How does the perfect circle test work?
You draw one loop in the box with a mouse, a finger or a pen. When you let go, your browser finds the true circle that fits your line best and measures how far your line strays from it. Your score is the circle's roundness as a percentage: 100% would be a mathematically perfect circle. There is no center to aim at, so you can draw anywhere in the box, at any size above the minimum.
How is roundness calculated?
The score comes from your line alone, in four steps:
- Even out the line. Your line is resampled into 180 points spaced evenly along its length. Slow parts of a stroke record more points than fast ones, and without this they would count for more.
- Fit the best circle. The center and radius that fit those points best are found by least squares, the standard way of fitting a shape to measured points.
- Measure the wobble. Each point's distance from the center is compared with the radius. The differences are combined as a root-mean-square and taken as a share of the radius, so a few large wobbles cost more than many tiny ones.
- Score it. Roundness = 100% × (1 − (wobble ÷ 14%)1.5), and never less than 0%. The score barely moves for the small wobbles of a careful circle, falls quickly as the shape stops being round, and reaches 0% when the line strays by 14% of the radius.
| Wobble (share of the radius) | Roundness |
|---|---|
| 1% | 98.0% |
| 2% | 94.6% |
| 3% | 90.0% |
| 5% | 78.6% |
| 8% | 56.8% |
| 11% | 30.3% |
| 14% | 0.0% |
Why not take the wobble straight off 100%? Because then every closed shape would score high: a square strays only about 11% from the circle that fits it best, so it would get 89.0%. With the curve, other shapes score what they look like. These are real scores, worked out by the same code that scores your drawing:
| Shape, drawn perfectly | Roundness |
|---|---|
| A slightly oval circle (10% wider than tall) | 88.0% |
| An egg shape (30% wider than tall) | 46.2% |
| A perfect square | 30.7% |
| A perfect triangle | 0.0% |
Because everything is measured against your circle's own radius, the score doesn't depend on how big your screen is or how many pixels it has. Next to the score you also see the plain average distance of your line from the fitted circle, as a share of the radius, and the best score from your visit so far. The score is shown rounded down to one decimal, so only a perfect line would show 100.0.
What counts as a circle?
To be scored, a drawing has to be one loop:
- It must go at least 330° round its center. An arc that stops early is asked to go all the way round.
- It may overlap where it started, but not go much past one turn: more than 450° is two loops.
- Its radius must be at least 40 pixels. Tiny circles are mostly the jitter of the pointer itself.
How to draw a perfect circle freehand
- Use your arm, not just your fingers. Moving from the elbow or shoulder gives a smoother curve than a wrist that has to change direction all the way round. Many artists practice large circles this way.
- Keep a steady speed. Speeding up and slowing down is where most flat spots and bulges come from.
- Look ahead of the line, at where it needs to go, rather than at the tip of your finger or cursor.
- Go bigger. A small shake costs less against a large radius, so within the box, larger circles are more forgiving.
Giotto's perfect circle
Freehand circles have been a test of skill for centuries. In his Lives of the Artists, first published in 1550, Giorgio Vasari tells how a messenger from the Pope asked the painter Giotto for a drawing to show what he could do. Giotto drew a circle in red paint with a single turn of his hand and sent that. Vasari says the story gave rise to a saying, "rounder than Giotto's O", a pun in Italian, where tondo means both round and slow-witted.
What can change your score
- What you draw with. A finger, a mouse, a trackpad and a stylus all feel different, and a mouse reports its position in small steps. Compare scores drawn the same way.
- Which way you go round. Many people find one direction easier than the other. Try both.
- Your setup. A mouse on a slippery surface, or a phone held in one hand, adds wobble that isn't yours.
This is a drawing game, not a test of your hand's health or steadiness, and the score can't tell you anything medical. For another test of precision, try the Time Perception Test, which asks how exactly you can feel time passing.