3DPrintCalcs
Gear Calculator — Spur Gear Dimensions
Design spur gears with correct module, tooth count and pitch circle dimensions.
How We Calculate This
Spur Gear Formulas
- Pitch diameter = Module x Number of teeth
- Outer diameter = Pitch diameter + 2 x Module
- Root diameter = Pitch diameter − 2 × Dedendum, where Dedendum = Dedendum multiplier × Module (default 1.25, giving 2.5 × Module)
- Circular pitch = Pi x Module
- Tooth thickness = (Pi x Module) / 2 - Backlash
- Base circle = Pitch diameter x cos(Pressure angle)
The module determines the size of the teeth. For two gears to mesh, they must share the same module and pressure angle. The pitch circle is where the teeth of meshing gears make contact. Backlash is realised by thinning each tooth by the clearance you enter, so the gears run freely without binding — typically 0.1-0.2mm for FDM-printed gears. The recommended face width (8x module) is a strength guide for printed teeth; you can compare it against your own face width input.
Frequently Asked Questions
For FDM printing with a 0.4mm nozzle, use module 1.0 or larger. Module 1.5-2.0 gives robust teeth that print well. Smaller modules (0.5-0.8) require a fine nozzle or resin printing for adequate tooth definition.
Both gears must have the same module and pressure angle. The centre distance = (teeth1 + teeth2) x module / 2. Add 0.1-0.2mm clearance to the centre distance for smooth operation of 3D printed gears.
20 degrees is the modern ISO/JIS standard and works well for 3D printing — it resists undercut and is stronger at low tooth counts. 14.5 degrees is largely legacy: it runs a touch quieter (higher contact ratio) but the teeth are weaker and undercut sooner. Do not mix pressure angles between meshing gears.
Face width should be 5-10x the module for adequate strength. For 3D printed gears, err towards wider (8-10x module) to compensate for the lower strength of printed material compared to metal.
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Last updated: February 2026
All calculations are estimates. Always verify settings with test prints before committing to final prints.