Math to the rescue! Yay! I'm one of those strange people that always loved math as a kid. I think I was the only student excited to go to calculus class. Back when I started designing, I had no idea how much math would be involved. Today we will be working with proportions. Need a quick refresher before we begin?
I'm going to show you how to calculate the area of the body and sleeves of a sweater, then create a propportion (or 'ratio') of the yarn used for the body to figure out how much yarn I will need to complete the sleeves. You'll need a schematic, a calculator, and an accurate measurement of how much yarn you've used for the body (thank you Postage Scale!). Are you with me? Let's begin.
The good old schematic, so useful throughout the whole knitting process.
I could break the body down into several trapezoids and calculate the areas separately, but instead I'll take an average (or 'mean') of the three circumference measurements and calculate the area as one big rectangle. The basic formula for finding the area of a rectangle is:
area= base x height.
So, let's first make an average:
There are 3 measurements, so divide the answer by 3:
Now multiply that answer by the height, the body length.
37.33 x 21.75= 811.99
So, the body is approximately 811.99 square inches. I'll round it up to 812 for the proportion.
Now let's calculate the area of the sleeve. For the sleeve I usually break it down into two trapezoids, the underarm down to the wrist, and the sleeve cap. The basic formula for find the area of a trapezoid is:
area= (base1 + base2)/2 x height
For the area of the underarm portion:
(9+12)/2 x 10.5= 110.25
For the area of the sleeve cap:
(12+4.25) x 5= 81.25
Add both together:
So the area of one sleeve is 191.5 square inches. We will need two sleeves, so double that measurement to get 383 square inches.
Great! We've got the areas calculated. Time for proportions! Now, to knit the body I've used 5 complete balls of yarn (250 grams) and a partial 6th ball. I weighed the partial ball on my postage scale to find that I've used 30 grams of yarn. So the total yarn used is 280 grams.
812 square inches (body) = 383 square inches (both sleeves)
280 grams of yarn ?
?= 383 x 280 / 812
?= 132.06 grams of yarn
So I will need 132 grams of yarn to complete my sleeves. There are 50 grams of yarn in each ball, so I will need 2.64 balls of yarn. I have 4 balls left in my stash, so it looks like it will work! Yay!