Gear Teeth Number Calculator

How are tooth counts chosen?

For a gear pair the ratio is the ratio of tooth counts: i = z₂ / z₁. Tooth counts must be whole numbers, so not every ratio can be hit exactly. A ratio of 3.5 comes out exactly with 18 and 63 teeth, but for something like 3.14 you look for the nearest pair.

This tool tries every pair between the minimum and maximum tooth counts you give and returns the one whose ratio is closest to the target, followed by the next best options with their deviations.

Why the minimum tooth count matters

With few teeth the cutting tool removes material at the tooth root. This is undercut and it weakens the tooth. For a standard gear with a 20 degree pressure angle the theoretical limit is 17 teeth. Fewer teeth need profile shift.

Coprime tooth counts

If the tooth counts share no common factor, every tooth meets every tooth of the mating gear in turn and wear is spread evenly. Choosing 20 and 61 teeth instead of 20 and 60 is a common habit for that reason. The tool reports the common factor of the pair it finds.

When the centre distance is fixed

For a standard spur gear pair z₁ + z₂ = 2 × a / m. With a centre distance of 120 mm and a 3 mm module the tooth sum is 80. For a ratio of 3 that gives z₁ = 80 / 4 = 20 and z₂ = 60. If the sum is not a whole number, adjust the centre distance or module, or use profile shift.

Limits

The tool only selects tooth counts. Whether the gears carry the load depends on module, face width and material, which is a separate strength calculation.