A Little Math

What could be better than a little mathematics to celebrate the back-to-school season?  I had a surprising amount of fun with this, and thought that I would share it.

Although I had a pretty good idea that I would be yarn shopping for my cardigan in New York, I stupidly left the pattern information at home in Boston.  I meant to photocopy it, or at least write down the yarn amounts before I left, but I forgot.

In the end it was for the best.  There was slightly more thinking involved with this yarn order than I would have been able to do while sitting at The Point, and I didn't have to lug around a pattern book all day.  I easily made plans with Helane to email her an order once I worked out the yarn amounts. 

Ready to do that?  Here we go.

Given (remember geometry class?):
DK gauge: 5.5sts/in
Fingering gauge: 6.75sts/in
Jaeger yardage: 2170 yards
Jaeger yarn weights:  main 500g (10 skeins, 50g each); accent 250g (5 skeins, 50g each), total: 750g
Downtown Yarns shrug yardage: main 200 yards; accent 150 yards
My yarn information:
Artyarns (main):  6.75 sts/in, 191 yards/50g
Claudia's Handpainted (accent): 6.5 to 7.5sts/in, 190 yards/50g

First question: I'll need more of the Artyarns than I will Claudia's Handpainted.  How will I accurately divide the yardage between the two yarns?

Using the yardages given in the Downtown Yarns shrug (because it contains the striping sequence that I want), I calculated what percent of the shrug's total yardage comprised the accent yarn.


DTY shrug total yardage: 350 yards
150 is 42 percent of the total yardage, leaving 58 percent for the main yarn.

This means that 58 percent of my total yardage must be from the Artyarns, and 42 percent from the Claudia's Handpainted.

Because I will be substituting a fingering-weight yarn for a DK-weight, I knew that I will need more yarn than the Jaeger pattern specifies.  But how much more?  I asked a few knitters I know, and consulted a few internet resources.  One knitter told me to work out a proportion between the gauges (new gauge/old gauge) and multiply the total yardage in the pattern by the result.

6.75/5.5 = 1.23
1.23(2170) = 2669.1 yards (or 2670 yards, rounding up)

The internet told me to keep the weight of the new yarn the same when substituting.

Total weight of the yarn used in the Jaeger pattern: 750g.

Using the percentages from above, I know that 58 percent of this weight must come from the Artyarns, with 42 percent from the Claudia's Handpainted.


.58(750)=435g of the Artyarns, leaving 315g for the Claudia's Handpainted.  Dividing each of those amounts by the weight of 1 skein of each yarn (50g), I will know how many skeins I will need.

435/50 = 8.7 skeins (9, rounding up), or 1667.1 yards

315/50 = 6.3 skeins of Claudia's Handpainted (7, rounding up) or 1197 yards

This equals a total yardage amount of 2864.1 yards.  That's a little more than the proportional calculation above, but I would rather err on the side of caution.

Any knitter knows that sometimes the yardage estimates in patterns can be little more than a big joke.  Let us also not forget that I'm changing the V-neck to a crew.  I suppose that I could figure out the area of extra fabric, compare it with the total garment area, cross multiply to figure out the additional yardage, and apply the above percentages to get the additional yardage for each yarn.

I would do that, except that Jaeger's schematics are just about worthless.  Let's just wing it!  I'll add five more skeins to the Artyarns, and four more to the Claudia's quantity.

I'll surely have yarn left over, but I would rather have lots of leftovers than be looking hopelessly for one skein of a particular dyelot.


Is this a shrug for a full-grown polar bear? You're going to have to post a picture of this baby, because I'm having a hard time envisioning a shrug that requires nearly 3000 yards of yarn! With the Artyarns and the Claudia's, though, I'm sure it's going to be beautiful!

I'm interested in seeing the finished shrug!

I really love your blog. I always learn something from you. Thanks for thinking aloud!

I saw MATH and FUN and the headache started, LOL. Good luck with that. Can't wait to see it finished. And, correct me if I'm wrong, you're actually making a cardigan, but using the shrug stripe sequence, right? Just clarifying.

The thing that scares me is I could totally follow you and the math. That Claudia's handpainted is gorgeous (I fondled it at The Point on Saturday) as is the Art Yarns. This should be really, really lovely....

I hate maths, but it made sense. If only my maths teacher could have used yarn as an example rather than x and y co-ordinates, things might have been alot clearer!

omg, this post gave me the biggest headache lol Thankfully I took geometry and calculus phew! Is this the cardigan from the last post or totally a different one (I havent seen the DTY one)?

Reading about math that I'm not doing tends to make my eyes glaze over...but I'm glad you are thinking aloud here with the calculations. And, I think you are very wise to order more than you think you'll need.

I can't even pretend to follow that at 1 in the morning. However, the plan to buy extra skeins is always a good one!

Outch. I know here to go should I ever change everything in a pattern.


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