 100m.  Will I have enough?

This is the easy part.  We have our magic number from above (1.571m/g).  We just have to multiply the grams to find out meters.  If you remember from school, what you do to the bottom, you do to the top.  So if we multiply the entire number by grams, the grams on the bottom will cancel out, leaving us with meters (and, more importantly, a number you can use!).
$x=1.571\textup{m/g} \times 55\textup{g} = \frac{1.571\textup{m}\times 55\textup{g}}{\textup{g}}= 86.43\textup{\textup{m}}$

... whoa, was it really that easy?  I'm kind of bummed that I only have 86m, but I guess I can go buy more yarn!

Formulas formatted using http://www.codecogs.com/latex/eqneditor.php