Can you draw a perfect circle?

This is not a game mechanic. It is the actual method.

Most “draw a circle” toys fit a circle through your points and measure the average error. That is not how roundness is assessed on real hardware, and it flatters you.

ASME Y14.5 defines circularity as a tolerance zone bounded by two concentric circles. Every point on the profile must lie between them. The circularity value is the radial distance between the two — and critically, it says nothing whatever about size. A bore can be 0.4 mm oversize and perfectly circular, or exactly on size and visibly oval.

The minimum zone circle

The honest way to evaluate that is to find the centre that makes the containing annulus as thin as possible — the minimum zone circle, or MZC. It is what a coordinate measuring machine reports when you ask it for roundness properly.

This page does exactly that, in two steps:

1. An algebraic least-squares fit gives a fast, stable estimate of the centre from your stroke.
2. A shrinking pattern search then moves that centre around, minimising max(r) − min(r) until it stops improving. The converged value of that difference is your circularity.

The dashed circles drawn over your stroke are the resulting maximum inscribed and minimum circumscribed circles. The shaded band between them is the tolerance zone your hand actually produced.

Why it checks the sweep

A short arc is trivially round. If you draw ninety degrees of a beautiful curve and stop, no roundness assessment is meaningful, so the tool measures the total angular sweep of your stroke about the fitted centre and will not give full credit below three hundred degrees.

Real inspection has the same problem in a less obvious form: a roundness trace taken over part of a feature can be made to say almost anything.

The score

The number out of a hundred is my own scaling, not a standard: it maps the ratio of zone width to mean radius onto a range where a genuinely good freehand attempt lands somewhere in the eighties. The engineering figures — the zone width and the percentage of diameter — are the real output. The score is there because it is more fun to lose to your father with a number attached.

What the numbers mean out in the world

The table opposite puts your result next to real manufacturing processes. It is worth looking at, because it explains why my father drawing a circle bare-handed was genuinely remarkable, and why a machinist quoting you a micron of roundness is quoting you something expensive.

A note on hands

A mouse is a poor instrument. A trackpad is worse. A finger on a phone is actually rather good, because it moves from the shoulder — which is precisely what my father meant by pinning the hand and letting the mind spin. Try it on a touchscreen and draw from the elbow, not the wrist.