I was reading: https://www.tec-science.com/mechanical-power-transmission/involute-gear/geometry-of-involute-gears/

Which goes over construction of involute gears, Everything else makes sense but I am still confused on what defines the tooth width.

Does someone have an intuitive/easy explanation on how you derive the tooth width for an involute gear and why it makes sense?

  • $\begingroup$ are you talking about the tooth width space? $\endgroup$
    – NMech
    Feb 24, 2021 at 19:37
  • 1
    $\begingroup$ Well, there is a difference between a ideal gear design and any real practical one. Theres a lot going on in there. One of the nifty features of involute geas is that they work even if you have a incorrect distance beween gears, and also slightly wrong values just as long as it can physically fit. $\endgroup$
    – joojaa
    Feb 24, 2021 at 21:33
  • $\begingroup$ Which you allways can as you can move slightly fufther. But due to tolerancing the gap tends to be larger. But it does not have to be. $\endgroup$
    – joojaa
    Feb 24, 2021 at 21:40
  • $\begingroup$ I was looking at the same page today. According to it, without any profile shift, then the empty spaces along the pitch circle are equal in arc/angle/distance to the tooth thicknesses. That's also what I got from equations 14-18 on their shape calculation tutorial. Intuitively, this makes some sense when you consider that two gears of equal sizes must be symmetric, so the spaces should equal the gaps in some way. $\endgroup$
    – Will Chen
    Feb 26, 2021 at 2:22

1 Answer 1


The circular tooth width (thickness) is the arc length of a tooth, generally measured at the pitch diameter.

Think of the gear profile as a simple circle with diameter equal to the pitch diameter. If your gear has 30 teeth the thickness will be the circle's circumference (pi * pitch diameter) divided by the number of teeth [30] to get the arc length of a single tooth/space sector. Then divide that by 2, since the tooth thickness is equal to the tooth space.

This reduces to pi/(2*diametral pitch) regardless of number of teeth. The corresponding tooth space is the same value. Usually the teeth are thinned a little to create backlash to prevent binding.

  • $\begingroup$ So the spacing is the same? This is for the base circle right? Is there a proof showing that the gears will mesh correctly with this? $\endgroup$ Feb 24, 2021 at 20:00
  • $\begingroup$ The spacing is the same as measured at the pitch circle, not the base circle. There are ways to calculate tooth thicknesses at varying diameters, you can do this to verify your tooth thickness is less than the corresponding space thickness of the mating gear. I'm not sure if there are empirical "proofs" but generally gears with the same pitch will mesh if operated at the correct center distance. $\endgroup$
    – jko
    Feb 24, 2021 at 20:32

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