Gear Geometry Calculator
Calculate spur gear pitch diameter, base diameter, addendum, dedendum, center distance, and undercut limit from module and tooth count.
Introduction
Given just module, tooth counts, and pressure angle, the Gear Geometry Calculator produces every dimension needed to make, buy, or inspect a spur gear pair: pitch, base, outside, and root diameters for each gear, addendum and dedendum, whole depth, circular and base pitch, center distance, contact ratio, and an undercut check against the minimum tooth count. These are the numbers that go on the gear drawing and into the CNC program — and the undercut and contact-ratio flags catch the two classic paper-stage mistakes: pinions too small to hob cleanly and pairs that won't mesh smoothly.
How it Works
All dimensions follow from the standard full-depth involute system: pitch diameter d = m × z, outside diameter da = d + 2m (addendum ha = m), root diameter df = d − 2.5m (dedendum hf = 1.25m), whole depth h = 2.25m, circular pitch p = π × m, base pitch pb = p × cos α, and center distance a = m(z1 + z2)/2. The undercut threshold is zmin = 2 ÷ sin²α — about 17.1 teeth at the standard 20° pressure angle — and any gear below it is flagged, since hobbing such a pinion thins the tooth root.
Usage Scenarios
- Detailing a 2:1 reduction (20T/40T, module 2) for a test rig and pulling pitch, outside, and root diameters straight into the part drawings.
- Verifying shaft spacing on an existing gearbox casting: a = m(z1 + z2)/2 must match the bored centers before ordering replacement gears.
- Catching an undercut 14-tooth pinion at the concept stage — below the zmin = 2 ÷ sin²α threshold — and fixing it with profile shift or a tooth-count change.
- Checking contact ratio on a proposed pair to confirm it exceeds the customary 1.2 minimum for smooth load transfer.
- Measuring an unknown gear: counting teeth and measuring OD, then solving for module to identify a metric replacement.
FAQ
What is module, exactly?
Module m = pitch diameter ÷ tooth count, in millimeters — the metric measure of tooth size. Two gears mesh only if module and pressure angle match; m is also the addendum height.
Why do small pinions get undercut?
Below the minimum tooth count (about 17 teeth at 20° pressure angle), a generating cutter's tip digs into the root flank, removing involute material and weakening the tooth. Profile shift or more teeth avoids it.
What does contact ratio tell me?
The average number of tooth pairs in mesh. Above 1.2 ensures the next pair engages before the previous leaves, keeping load transfer smooth; higher values run quieter.
Why is the dedendum larger than the addendum?
The 1.25m dedendum versus 1.0m addendum provides root clearance so the mating tooth tip never bottoms in the root fillet, leaving space for lubricant and manufacturing tolerance.