hat math

two fridays ago, i wrote a guest post for the kids clothes week blog about summer hats. i showed off the sideways-on-ya-head hat, and promised that i’d share the math i used to make lusa organics sunhat tutorial fit my kids noggin perfectly. so hold onto your hats (ha! do you see what i did there?) ’cause here comes some math!

before we start, i just wanted to share a pic of the inside of her hat…



ok, first, go get the lusa organics tutorial. it’s stellar. get those instructions and pattern pieces.

then, measure your kid’s head. measure it again. maybe a third time, just to be sure. now go ahead and give them that cookie or jellybean that you had to promise in order to get them to let you do that.

if you look at the pattern pieces for the lusa organics sunhat, there are only two pieces to print out (the crown and brim), and rachel gives you the measurements for the third (the band). what we’ll do first is create a new band piece from your measurements, then move onto the crown and brim. for reference, her band piece measures 21.5″ x 4″. i probably could’ve gotten away with using her measurements, but i didn’t think of that at the time.

the bee’s head is 20″ around. i made the hat fit for exactly this size head, but i would recommend adding a 1/4″ to grow into. give them a little space!

so take your measurement and add a 1/2″ to each side for seam allowances. 20″ + 1/2″ + 1/2″ = 21″

rachel at lusa organics used a height of 4″ for the band (which will give you a hat 3″ tall once it’s sewn). i used the oliver & s reversible bucket hat pattern as a reference and made the bee’s band piece 3 3/4″ tall (1/2″ seam allowances already included). i knew that this hat fit well and didn’t fall over her eyes, but i do think it could have been a little deeper. if you have an existing hat or hat pattern, you can use that as a reference like i did.

so my final pattern piece for the hat band is 21″ x 3 3/4″.

now the crown, and here’s where there’s math involved! you need to create a circle with a circumference (that’s the outside measurement of the circle, all the way around) that matches the measurement of your band pattern piece BEFORE you added seam allowances. in my example, the circumference needs to be 20″. i’m going to tell you a secret (not a secret): i literally googled “diameter of circle whose circumference is 20.” and i found this:

diameter = circumference / pi (remember pi?!)

d=c/pi, and let’s solve for d!



next i googled “6.37 into fractions of an inch” (i’m not even kidding. i feel like google made this hat.), and learned that you can take the remainder (.37) and divide by .125 to find out how many eighths of an inch that is. if that’s not good enough, dividing by .0625 will tell you how many sixteenths of an inch.

.37/.125 = 2.96, which i am gleefully rounding up to 3.

so the diameter of my circle is 6 3/8″. (you remember that the diameter is the one that goes straight across your circle, right?)

next, you need to add a 1/2″ seam allowance to the outside of the circle. this will change the diameter of your circle, increasing it by 1″. in my example, it becomes 7 3/8″.

here’s where i took out my trusty compass, and drew a circle that was 7 3/8″ across on a piece of paper. if you’re good with photoshop or illustrator, you could use one of those programs to draw your circle too. a pencil and a piece of string would work as well. you might also walk around your house, measuring all of your round things until you find a circle that is exactly the size you need, then trace it. or hey, do a google image search for circle in the size you need. i would not be surprised if google had it for you.

yay! two pieces down!

last is the brim. i just kind of winged the brim. it looked to me like the original brim went about half way around the hat, so i just kind of guessed at how much i needed to take off to make it look in proportion to the cap. i subtracted about a 1/4″ from all the sides of the brim. sorry that’s not more precise! i will take some notes while making the next hat, and see if i can make some sense of how to keep the proportions similar.

and there you go! i’m starting a hat for mister soon, and i’m going to use this same math to size it up, instead of down. he wanted the reverse colors of the bee’s hat, with solid blue on the outside and minty green on the inside. i really wanted a nautical theme, so we compromised on this…


i love the little anchors and life savers (also called ring buoys)!

if you have any questions (or suggestions!), leave me a comment. i’ve never written about math before, and i think it’s pretty clear, but if you disagree, please let me know!

2 responses to “hat math

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