Spur Gear Calculator.
Calculate every dimension of a spur gear pair: module, diametral pitch, pitch diameter, addendum, dedendum, root diameter, outside diameter, tooth thickness, and center distance.
mm — standard: 1, 1.25, 1.5, 2, 2.5, 3, 4, 5, 6, 8, 10
mm — typically 8–12 × module
Center distance
—
mm — m × (Z₁ + Z₂) / 2
Pinion (Z₁)
Pitch diameter (d₁)—
Outside diameter (da₁)—
Root diameter (df₁)—
Base diameter (db₁)—
Gear (Z₂)
Pitch diameter (d₂)—
Outside diameter (da₂)—
Root diameter (df₂)—
Base diameter (db₂)—
Common dimensions
Addendum (ha)—
Dedendum (hf)—
Whole depth (h)—
Circular pitch (p)—
Tooth thickness (s)—
Gear ratio (i)—
Gear Calculation Basics
Spur gears are the most common gear type. Sizing them correctly requires balancing tooth count, module/pitch, center distance, and torque/speed requirements.
Core Gear Formulas
Pitch diameter: D = m × Z (metric) or D = Z / DP (imperial)
Center distance: a = (D₁ + D₂) / 2
Gear ratio: i = Z₂ / Z₁ = D₂ / D₁
Where m = module (mm), Z = tooth count, DP = diametral pitch (teeth/inch).
Common Module / DP Sizes
- m = 1.0, 1.25, 1.5, 2.0, 2.5, 3.0, 4.0, 5.0, 6.0, 8.0, 10.0 (preferred metric series)
- DP = 24, 20, 16, 12, 10, 8, 6, 5, 4 (imperial — coarser as DP decreases)
Worked Example
Gear ratio 3:1, module 2, pinion 20 teeth.
- Pinion teeth Z₁ = 20
- Gear teeth Z₂ = 60
- Pinion D = 2 × 20 = 40 mm
- Gear D = 2 × 60 = 120 mm
- Center distance a = (40 + 120)/2 = 80 mm
Gear Design Rules of Thumb
- Minimum pinion teeth: 17 (for 20° pressure angle, avoid undercut)
- Maximum single-stage ratio: 7:1 (above this, use compound gears)
- Face width: 8-12 × module typical
- Material pairing: harder pinion (small gear takes more cycles)
Related Tools
For belt drive alternatives, see V-Belt Calculator. For motor sizing, Motor HP Calculator. For shaft fits, ISO 286 Fits.