The mathematics of determining a hat circumference

Posting my first selling design, Diamond Trinity, on Ravelry has been so far rewarding. Not with sales (as I hoped) but more with views and favs. The Ravelry community seems to like my work. Yay! I was so scared that nobody would look at it or want to make it but that doesn't seem to be the case. And I couldn't be happier. Well maybe with more sales but that'll come I'm sure.

Moving onto to more design with the feeling of accomplishment I have been faced with difficulty. My latest design for a hat was unsuccessful because it came out too big. I forgot about negative ease and while blocking the hat came out wayyy too big. So I was forced to frog the entire item and make some adjustments. I didn't realize coming into designing that it requires so much math! But to be proficient you have to get things right the first time.

But I thought the way I thought this through would be a good idea to mention to my fellow readers as some might be interested in how a designer determines the hat circumference especially with a stitch repeat pattern involved. And this will help you if you want to change a hat size if the designer didn't include the size you want.

It's really all about mathematics and a little swatching. As long as you know the circumference you wish it to be, the stitch repeat (if there is any), and the gauge, you can potentially design any hat you want without guessing. The gauge you get by swatching a 4x4 square. Make sure it measures out as a whole number of stitches, that'll make it easier to work even if it's by 1", 2", or 4". The stitch repeat you'll need to make sure that the numbers match up especially if your stitch repeat and gauge are two different numbers.

For example:

• The circumference of an average adult woman is 22". Subtracting 2 for the negative ease (22-2) that'll equal 20 for the total circumference of the hat.
• The stitch repeat for this hat will be 12 st.
• The gauge is 11 sts = 2", 8 rows = 1".

Now to figure out how many stitches are needed for a 20" hat with a 11/2 gauge you multiply the circumference by the gauge. (Note: Make sure to keep the gauge a ratio (11/2) as to make sure you don't end up with an inaccurate sized hat. If the gauge was 23 sts = 4" you'd write that out as 23/4, it won't come out as a whole number but it's a more accurate measurement then if you estimated it to 1" yourself.)

So 20 * (11/2) = 110 st.

Now if you didn't have a stitch repeat (like a basic stockinette hat) that would the number of stitches needed for a hat that would fit that gauge and be snug on an average woman's head (22"). You just cast on 110 sts and start knitting.

But this hat has a 12 st repeat. Which will complicate farther because dividing 12 by 110 doesn't equal a whole number. So how do you figure this out? I do it by dividing 12 by 110 and round to the nearest whole number. It won't all perfectly fit but it gets me as close to the size I need that it won't make too much a difference. 110/12 = 9.166... That rounds to 9. Which makes 9 repeats of a 12 st repeat. Now to get the accurate number of stitches you multiply 9 by 12. 9*12 = 108. Which isn't that far off from the original number of 110. So really it won't affect your sizing that much but keeps you from having a wrong number of stitches for your hat. Cast on 108 and start knitting. I'll post more about determining a length in another post.

Advanced things to keep in mind:

If you are making a hat with ribbing don't forget that your stitches need to also equal your ribbing. Like if you wanted your hat to have a 4 st ribbing (k2, p2) and your number of stitches were 110, your ribbing would be off because 110/4 = 27.5. Now to fix this you would need to either increase or decrease the number of stitches to make the ribbing then decrease or increase the number before starting on the stitch pattern. For a 4 st repeat you could either cast on 108 or 112. With 108 you'd have to increase by 2 sts somewhere after finishing the ribbing or with 112 you'd have a decrease by 2 sts somewhere after finishing the ribbing to get back to 110. Now since the ribbing is usually smaller than the hat because of it's elasticity I'd suggest making it a little bigger than decrease the hat, it won't make that much difference with the sizing. Decrease after the ribbing can be easy if you knit the entire first row before starting on the stitch repeat pattern because you can just knit 2 together twice equally without too much problem. If not then just try to figure out where you can inconspicuously knit 2 together twice in your pattern without much notice.

And it's just like that. Now if you're a little math challenge this might not be easy for you understand and I'm sorry. I wish I knew a way that was simpler and brought the same results. But as of yet I don't :( If I do though, I won't hesitate to post about it. Now off to finish this hat!