For Spirograph and any other hypotrochoid and epitrochoid drawing tool.

This chart shows only the rings and wheels included in the old Spirograph and the new version of it made by Kahootz Toys. Note that the Kahootz Toys version as well as some later editions of the old version have the shaped wheels (not shown here) but do NOT have wheels 36, 50 and 64.

If you are drawing around a wheel instead of a ring, or using Wild Gears or any other set with different numbers of teeth, see a more complete table here.

You can also see the hypotrochoid (inside) patterns on this page.

Find the number of points in a pattern made by any combination of ring and wheel, given the number of teeth in the moving wheel and either of the two rings.

From the top row, choose the teeth in the ring.

• Ring 144/96 (blue columns) has 144 teeth on the outside and 96 teeth on the inside.
• Ring 150/105 (green columns) has 150 teeth on the outside and 105 teeth on the inside.

From the left column, choose the number of your wheel.

This table will work for the racks (long bars) as well. The new Spirograph has a 150-tooth rack. The old one has a 144 and a 150.

You can also view the above table in Google Docs.