Gear Module Calculator (Metric Spur Gear)
Compute the complete geometry of a metric spur gear from any two known parameters. Module, number of teeth, pitch diameter, tip diameter, root diameter and centre distance are derived with standard ISO metric gear formulas (pressure angle 20 degrees, standard addendum 1.0 x module, dedendum 1.25 x module).
How to use this calculator
- Enter module m (mm) and number of teeth z, or enter pitch diameter and teeth to solve for module.
- Optionally enter the mating gear tooth count to get centre distance and gear ratio.
- Read the full geometry table: pitch, tip, root diameter, circular pitch, base circle and tooth height.
Frequently asked questions
What is the module of a gear?
Module m is the ratio of pitch diameter to number of teeth, m = d / z, expressed in millimetres. Two gears mesh only if they share the same module. Standard ISO metric modules are 0.5, 0.8, 1, 1.25, 1.5, 2, 2.5, 3, 4, 5, 6, 8, 10, 12, 16, 20.
How do I calculate the outer (tip) diameter of a spur gear?
Tip diameter da = m * (z + 2) for a standard gear with addendum equal to one module. Root diameter df = m * (z - 2.5).
Why does my calculated centre distance differ from the actual housing?
Profile shift (addendum modification) changes working centre distance, as does backlash allowance and thermal growth. This calculator assumes zero profile shift.