What is the gear module?

The module (m) is the ratio of pitch diameter to the number of teeth (m = d / N). It defines the size of the teeth and must be the same for two gears to mesh correctly. Common modules include 1, 1.25, 1.5, 2, 2.5, and 3 mm.

What is the standard pressure angle?

The most common pressure angles for spur gears are 20 degrees (modern standard) and 14.5 degrees (older standard). The pressure angle affects tooth strength and contact ratio. 20 degrees provides stronger teeth.

What is addendum and dedendum?

Addendum is the radial distance from the pitch circle to the tooth tip (= 1 × module). Dedendum is the radial distance from the pitch circle to the tooth root (= 1.25 × module for standard gears), providing clearance for meshing gears.

How is whole depth calculated?

Whole depth = addendum + dedendum = 2.25 × module for standard full-depth teeth. It represents the total height of a tooth from tip to root.

What is circular pitch?

Circular pitch is the distance from a point on one tooth to the corresponding point on the adjacent tooth, measured along the pitch circle. It equals pi times the module (p = π × m).

What is the minimum number of teeth to avoid undercutting?

For a 20-degree pressure angle, the minimum number of teeth to avoid undercutting is 17. Below this, the dedendum circle dips below the base circle, weakening the tooth root. For 14.5 degrees, the minimum is 32.

Gear Tooth Calculator

Name: Gear Tooth Calculator
Availability: InStock
Author: Nham Vu

Enter the number of teeth and gear module to instantly calculate all key spur gear dimensions.

Gear Inputs

Enter teeth count, module, and pressure angle to calculate all spur gear parameters.

Number of Teeth (N)

Integer value, typically 3–500

Module (m) — mm

Pitch diameter divided by number of teeth

Pressure Angle (°)

Calculated Parameters

All dimensions in millimeters unless noted.

Enter values and click Calculate to see results.

Spur Gear Formula Reference

Pitch Diameter

d = N × m

Addendum

a = 1.000 × m

Dedendum

b = 1.250 × m

Whole Depth

h = 2.250 × m

Outside Diameter

dₐ = (N + 2) × m

Root Diameter

dₑ = (N − 2.5) × m

Circular Pitch

p = π × m

Base Circle Diameter

dᵇ = d × cos(φ)

Tooth Thickness

t = π × m / 2

φ = pressure angle. Formulas follow ISO 21771 / AGMA 913 standards for full-depth spur gear teeth.

Summary

Enter the number of teeth and gear module to instantly calculate all key spur gear dimensions.

How it works

Enter the number of teeth on the gear.
Enter the gear module (m) in millimeters.
Optionally enter a pressure angle (default is 20 degrees).
Click Calculate to see all spur gear parameters instantly.
Use the Reset button to clear inputs and start over.

Use cases

Verify gear dimensions during mechanical design review.
Quickly prototype gear sets for robotics or machinery projects.
Teach gear geometry to engineering students.
Cross-check CNC machining drawings for spur gears.
Determine outside and root diameters for gear blanks.
Calculate circular pitch for gear mesh compatibility.

Frequently Asked Questions

Related tools

Gear Ratio Calculator Belt Length Calculator Bearing Load Calculator Torque Calculator

Last updated: 2026-05-23 · Reviewed by Nham Vu