FO: Elizabeth Hat and some crazy math

A couple weeks ago, I decided I needed a warmer hat. Good for me, I decide this just as the weather is slowly starting to get warmer. lol I have been enjoying wearing it though, and for the colder days have really enjoyed having something warm this is more stylish than my other winter hats.

The pattern is the Elizabeth Hat by Jane Richmond (Ravlink). The pattern is available for free through Ravelry as a download, but she does have an Etsy shop. This pattern is awesome because it can be worn two ways; slouchy or as a typical folded hem hat. The yarn I used is thick so it’s warm, and the cable pattern kept things interesting. I also managed to whip this one off in just a few hours, so it’s an instant-gratification kind of knit.

I have a few notes about this pattern, and how I went about it. Mainly because I’ve come up with a way to handle gauge and sizing differences in patterns; basically I wanted an easier way to modify patterns to suit ME, instead of just pushing on forward and hoping for the best.

The first thing I want to talk about is yarn gauge, theirs and yours, and what to do if you have a different one from the pattern. I really hate that most instructions say to just go up or down a needle size until you get it right. My main problem with this is that, you should be going up or down a needle size to get the DRAPE and FABRIC you want, not necessarily the stitch and row count. A better solution is to modify the pattern itself to suit the stitches and rows per inch that you’ve obtained, once you’re happy with your gauge swatch.

Yes, I said gauge swatch. I hate them, but you must do them. I know the YarnHarlot says they lie (and they do), but we must do them anyway. Humour me. Knit up your gauge swatch, and compare yours to theirs. When I did this, this is what I found (and I ignored row gauge on this particular piece, since I knew that it wasn’t terribly important):

Their gauge: 16 stitches = 4 inches
My gauge: 14 stitches – 4 inches

The first thing we take away from this information is that we have fewer stitches per inch than the pattern. This means, we need to cast on LESS stitches than the pattern calls for. But wait! How do you know how many stitches to cast on? Here’s your answer. Take out your calculator (don’t panic!!) and divide your gauge by their gauge. Example:

16 stitches ÷ 14 stitches = 0.875

Now what do you do with this information? Well, the pattern says to cast on 64 stitches. Since we know that we have to cast on less than that to match our gauge, we multiply their cast on, by that magical number up there:

Their cast on X 0.875 = Your cast on

Example: 64 X 0.875 = 56

So now we can be all excited! We now know that we need to cast on 56 stitches, and that we’ll get the exact same size as the pattern requests! This is great! But wait, doesn’t this pattern have a cable? It does! We need to make sure that our cast on is divisible by 8. 56 is, so we’re safe. But if it wasn’t we would have to decide whether to go up or down a few to make sure that it was. The same thing if you get a decimal. I usually round up, rather than down, since you generally don’t want things to wind up too tight because of faulty math.

Okay, so now we know that Instead of casting on 64, we’re casting on 56 to accommodate the difference in our yarn gauge. So I had another thought; what if my head is a different size from her head? So I went and got out my measuring tape and measured my head. 21 inches. Pretty standard. Okay, So we know their gauge was 16 stitches over 4 inches and their cast on was 64 stitches, so the pattern is going to make a hat that’s 16 inches in diameter. That formula is:

CO ÷ (STS p INCH ÷ 4)  = Final Size.

Example: 64 ÷ (16 ÷ 4)  = 16

Hmmm so with my head being 21 inches, does that mean the hat would be too small? Let’s find out. If I subtract 15% ease from 21, I get 17.75 inches. That means I need to make my hat 1.75 inches larger in diameter than the pattern calls for. Well, that changes everything! Back to the calculator we go.

Desired size ÷ Their size x CO = Revised CO

Example: 17.75 ÷ 16 x 56 = 62.125

Round that number either up or down, and in this case, make sure it’s divisible by 8 and you’re ready to go. So, my final revised cast on is 64. Now, we don’t want to have to go and do this every single time we get to a new instruction in the pattern. That would be crazy! So instead, just divide your new cast on by the original cast on in the pattern to get a new number.

Your new cast on ÷ Original pattern cast on = new number

Example: 64 ÷ 56 = 1.143

Now all you have to do is multiply every stitch reference in the pattern by 1.143 to get your new instruction. This is really easy for a hat pattern, because often the only stitch reference is in the cast on, so you only need to do all that work once. But if you are working on something with shaping, and it tells you to Knit 10 stitches, then do something else, all you do is multiply 10 by your magic number up there, and instead of knitting 10 stitches, you would knit 11.4 stitches, or round it down to 11.

You can use this same theory for row guage too. But often instructions are given in terms of length, not in terms of rows and you probably don’t need to worry as much about it. I hope this has been helpful, because i know that this has changed the way I think about knitting and gauge.

It gets pretty complicated if your completely changing a pattern based on both gauge and size, but if you only have to change one of the two factors (size OR gauge) I’ve summed it up for you. Follow the above directions as a guide to changing a pattern completely.


Their gauge ÷ your gauge = magic number (to be applied to all references to stitches)


Their cast on X Their stitches per inch = x

Your size (plus or minus ease) ÷ x X  their cast on = y

y ÷ Their cast on = magic number (to be applied to all stitches)

Happy Knitting!

6 thoughts on “FO: Elizabeth Hat and some crazy math”

  1. Great entry! Its so handy to have people clarify exactly how they do all this stuff.

    One thing I can’t not point out, as a card-carrying mathematician … the number you’re coming up with is not an integer. Its a decimal representation of a fraction, its a real number, but its not an integer. The integers are the set of whole numbers between -infinity and infinity. i.e. (… -3,-2,-1,0,1,2,3, …)

  2. Thank you so much for the tip. It’s always nice to be validated by a mathy. I’m not one, but I feel I have to give some credit to my fiance for helping me at least get started with this. He took Math/Physics in University.

  3. On changing needle sizes to get gauge:
    Normally a designer will have chosen a gauge that gives a fabric with a good amount of drape in a pattern. If you’re using the same yarn, the same gauge will give you the same amount of drape… and, therefore, a fabric that works well.

  4. Oh I agree, but sometimes, the numbers just don’t work. And sometimes, you’re doing something like I’ve done before and knit a lace pattern in worsted weight yarn. It’s helpful to be able to convert a pattern to suit your needs when your gauge seems to be failing you.

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