How to calculate different hat sizes for knitting patterns using a simple formula
If you've enjoyed this article you may also enjoy my article on How to Calculate Hat Math.
In the course of being a knitting designer I field a lot of questions on how to change the sizes of various knitting patterns, some written by me and some not. Because I'm limited on time and would rather teach a proverbial woman to fish I thought it'd be beneficial to write up my process on how I determine how to knit additional hat sizes that aren't included in the knitting pattern.
For this discussion let's look at changing an existing knitting pattern to a pattern that will work for a larger sized head. A great teaching question is:
I'm trying to convert a baby hat pattern to a size that will fit a 7yr old. The gauge is 5 st/inch. The size for 2 year olds has 88 CO. The 7 year old has a head size of 21".
1. The first thing you need to do is examine the rate of decrease at the crown of the hat. This assumes the hat is knit from the brim to the crown, where the decreases begin. For this example the hat has an 11 stitch decrease, or in other words, *k9, k2tog* for the first decrease row over all stitches.
You have two options for determining a new cast on for the larger size. I'll list both with the easier and less mathy version first.
2. In physics we use official terms like WAG, which means (Educated) Wild Assed Guess. The simplest way to WAG the new size is to add portions to the cast on in blocks of 11. So adding a new block of 11 stitches won't change the written pattern instructions except to add one or more repeats to the crown decreases.
We know that the gauge on the pattern is listed as 5 st/inch so one block of 11 stitches will add approximately 2 inches of circumference to the hat. That number was found by WAGging again, assuming 10 stitches for simpler math and figuring what number times 5 will give an answer of 10. If you want to be mathy here there is a more precise way to calculate the circumference and it's still fairly simple. There are 5 st/inch and 11 sts so the proper way to figure the actual number of inches is to divide 11/5 = 2.2 inches.
But what size is finished size of the 2 year olds hat? Well, that's pretty simple too. Divide the number of cast on stitches by the gauge and you have the circumference of the hat, 88/5=17.6 inches. Being the WAGger I am, I'd round 17.6 to 18 inches. And in the original question the knitter wants a hat to fit a 21 inch head.
So the official WAG way of estimating how many stitches to cast on goes as follows:
Each group of 11 stitches is approximately 2 inches. You can add one group of 11, making the new cast on total 99, for a finished hat size of about (18+2=) 20 inches around, or if you want a larger hat for growing heads you can add two groups of 11 for a cast on total of 110 and a finished size of (18+2+2=) 22 inches.
Please note that casting on 99 or 110 stitches will not change the written pattern instructions! You'll be able to knit the hat as before. The only change is you'll be adding extra repeats to the decrease section that begins with *k9, k2tog*.
3. The more mathy way of figuring the new size uses ratios. Don't be intimidated though. Ratios are actually quite easy once you get used to them and are a resource for calculating all sorts of amazing things. A ratio helps you compare two things. You have four slots in a ratio, and three of them are predetermined with whatever you are comparing. The empty slot is the number you're calculating. Sound like greek?
Do not fear. I will teach you. In our example we have the finished size of the 2 year old's hat, the cast on number, and the finished size for the 7 year old's hat. Let's list these numbers and then arrange them into a ratio, shall we?
2 year old cast on = 88. 7 year old cast on = ?.
2 year old size = 17.6 7 year old size = 21.
? is commonly called "x" but you can call it what ever you want. I once used a set of very similar, but untoward variable names on a huge project as an undergrad just to be subversive. It cost me about 20 hours of lab time trying to understand what the hell I had wrought.
Anyway, to find x you'll do a little rearranging. Your goal is to have all of the numbers on one side and the x on the other. Let's simplify the ratio above so you can see what I'm doing a little easier.
To get x on one side you'll need to multiply 88*21 and then divide by 17.6. The answer is 105. But wait a minute. I spent five minutes up above going on and on about the first decrease row in the crown of the hat. And I'm pretty sure that 11 (from *k9, k2tog*) doesn't go into 105.
So you have to find the closest number to 105 that is divisible by 11. And it turns out that we already know 110 will work and 99 will do that. Remembering the gauge figure above (5st/in) we know that adding 5 sts to get to 110 cast on will add about an inch to the finished size, meaning we'll have a hat that measures 22 inches. If we subtract 6 sts to get to 99 we lose an inch and end up with a finished hat of about 20 inches.
Funny how we ended up with the same answer using two different methods, isn't it? In the end I hope you realize that knitting physicists are crafty, but sometimes sneaky individuals who will teach you sums and ratios under the guise of adjusting hats for bigger heads.
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