I'm going to preface this with a disclaimer: I am not a math person. Actually, my personal math nerd is away, so I'm basically pulling what I remember out of high school math. (In case you were curious, I did do calculus in high school and again for credit in university, but I could not have passed either without the help of my friends who actually knew what they were doing!) I am training to be a teacher, so this series is an exercise for me in a) teaching things that most people don't understand and b) learning something well enough so I can teach it to others.
If you got to grade 10 math, or have done physics or chemistry in high school, this should be simple enough for you to understand. Math for Knitters is simply rearranging equations. You don't necessarily have to understand how it works but you do need to be able to take my examples and apply them yourself.
If you want to know why you'd want to do this math, I'm going to tell you. If you have mystery yarn and want to know how much you have (or if you have enough to make something), you could unwind it, run it through a yardage counter, then wind it back up again. Or, you could save yourself the money on the counter, do a bit of quick and easy math, and get the same result. If you need to substitute yarns, but only the meterage or only the mass of the yarn are given, then you can change more easily. Some yarns are denser than others, so using meters makes sense in that context. But if a pattern tells you "400 meters of Cascade 220", how much of that nice cotton from your stash would you need?
I'm going to ask you a silly question: "what weighs more: a pound of feathers or a pound of bricks?" Think of yarn like that. Laceweight is feathers, and bulky is bricks. You could have 50g of each, but you would have a lot more laceweight (meterage-wise) than you would of bulky in that 50g. Also, not all fibres are created equal. Some are heavier/denser and others are lighter. The heavier and denser it is, the more it will weigh. You could have a string of lead at the same gauge as laceweight silk. The lead will be much heavier than the silk.
Note: when meterage/grams are given for yarn, it is often from a controlled environment in a factory. Weighing at home always has a margin of error because your scale probably isn't professional trade-quality. If you need an exact measurement, like to the inch, a yard counter is your best bet. Or, just to be on the safe side, get an extra skein of yarn, and hopefully you can return it (or use it for something else).
If you have any questions, please don't hesitate to comment or contact me otherwise (my name on Ravelry is andreabrightside).
Last thing: I have created this document through my hard work and fiddling with LaTeX builders online. (It hopefully looks effortless but it took quite a lot of thought) Please don't reproduce this or use it as your own. If you would like to use it for commercial purposes or spread it elsewhere, either link straight to this entry or contact me for more information.
Thank you and I hope you enjoy this post!
Math for Knitters Part 1: The Math
Math for Knitters Part 2: The Weight
PS: this math is for crocheters too, anyone who likes yarn, and anyone who likes math!!