How a Spirograph works, lap by lap

Open any classic Spirograph set and you will find the same cast: rings with teeth inside and out, wheels with teeth around the edge and a scatter of numbered holes, a straight rack, and a small lump of putty. Nothing in the box is powered, and nothing needs to be. The teeth do all the work.

The three parts of every design

The ring

The ring stays still. Our reusable putty holds it to the paper, three or four small pinches pressed under the rim. It lifts away afterwards and leaves no holes.

The wheel

The wheel rolls. Its teeth mesh with the ring's, so it cannot skid; it can only turn as it travels. Each wheel has its tooth count moulded into it.

The hole

The pen rides in a hole. Hole 1 sits nearest the wheel's edge and draws the widest loops. Higher-numbered holes sit closer to the centre and draw tighter, rounder ones.

Why the pattern closes

Take the 96-tooth inside of a ring and a 40-tooth wheel. Both numbers divide by 8. After the wheel has gone round the ring five times, every tooth is back where it started, and the pen with it. Along the way it has drawn 96 divided by 8, which is 12, points. Swap in the 45-tooth wheel, which shares only a factor of 3 with the ring, and you will be pushing for fifteen laps to finish a 32-point design.

That is the whole secret, and it is why Spirograph is filed under both art and mathematics. Children find the rule by drawing; the formal names, hypotrochoid for inside the ring and epitrochoid for outside, can wait.

Six habits for clean loops

1. Work on a flat, firm surface with a spare sheet under your paper in case the pen bleeds through.
2. Press the putty down properly. A ring that creeps will blur the design.
3. Hold the pen upright and let it push the wheel. Aim the pressure outward, into the ring's teeth, as well as forward.
4. Go slowly through the first lap. Speed comes on its own once the hand learns the motion.
5. If the teeth jump, stop, re-seat the wheel at the same tooth and carry on. One skipped loop rarely shows.
6. For layered colour, keep the ring where it is, move the pen to the next hole and change pens.

Beyond the ring

Run a wheel around the outside of a ring and the loops flip outward into petals. Run it along the straight rack and the pattern stretches into a border. Super Spirograph goes further with Spiro-Tracks that snap into outlines of your own. And if loose wheels sound like too much to manage, Cyclex locks the wheel inside the tool and advances it for you.

Keep reading

• Which Spirograph for which age
• Spirograph since 1965: a short history in loops

Design guide 01 · updated October 2026