Crochet Circle & Amigurumi Calculator
The amigurumi "six per round" is 2π rounded off. Work out the rate your own gauge wants, and why a bad one never settles down.
| Round | Stitches | Diameter | Work |
|---|
The famous 6 is 2π
Every amigurumi pattern opens the same way — six into a magic ring, then six more every round — and it is never explained, so it reads as a crochet tradition. It is not. It is a fact about circles that would be true if you were laying paving slabs.
After n rounds the disc has radius n·h, where h is the height of one round. Its edge is therefore 2π·n·h long, and at a stitch width w that edge holds 2π·h·n/w stitches. That is a straight line in n. Difference it and the stitches you add per round come out as
2π · h / w
with no n left in it. The rate does not depend on how big the disc is. Round 3 and round 30 take the same number of increases. And when your rows come out about as tall as your stitches are wide — which single crochet roughly does — that quantity is 2π, or 6.28 stitches. Rounded to something you can actually work: six.
Precisely, six is exact when h/w = 6/2π = 0.9549 — when your rounds are about 4.5% shorter than your stitches are wide. Yours are measurable, so the box above uses yours instead of the tradition.
A bad rate never settles down
The thing people wait for does not happen. If you work I stitches a round where the geometry wants N, the edge comes out I/N times the length it needs to lie flat — and because both sides carry the same round count, it cancels. The disc is exactly as wrong at round 40 as at round 4.
That is genuinely good news, and it is the practical point of this page. You can tell in the first four rounds. If it is starting to bowl or starting to lettuce, it will keep doing that in exact proportion, so frog it now rather than at round twenty hoping it blocks out. And if it lies flat at round four, it will lie flat at round forty.
Which rate suits which fabric
Read this the other way round from how it looks: pick the row your own stitch aspect is nearest to. Every figure here is 2π divided by the rate, so the table is the formula rather than a lookup someone typed.
| Increases per round | Exact at h/w | Rounds are… |
|---|---|---|
| 4 | 0.6366 | 36% shorter than stitches are wide |
| 5 | 0.7958 | 20% shorter than stitches are wide |
| 6 — the amigurumi default | 0.9549 | 5% shorter than stitches are wide |
| 7 | 1.1141 | 11% taller than stitches are wide |
| 8 | 1.2732 | 27% taller than stitches are wide |
| 9 | 1.4324 | 43% taller than stitches are wide |
| 10 | 1.5915 | 59% taller than stitches are wide |
| 12 | 1.9099 | 91% taller than stitches are wide |
Taller stitches need a faster rate, which is why a double-crochet circle uses twelve where a single-crochet one uses six: a dc round is roughly twice as tall, so its edge has to grow twice as fast to keep up. Same formula, different h.
Where this stops being true
- Amigurumi is supposed to cup. A ball is a disc that was deliberately under-increased. If you are making a sphere rather than a coaster, the flat rate is the thing you stop doing — this page tells you where flat is so you know what you are leaving.
- Stiff fabric hides a bad rate for a while. Tight amigurumi at a small hook can absorb a ruffle by standing up instead of waving. It is still wrong, and it shows the moment the piece is stuffed.
- Joined rounds versus a spiral. The geometry is identical; the seam is not. A joined round leaves a visible column of joins that pulls slightly, which is a cosmetic problem rather than a shaping one.
- Measure the gauge on the actual disc. A flat swatch worked in rows and a spiral worked in the round rarely give the same h/w, and it is the disc that decides.
How to use
- Measure your stitches and rounds per inch on a piece worked in the round.
- Read the increases per round a flat circle wants at that gauge.
- Compare it with what your pattern says and check the verdict.
- Work the round-by-round plan, or change the rate and watch it update.
Frequently asked questions
Why do amigurumi patterns always start with six?
Because six is 2π rounded to a whole stitch. A disc of radius n rounds has an edge 2π·n·h long, so it holds 2π·h·n/w stitches — which is linear in n, meaning you add 2π·h/w stitches every round no matter how big it gets. When rows come out about as tall as stitches are wide, as single crochet roughly does, that quantity is 6.28. It is a fact about circles, not about crochet.
Does the increase rate change as the circle grows?
No, and this surprises people. The rate is 2π·h/w with no round number in it at all. Round 3 and round 30 take the same number of increases. What grows is the number of stitches you work between them, not how many you add.
My circle is ruffling. Will it settle down if I keep going?
It will not, and the arithmetic says so cleanly. If you work I stitches a round where the geometry wants N, the edge comes out I/N times its flat length — and the round count appears on both sides, so it cancels. The disc is exactly as wrong at round 40 as at round 4. Frog it now.
What if my circle is cupping into a bowl instead?
Same problem, opposite direction: you are adding fewer stitches than the edge needs, so the fabric has to buckle to fit. Either increase faster or accept it, because deliberate under-increasing is exactly how a sphere is made. If you wanted a coaster, it will not flatten with blocking.
How soon can I tell if my rate is wrong?
By about round four. Since the error ratio is constant with size, whatever proportion of excess or shortfall you can see early is the same proportion you will have at the end. That is the practical value of the constant-ratio result — early diagnosis is reliable rather than a guess.
Why do double-crochet circles use twelve instead of six?
Because a dc round is roughly twice as tall as a sc round, and the rate is 2π·h/w — double the h and you double the rate. Same formula, different stitch. This is also why half-double sits awkwardly between the two and why so many hdc circle patterns disagree with each other.
Should I measure gauge flat or in the round?
In the round, on the actual piece. Most people work a different tension in a spiral than in rows, and it is the ratio of round height to stitch width that decides everything here. A flat swatch can give an aspect ratio several percent out, which moves the required rate by a noticeable fraction of a stitch.
Does the tool handle spheres and cones?
Not directly — it tells you where flat is. A sphere is a disc that was deliberately under-increased and a cone is one under-increased by a constant amount, so knowing the flat rate tells you exactly what you are departing from. That is more useful than a shape preset, because it works for any shape you invent.
Why does my stiff amigurumi look fine at the wrong rate?
A dense fabric at a small hook can absorb a small excess by standing up rather than waving, so a mild ruffle hides. It is still there, and it usually shows once the piece is stuffed and the fabric is under tension. The number does not care how the fabric is behaving today.
Does this send anything anywhere?
No. Everything is calculated in your browser and nothing is stored or uploaded.
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