For Spirograph, Wild Gears or any other hypotrochoid or epitrochoid drawing set. Find the number of points (or “petals”) in any design, given the number of teeth in each of the two parts.

Vertical axis = Number of teeth in rotating part. Horizontal axis = Number of teeth in stationary part.

Colored lines show common rings and wheels in Spirograph sets. I’ve made a more compact version of this table for Spirograph only. The larger numbers in this set, 312, 336 and 360, correspond to some of the Super Spirograph layouts. See this post on Super Spirograph by the Numbers for an explanation.

You can also view the spreadsheet in Google Docs where the header row and column may or may not stay still for you, making the chart easier to use.

With thanks to the following (visit the links for more details)


Expanded table of points for drawing hypotrochoids and epitrochoids — 11 Comments

  1. Is there a downloadable version of this chart where it’s possible to see the entire chart without scrolling?
    If not, it would be a very useful device to consider.
    I had the full page Wild Gears for Christmas and this doesn’t come with any points chart like Spirograph does (the pics of each gear used in hole 1). It would be great if the above points graph were downloadable.

    • Did you click the link to view the spreadsheet in Google Docs? It’s a big chart, so you’d need a pretty big monitor to see it all.

      You can also make your own chart, depending on the gears you have in your set, using Excel or Google Docs. Put the gear numbers you have along the top and the left side, then use the formula below. Use it in the first box (cell B2) then copy to the rest of the cells. These are basic spreadsheet skills, so if you don’t know how to do it, get someone to show you.


      • Thank you. I’ve recently started using the Full Page V2 Wild Gears and it’s maddening not knowing how many points are going to happen. I’m not very good at maths.

      • On your chart, you do not have the same numbers at top as on left side (B2 has 50 & A2 has 15). According to your instructions “Put the gear numbers you have along the top and the left side..”, so I would think that you would list 15 both at top and bottom. We are trying to make our own chart, so could you please clarify? Is the top the inner circles (large fixed) and the left the smaller circles? Thanks in advance.

        • Yes, the fixed gear is along the top and the moving gear is down the side. The formula in cell B2 is =LCM(B$1,$A2)/$A2. I could delete the impossible combinations where the moving gear is larger than the ring. However, those numbers are useful for epitrochoids in cases where a large gear moves around the outside of a smaller fixed gear.

  2. Thank you for this table. It’s been a great help for sorting out the most usefull epitrochoids using the wheels. It is now easy to combine different outside wheels for a nice result with equal petals. Too bad the chart starts only at wheel 50, but there is very very much to try and figuring out!

  3. I have an old 1990s hasbro spirograph with a circular ring that has only 48 teeth plus 7 wheels: 17,18,22,27,29,30,33. Too bad the list only starts at #50 ring.

    • Interesting! If the teeth are the same size as the regular spirograph, it must be small! Can you send me a picture?

      Actually, given the wide range of rings in Wild Gears, expanding the table would be a good idea.

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