When we create a beanie what we are essentially doing is knitting a cylinder that's finished off with a circle on top. The schematic above shows that the length of a Hat, from the crown to the base of the ears, is the length from the centre of the crown to the brim edge – or the radius of the top circle plus the length of the cylinder.

With negative ease, this method works, as the edge around the top of the cylinder is smoothed off when worn.

The common formula for a circle is to decrease 8sts every other round, or 4sts average per round. This works well in something like stocking stitch, where the row and stitch gauge have a common relationship, or in lace, whereby blocking helps all the proportions settle.

**THE ROLE OF THE CIRCUMFERENCE AND RADIUS**

We'll remember from school that the circumference of a circle is 2 x pi x the radius, where pi can be rounded to 3.14. In short, the circumference is 6.28 x the radius.

The circumference of our Hat is the number of stitches on our needles right before we start the crown shaping – it's the widest part of the knitting, and the part that determines fit in a beanie. To know this measurement we'll also want to know our gauge.

Let's use an example of a Hat knit in DK with a gauge of 22sts/10cm. With a circumference of 100sts it will measure 45.5cm – the perfect finished size for the average adult female (allowing for 6.5cm of negative ease).

If we want to knit a beanie, and have the top of that Hat flat as a circle, we'll be able to calculate the radius of our circle, which in turn helps us calculate the number of rounds over which we will decrease.

**45.5cm/6.28 (2 x pi) = 7.25cm crown circle radius**

If our row gauge follows a typical fashion of 3:4, our row gauge would be approximately 30rows/rounds to 10cm, or 3rows to 1cm, and so we would have to work our decreases over 22 rounds:

**7.25 (length of radius in cm) x 3 (number or rows/rounds per cm) = 21.75 rounds**

We have 100sts we wish to decrease, so we would aim to decrease 4.5sts per round on average. (100/21.75)

Except, that as we close the top of the Hat we don't want to decrease down beyond say 6 or 8 sts, as this creates an unfortunate bump at the very top of the Hat, so we would change our decrease ratio slightly:

**(100-6)/21.75 = 4.32 sts decreased per round, average.**

Knitting is forgiving enough to allow us to decrease on average 4sts per round, and it would usually even out with blocking.

And don't forget that that 4sts is an average figure – you could decrease 8sts every other round, or 12sts every third round and so on – it allows for quite a bit of flexibility when you need to adapt stitch patterns.

**TAKING THE NUMBERS BEYOND STOCKING STITCH**

But what if your row gauge and stitch gauge differ wildly, or your stitch pattern gauge doesn't match that of your stocking stitch?

A good example would be a fairisle Hat where the row and stitch gauge are almost square, e.g. 22sts x 24rows, and the numbers would look a little different. Assuming we're still working with an example of 100sts cast-on:

**45.5cm/6.28 (2 x pi) = 7.25cm crown circle radius**

Our row gauge gives us 2.4rows per 10cm, so we would need to decrease over 17.4 rounds:

**7.25 (length of radius in cm) x 2.4 (number or rows/rounds per cm) = 17.4 rounds**

We have 100sts we wish to decrease down to 6sts, the numbers would look like this:

**(100-6)/17.4 = 5.5sts decreased per round or 11sts decreased every other round.**

Another example might be garter stitch, where the row gauge is invariably double that of the stitch gauge, e.g. 22sts x 44rows to 10cm

**45.5cm/6.28 (2 x pi) = 7.25cm crown circle radius**

Our row gauge gives us 4.4rows per 10cm, so we would need to decrease over 31.9 rounds:

7.**25 (length of radius in cm) x 4.4 (number or rows/rounds per cm) = 31.9 rounds**

We have 100sts we wish to decrease down to 6sts, the numbers would look like this:

(1**00-6)/31.9 = 3sts decreased per round or 6sts decreased every other round.**

**BEANIES vs BERETS**

A beret essentially is the same idea as a beanie, except it's a wider circle on top of a wider cylinder.