Spur Gear Geometry Calculator
Full dimensional analysis for external spur gears — ISO 54 / DIN 780 standard
Module (m) — ISO standard
Pinion Teeth (z₁)
teeth
Gear Teeth (z₂)
teeth
Pressure Angle (α)
Face Width (b) — optional, for force calc
mm
Input Speed (n₁) — optional
RPM
Key Formulas
Pitch Circle Dia.d = m × z
Outside Diameterda = m × (z + 2)
Root Diameterdf = m × (z - 2.5)
Base Circle Dia.db = d × cos(α)
Center Distancea = m × (z₁ + z₂) / 2
Circular Pitchp = π × m
Whole Depthh = 2.25 × m
Gear Ratio & Speed
Gear Ratio (u)
—
z₂ / z₁
Output Speed (n₂)
—
RPM
Center Distance (a)
—
mm
Contact Ratio (ε)
—
> 1.2 recommended
Pinion (Driver — z₁)
Pitch Circle Dia. (d₁)
—
mm
Outside Dia. (da₁)
—
mm
Root Dia. (df₁)
—
mm
Base Circle (db₁)
—
mm
Gear (Driven — z₂)
Pitch Circle Dia. (d₂)
—
mm
Outside Dia. (da₂)
—
mm
Root Dia. (df₂)
—
mm
Base Circle (db₂)
—
mm
Common Tooth Dimensions
Addendum (ha)
—
mm = 1.0 × m
Dedendum (hf)
—
mm = 1.25 × m
Whole Depth (h)
—
mm = 2.25 × m
Circular Pitch (p)
—
mm
Tip Clearance (c)
—
mm = 0.25 × m
Face Width (b)
—
mm
Pitch Circle Diagram
Solid = PCD | Dashed outer = Outside Dia | Dashed inner = Root Dia
Contact Ratio should be > 1.2 for smooth operation. Values below 1.0 indicate
non-conjugate action. Recommended: 1.4–1.8 for standard industrial gears.
Increase face width or module to improve contact ratio.