Spirograph Art Generator β€” Free Online Spirograph Maker

How the Spirograph Works

This free online spirograph generator creates patterns called hypotrochoids β€” curves traced by a point on a small circle rolling inside a larger fixed circle β€” and their outside-ring cousins, epitrochoids. The pattern you see is entirely determined by three numbers: the ring's tooth count, the wheel's tooth count, and where on the wheel the pen sits. Layer a few combinations on the same center and you get precise, symmetric mandala designs β€” ready to color on the printable patterns page, or record spirograph animations as video to share what you made.

New here? Start with the beginner guide, browse all 72 gear combinations with live previews, dig into the math behind the curves, or look up a term in the glossary.

Teeth Count β†’ Petal Count

The number of petals (lobes) in a pattern equals the least common multiple divided by the wheel size. When the ring has 96 teeth and the wheel has 45, the LCM is 1440, giving 1440 Γ· 45 = 32 petals.

petalCount(ring, wheel) = lcm(ring, wheel) / wheel
Example: lcm(96, 45) = 1440 β†’ 1440 / 45 = 32 petals

Why Patterns Close

The pattern closes after the wheel has gone around exactly lcm(ring, wheel) / ring times. For 96/45, that's 1440 Γ· 96 = 15 rotations. After 15 laps, the wheel is exactly where it started and the pen returns to its origin.

Pen Position

A pen at the center of the wheel (0%) draws a circle. At the edge (100%) it draws the sharpest, most star-like pattern. Positions in between create the classic rounded-petal spirograph look. Experiment with 60–85% for the most satisfying results.

The Parametric Equations

x(ΞΈ) = (R βˆ’ r) Γ— cos(ΞΈ) + d Γ— cos(((R βˆ’ r) / r) Γ— ΞΈ)
y(ΞΈ) = (R βˆ’ r) Γ— sin(ΞΈ) βˆ’ d Γ— sin(((R βˆ’ r) / r) Γ— ΞΈ)

R = ring teeth  |  r = wheel teeth  |  d = pen distance (r Γ— pen%)

Frequently Asked Questions

A hypotrochoid is the mathematical name for the family of curves traced when a small circle rolls inside a larger circle. "Hypo-" means inside. The classic spirograph toy produces hypotrochoids. When the rolling circle is outside, the curve is called an epitrochoid.
When the ring and wheel teeth share common factors, the pattern closes sooner. For example, ring 96 / wheel 48 gives lcm = 96, so just 2 petals and 1 rotation β€” the wheel makes exactly one trip around before returning to the start.
Yes. The ring values (96, 105, 144, 150) and all 18 wheel values come from the Hasbro/Kahootz Deluxe Spirograph set. All petal counts match the published reference tables at SpiroGraphicArt.com.
Absolutely. The SVG export produces clean vector paths that scale to any size. Use it for high-resolution prints, laser cutting, vinyl cutting, or as a source for further design work β€” or click πŸ–¨ Coloring page for an instant black-line-on-white printable version.
Every press of Draw (or Instant) adds a new layer on top of what's already on the canvas β€” change the gears or color between draws, or turn on Auto-cycle to step through the palette automatically. Click a layer chip's swatch to toggle its visibility, click its label to edit it, or Γ— to remove it.
Yes. 🎬 Animate re-draws all layers with animation while recording, then downloads the result as a WebM video β€” great for sharing. The β–Ά Draw button also animates live in the browser, without recording.