What is the gear module?

The module (m) is the ratio of pitch circle diameter to number of teeth (m = d / N). Both gears in a meshing pair must have the same module. Common metric modules are 1, 1.25, 1.5, 2, 2.5, and 3 mm.

What is the contact ratio and why does it matter?

The contact ratio is the average number of tooth pairs simultaneously in contact. It must exceed 1 for uninterrupted theoretical contact; designers commonly seek additional margin, subject to load, accuracy, speed and noise requirements.

What pressure angle should I use?

20 degrees is the modern standard for most spur gears and provides stronger teeth with lower sliding friction. 14.5 degrees is an older standard still used in replacement parts. Both are supported by this calculator.

How is center distance calculated?

Center distance C = m × (N1 + N2) / 2, where m is the module and N1, N2 are the tooth counts. This is the distance between the two gear shaft centerlines required for proper meshing.

How do I calculate spur gear module from center distance?

For an unshifted external gear pair, module m = 2C / (N1 + N2). Enter the target center distance here and the calculator solves that theoretical module automatically.

What is the gear ratio?

Gear ratio i = N2 / N1 (driven teeth / driver teeth). If i > 1 the driven shaft is slower (speed reduction, torque increase). If i < 1 the driven shaft is faster (speed increase, torque decrease).

Does this tool handle helical or bevel gears?

No — this tool is specific to standard involute spur gears (parallel-axis, straight teeth). For helical or bevel gears, the geometry formulas differ significantly.

Spur Gear Calculator

Calculate a standard metric spur-gear pair from teeth and module, or enter a target center distance to solve module, with ratio, speed, contact ratio and tooth geometry.

Gear Pair Inputs

Shared Parameters

Module (m) mm

Pressure Angle

Target Center Distance (mm) (optional)

Overrides module using m = 2C ÷ (N1 + N2).

Driver (Pinion) — Gear 1

Teeth N1

Speed N1 (rpm) (opt.)

Driven — Gear 2

Teeth N2

Speed N2 (rpm)

Gear Pair Summary

Gear Ratio

—

Center Distance

—

Contact Ratio

—

Driven Speed

—

Gear Geometry

Parameter	Driver (Gear 1)	Driven (Gear 2)
Number of Teeth	—	—
Pitch Diameter (mm)	—	—
Addendum (mm)	—	—
Dedendum (mm)	—	—
Outside Diameter (mm)	—	—
Root Diameter (mm)	—	—
Base Circle Diameter (mm)	—	—
Circular Pitch (mm)	—	—
Whole Depth (mm)	—	—

Formula Reference

Pitch diameter d = m × N Addendum a = m Dedendum b = 1.25 × m Outside dia. d_o = d + 2m Root dia. d_r = d − 2.5m Base circle d_b = d × cos(φ) Circular pitch p = π × m Center dist. C = m(N1+N2)/2 Gear ratio i = N2 / N1 Contact ratio ε = arc-of-action / base-pitch

Summary

Calculate a standard metric spur-gear pair from teeth and module, or enter a target center distance to solve module, with ratio, speed, contact ratio and tooth geometry.

How it works

Enter the number of teeth for both the driver (pinion) and driven gear.
Set the shared gear module and pressure angle, or enter a target center distance to solve module.
The calculator derives pitch diameters as d = m × N for each gear.
Center distance is computed as C = m × (N1 + N2) / 2.
Contact ratio is determined from the arc of action divided by the base pitch.
All results update instantly — adjust any input to explore gear combinations.

Use cases

Size a gear pair for a gearbox or power transmission system.
Verify center distance and clearance in a mechanical assembly.
Determine speed and torque ratio between driver and driven shafts.
Check contact ratio to confirm smooth, quiet gear meshing.
Calculate gear blank diameters for CNC machining.
Teach gear kinematics to mechanical engineering students.
Cross-check catalog gears for compatibility before purchasing.
Prototype gear sets for robotics, automation, and hobby projects.

Frequently Asked Questions

Last updated: 2026-09-22 · Reviewed by Nham Vu