ages ago, i did a couple of posts on math for knitters. i've been meaning to do more, but have been busy with other things. now it's time for another installment.
i was working up another design in my collection for Curious Creek. #11 for anyone counting. if you wonder why i'm not posting, that's one of the reasons. 11 designs since late summer. more than half of them have been knit (only a couple by me!) and i'm still very excited about them. it's weird to hand off the production end of a project (i.e. not knit it), but it definitely frees me up to do more.
so anyway, i am working on a basic men's sweater pattern and after the design is done i need to figure out how much yarn it's going to take (in five sizes). how? i could guess, based on past experience. i could consult one of those charts that gives you a ballpark for certain sizes for certain weight yarns. if i were knitting it for myself that would be fine, but this pattern will be in the hands of other people. other people who don't want to buy two more skeins of yarn than they need, or worse, find themself a skein short of small-batch hand-dyed yarn!
the way i do it is this: since i have already swatched and know what my stitches per inch and row are supposed to be, i cast on EXACTLY 4 inches worth of stitches. say the gauge is 4.5 sts per inch, i cast on 18 sts. and i knit in the appropriate stitch pattern for exactly 4 inches. (you could do some other number of exact inches, but the larger it is, the more accurate your result will be.) don't bother to bind off. make a knot at each end of the yarn right where the swatch stops and starts.
then, Unravel your swatch. Measure the length of the yarn accurately, without pulling it too tight. I have a mark on my table one yard from the edge, so I just hold the yarn from edge to mark and keep track of the number. Measure it a few times until you are confident you've got it right.
write the number down and label it. seems like you'll remember, but you might not, or ages from now, you might decide to design something in the same yarn and the same stitch pattern and you'll be very glad you have something that says, "Serengeti Half Linen Stitch on #5's: 16 square inches = 17.6 yards -- 1.1 yd = 1 inch square".
let me back up and explain that last bit: my whole 4 x 4 inch swatch unraveled and measured knot to knot was 17.6 yards long. (you can work in yards, meters or inches, as long as you are consistent.) i know that that length of yarn made 16 square inches of fabric (4 inches x 4 inches equal 16 square inches). if i divide my result by 16 then (17.6 yds/16 square inches) i get my yarn use per square inch -- 1.1 yds per square inch. cool.
now i need to make my sketch of the sweater:
this sweater has very little shaping. I am ignoring the bit cut out of the front for the collar. This sweater has a crew neck and the amount lost isn't substantial enough to bother with. And this gives me a little extra cushion on yarn needs.
If your garment has more shaping, you can draw lines a little straighter than they are in real life, but it's better to be generous than stingy. You want an accurate sketch of your sweater, but you also want shapes that are as regular as possible. Squares, rectangles, circles, etc.
Now that I've got my sketch and my numbers I am ready to do the math. You will recall from the dark ages of your education that the area of a rectangle is equal to its length times its width. We already used this formula above with our swatch. Looking at the sketch, you can see that the body is a rectangle. That's easy then: 25 x 20 = 500 square inches.
But what about the sleeve? Not a rectangle.
We could just sketch it accurately on graph paper and count up all the little squares (and with irregularly shaped items, you might have to do some of that), but that's tedious.
If you look at it again, you can see that the center portion of the sleeve IS a rectangle and we know it's measurements -- cuff width and sleeve length. So that's 10 x 22. 220 square inches, but what about the extra bits on the side? They are two triangles. The length we know (sleeve length = 22), but what's the width? We know that the top of the sleeve measures 20 inches. And we took 10 away with our center rectangle. 20 - 10 = 10, but there are two triangles. 10/2 = 5. Each triangle is 5 inches wide and 22 inches long.
And if you put them together they make another rectangle, 5 inches wide and 22 inches long. So the "wings" of the sleeve add another 110 square inches (5 x 22 = 110). The formula for the area of a right triangle is length x width divided by 2, but since we have 2 exactly the same, the rectangle is less work.
So, the body piece is 500 inches square, the sleeve has two parts, one 220 square inches and one 110 square inches. This is only half the sweater though! There's also a front and a second sleeve. One of the biggest hurdles in this whole process is making sure that you have all your body parts properly accounted for. Adding it up then we've got (500 + 220 + 110)x2 = 1660. Our sweater has 1660 square inches.
Going back up to our unraveled swatch (and the numbers we wrote down), we will remember that we used 1.1 yards of yarn per square inch. 1660 x 1.1 = 1826 yards. The yarn that I am using has 123 yards per skein, so 1826/123 = 14.846. So I will need 15 skeins of yarn. If you are being generous in your measurements and rounding, you can be fairly confident. It's never a bad idea to add 10% for error. 14.846 x 110% = 16.33. or at least an extra skein. Better too many than too few.