The increase rule
A crochet circle is worked in a spiral or in joined rounds, from a magic ring. Every round makes the edge of the disc longer, and you add stitches so the fabric stays flat. The number to add does not change from one round to the next: 6 more stitches in single crochet, 8 in half double crochet, 12 in double crochet. Round n therefore has 6 × n stitches in single crochet, 8 × n in half double and 12 × n in double.
The reason is geometry. The edge of a circle is about six and a quarter times its radius, and each round adds the height of one stitch to that radius. The taller the stitch, the faster the edge grows, and the more increases you need. Six in single crochet and twelve in double crochet are the established values. For half double crochet you will meet eight or nine depending on the pattern; this page uses eight, the most common choice, and you can add one more if your disc turns into a bowl.
Reading the rounds
The first round places the starting stitches in the magic ring. The second doubles every stitch: an increase, meaning two stitches in the same stitch, in each one. From the third round on, you repeat a pattern: a few plain stitches, then an increase. In round 3 one plain stitch separates two increases; in round 4, two; in round 5, three, and so on. That is why the pattern is written "[2 sc, inc] x 6" and no longer "inc in each st".
The number in brackets at the end of the line is the stitch total for the round. Count it at the end of every round: it is the best way to catch a forgotten increase straight away, before it distorts the disc. The increases of one round do not go directly above those of the previous round; shift them by a stitch to get a circle rather than a hexagon.
A disc that ruffles, a disc that cups
If the edge ripples like a frill, there are too many stitches: the fabric is longer than the circle it has to fill. Check the count of each round first. If the counts are right, you are working more loosely than the piece needs: go down a hook size, or pull the yarn tighter. The gauge calculator helps you check that the fabric has the tension you expect.
If the disc cups into a saucer, it is the opposite: stitches are missing, and the edge is too short for the surface. Go back to the last correct round, count, and add the forgotten increase. A slightly cupping disc can also mean you are working very tightly; a hook one size up relaxes it.
A flat disc or a slightly domed one
The rule on this page gives a flat disc, the kind you want for a rug, a trivet or the base of a basket. For the top of a hat or the head of an amigurumi you want the opposite, a slightly domed cap: you stop increasing sooner, or skip some of the increases, then work a few rounds without increasing so the sides rise. That is a variant, not the rule: the exact number depends on the stitch, your tension and the shape you want, and the page does not make one up.
The base of a hat, a basket or an amigurumi
Anything crocheted in the round starts with a disc. The base of a basket is a flat disc, then you stop increasing to build the walls. A hat starts with a disc that you stop growing when its diameter reaches that of the top of the head, then you work straight. An amigurumi piece follows the same logic, with a cap that closes again when you decrease, the reverse of what you read here.
To know how many rounds you need, measure the diameter you want and compare it with your gauge: each round adds about the height of one stitch to the radius. The hook size chart gives the tool that goes with your yarn, and if you follow a pattern written in the other language, the page that explains how to read it will spare you false friends.
Frequently asked questions
How many stitches in round 5 of single crochet?
Thirty: round n has 6 × n stitches, so 6 × 5.
Why 12 increases in double crochet?
A double crochet is about twice as tall as a single crochet: the edge of the disc grows twice as fast every round, so it takes twice as many stitches to fill it.
Is the circle closed in a spiral or in rounds?
Both work. The page writes the rounds without the closing chain or slip stitch: your pattern or your habit says how to end them.