How To Design a Hat (Part 2: The Math)

how to design a hat lt background
how to design a hat lt background

For the Math-a-phobic, stay back.  There are sime heavy calculations going on below.  There is nothing wrong with making a hat by eyeballing it or going by a pattern.  This is just the way I like to torture blog readers.

No really, this is most useful for people wanting to write their own designs in multiple sizes or those who want to use a more complicated stitch pattern that requires forward planning. For everyday hat making, its a lot of work to go to and as Joxy eloquently said in yesterday's comments, crochet is so versatile, you just need to know how to increase and decrease, then you are sorted. I would add that hats are stretchy and can forgive a number of sins. Now please forgive me for any that may appear below ;)

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So, I said yesterday that the method I described was the "easy way".  You basically pick a stitch, crochet a flat circle until it measures close to your diameter and then work even until its the right height.  Its all fine and dandy and pretty no-fool when you are working in simple stitches and in lighter weight wool.

You can run into problems when you are working in more complex designs and bigger wools.  Basically a completed round may not be anywhere near the diameter of a circle you are needing or you may have a stitch pattern that requires a certain number of stitches in a round. This is where maths can play a crucial role.

The example below is using a US Half Double Crochet (UK Half Treble) for ease. With such a straight forward stitch, you probably will be fine with using a 6 or 8 stitch increase for the flat circle to get to the desired number of stitches to reach your hat circumference. You can just use step 1 to formulate that.  However, I go into the further detail for when we look at lace and more complicated stitches in future posts, where increases need to be more precise. 

You need to know:

- your gauge

- your HAT circumference

- your HAT diameter

Age

Head Size

Hat Size

Hat Height

Flat Circle Diameter

0-6 months

13 - 15in

12 -14  inches

4.5 - 5 inches

4 inches

6-12 months

16 - 19 inches

14 – 18 inches

5.5 inches

4.5 inches

1 – 3 Years

18 - 21 inches

17 – 20 inches

6.5 inches

5.5 inches

4+ years

20 – 22 inches

19 – 21 inches

7.5 inches

6 inches

Women

22 inches

20 inches

8.5 inches

6.5 inches

Men

23 inches

21 inches

9.5 inches

6.75 inches

As an example, I am going to do the equations for a 1-3 year hat, with a 17inch hat circumference and a 5.5inch diameter. 

GAUGE

First you need to gauge swatch.  For Cascade 220 and a 5mm hook, my gauge is:

14HDC and 11.5 rows = 4inches

In order to simplify things, its easier to use your 1 inch gauge, based on your normal swatch size, in my case:

3.5 HDCs and 2.9 rows in 1 inch

Armed with this information, I need to figure out how many stitches will make up my circumference and over how many rounds I need to build up those stitches for a nice even crown.

Step 1: Stitches in Hat Circumference

First, lets figure out how many stitches are required for the HAT circumference.

To do this, you need to multiply the hat circumference by the number of stitches in your gauge.  The number you get is the # of stitches around your final circumference will be.

HAT CIRCUMFERENCE x # of STITCHES IN GAUGE = # of STITCHES in CIRCUMFERENCE

In my example: 17inches x 3.5stitches = 59.5 stitches in circumference

Step 2: Rounds in Hat Diameter

Then, you need to multiply the diameter of the required hat size by the number of rows in your gauge swatch. Then, because when measuring across a flat circle, each round equals two rows, you need to divide this figure by 2. This is the number of rounds that will make up your diameter.

(HAT DIAMETER x # of ROWS in GAUGE)/ 2 = # of ROUNDS in DIAMETER

In my example: (5.5 inches x 2.9 rows)/ 2 = 7.97 of rounds in diameter

Step 3: Calculating the Increases

So now you have 2 figures:

the number of stitches that will make up the circumference (59.5)

the number of rounds that will make up the diameter (7.97)

Now, obviously you can't have 0.5 of a stitch or 0.97 of a row.  You'll need to make a judgement on each. Generally speaking, I estimate the rounds to the nearest complete number.  In my example, its obviously 8.

Next, you need to figure out how many stitches to increase in each round, or what number stitches you'll crochet into your first loop and then increase by over the rounds. This is calculated by dividing the stitches in the circumference by the rounds in the diameter.

# of STITCHES in CIRCUMFERENCE/# of ROUNDS in DIAMETER = Stitches to increase per round

In my example: 59.5/ 8 = 7.43 stitches per round.

You'll often come out with an uneven number. This is where you need to make a judgement. You can:

- Leave the remaining stitches out (in my example: I could make 8 rounds of 7 stitches each with a total of 56 stitches, which would change the hat size from 17 inches to 16 inches)

- Add stitches in to make a next full increase round (in my example, I could round it up to 8 stitches over 8 rounds, for a 64 stitch hat circumference, but this would mean about an 18inch hat circumference)

- To get the correct sizing, round down to the nearest number (in my case 7).  Then in an additional round (in my case, round 9) increase evenly by the remaining 'hanging stitches' (in my case 3).

Then you need to work even until the hat height measures your desired size.

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There are so many variations to this process, which I can not go into in this kind of format.  However, once you get this basic principle, the possibilities are endless, including sizing up and down for writing a pattern.

For other varieties:

- Slouchy hats tend to have longer heights and a diameter that will fit snugly on the wearers head so it doesn't slip down over their eyes.

- Beret styles are larger circles so the diameter of the circle makes up much of the hat height.  Obviously the bottom few rounds need to be decreased to a good snug fit.

- Hats with pointy tops can be made by alternating each increase rows with rows that do not increase stitches at all. This will form a cone. To measure the diameter, just rely on the stitch count

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Notes: Though I write about inches, it will work just find if you measure in centimeters.

Even though this all sounds very complicated, it is actually relatively straight forward to implement once you get the hang of it (she says, with optimism).  However, if it makes no sense to you at all, try drinking a glass of wine, and if that still doesn't work, I accept full responsibility ;)

There is soooo much more I could say about hat design and pattern writing, but I am going to leave it here for now, as this gives a very basic foundation.  I am toying with the idea of putting all of this (and the other important information) in a pdf, but time is limited at the moment.  However, if you have any questions, please ask either in the comments section or on facebook and I will do my best to answer.

How to Design a Hat, Part 1 is here.

The full interactive eBook is available here.

Subscribing in a reader or liking Slugs on the Refrigerator on Facebook are great ways to be alterted to when I post part 3.