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Gear Tooth Count, Pitch Diameter & Module

Relate positive whole tooth count, pitch-circle diameter, tooth density and gear module.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

A 20-tooth gear with a 40 mm pitch diameter has module 2 mm and a tooth density of 0.5 per mm, equivalent to diametral pitch 12.7 per inch.

Tooth density = tooth count / pitch diameter; module = pitch diameter / tooth count

Worked example

Enter these known values and leave the other values blank.

Whole tooth count
20
Pitch-circle diameter
40 mm
Tooth density / diametral pitch
0.5 / mm
Module in selected length units
2 mm

Assumptions and limitations

  • Tooth count is a positive whole number; diameter, density and module are positive. Use pitch-circle diameter, not outside tooth-tip diameter.
  • Conventional metric module is expressed in millimeters, and conventional diametral pitch is teeth per inch. Select the corresponding units before comparing catalog values.
  • The reciprocal relationship assumes the same reference section. Helical gears require care with normal versus transverse module; this model does not include helix or pressure angles.

Common questions

How do I convert module in millimeters to diametral pitch per inch?

Divide 25.4 by the metric module. For module 2 mm, conventional diametral pitch is 12.7 per inch.

Can I use the outside diameter measured over the tooth tips?

No. This relationship uses pitch-circle diameter. Outside diameter depends on additional tooth geometry and profile details.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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