I was in a yarn store a week or two ago and overheard someone asking for a pattern for a scarf. It was all I could do not to say, you don't need a pattern for a scarf! Cast on until it's wide enough, then knit until it's long enough! Done! But I was good.
Hats are slightly more complicated if you want a nice round bit at the top, but not so much that you really need a pattern for them either. If you've done a little knitting, and know how to knit, purl, cast on, etc., a patternless hat is well within your skill level. A bit of math and a swatch, and you're golden. Here's how.
Step 1: Tools & Materials
You'll need yarn and circular needles at a reasonable size, and some double-pointed in the same size (or close, no more than a size off in either direction). A tapestry needle is nearly but not quite necessary for hiding the yarn tails when you're done.
Depending on the particulars of your yarn, you will almost certainly need just one ball. Check the yardage on the ball so you know whether you need to adjust your calculations. My yarn came in balls of 100 meters.
Step 2: Make a Gauge Swatch and Do the Math
Mark the yarn where it comes off the swatch - a binder clip works well for this, or a slip-knot. Now rip out the swatch and measure the length of yarn used. Call this Y. Mine was about 11 yards. Dividing by the number of square inches in the swatch, I find my yarn usage on these needles. For my measurements, Y / S is 11 / 17, or about .65 yards per square inch.
My head is 22" around (C for circumference) and I wanted the hat to be 8" tall (or 16" measured from ear to ear). The first 6 inches of this (H for height) are a simple tube, and the last 2 inches are curved like the top of a ball (X because I can't think of a mnemonic). The formula for the approximate number of square inches in the hat is thus
X * C H * C + --------- nwhere n is a divisor to account for the curvature. Its actual value would be something involving pi, but because knitting is so forgiving, I approximated it to 2 and my calculations came out just fine.
So plugging in my values, I get
2 * 22 6 * 22 + --------- 2(See why I chose n = 2?) That works very nicely out to 7 * 22 or 154 in2. Multiplying by my yards per square inch, I get .65 * 154 = 100.1 yards. I've got 100 meters, which is plenty.
If your calculations come out closer than this, you can always decide to make a shorter hat, reducing the value of H. As you can see in the front pic, this hat is somewhat long (I prefer that for ear coverage).
Step 3: Knit the Hat Body
At 22" around, and a gauge of 20 stitches per 4 - 1/4 inches, well that's ... 22 * 20 / 4.25 = 103.52-something stitches. My chosen pattern, 2x2 ribbing, has a repeat of 4 stitches. I round to a nearby multiple of 4, 104, and cast on that many.
From there it's a simple matter of knitting in the round, in my pattern stitch, for six inches. Of course, it is always a risk when starting in the round, that your cast-on stitches may get twisted on the needles when you bring the ends together. Most styles of casting on tend to want to curl around the needles like a candy cane stripe, but you must prevent this vigorously. If you get it twisted, you will have to pull out all your work, so be careful when starting the first row.
Once you have your H (6" for me) it is time to start decreasing.
Step 4: Decreasing
You have about 2 inches left to go, and you need to reduce the number of stitches down to a small number, ideally in the ten to fifteen range. Decrease one each X stitches every Y rows, and let X and Y get smaller as you go along. I decreased within my 2x2 rib pattern as below (you'll want to work out a decrease strategy that fits with the pattern you're knitting). Really I just worked it out as I went along. Knitting is stretchy and forgiving and it's hard to go very wrong.
First decrease row: purl 2 together every other 'ditch', or each 7th & 8th stitch. This brings the number of stitches down by an eighth.
Knit 4 rows around without decreasing, matching the new 2,2,2,1 rib pattern.
Second decrease row: purl 2 together every remaining 2-stitch 'ditch', or each 6th & 7th stitch. Now I'm down to three quarters of my original number of stitches, and a 2x1 rib pattern.
Knit 3 rows around without decreasing, in 2x1 rib.
See how it's going? Next, knit 2 together every other raised rib (5th & 6th stitch). Knit 2 around. Knit the rest of the knit pairs together to get a 1x1 rib. Somewhere around here you'll find the circular needles are too big for the number of stitches you have, and you'll want to switch over to the double-pointed.
Decrease every row from here on out, knitting 2 together every few stitches each row until you've got only a few left.
Step 5: Finishing
Cast off by simply threading the tail of the yarn through all the remaining stitches and slipping each off the needle. This can be done with the knitting needles but a tapestry needle is easier. Tighten the loop so no hole shows through the middle, then knot it. Thread the tail around the needles a few more times and then cut the yarn. The top is done!
There is one more yarn tail, at the beginning. Use the tapestry needle to weave this in a couple times around the border, then up one inside one of the ribs for an inch or two, and cut it off too.
Hat done! Look ma, no pattern!