Gear Formulas & Calculators
This page provides the essential formulas for gear geometry, strength, and transmission calculations used in engineering practice.
Gear Geometry Formulas
Pitch Diameter: d = m × z
Tip Diameter: da = m(z + 2)
Root Diameter: df = m(z − 2.5)
Center Distance: a = m(z₁ + z₂) / 2
Lewis Bending Stress Formula
The Lewis formula calculates bending stress at the root of a gear tooth:
σ = Ft / (b × m × Y)
Where Ft = tangential force (N), b = face width (mm), m = module, Y = Lewis form factor (depends on tooth count).
Hertz Contact Stress
Contact (Hertz) stress at the pitch point determines pitting resistance:
σH = ZH × ZE × √(Ft / (b × d₁) × (u+1)/u)
Where ZH = zone factor, ZE = elasticity factor, u = gear ratio.
Using KHK’s Gear Torque Calculator
KHK USA’s online Gear Torque & Load Calculator automates Lewis bending analysis for 9 common materials, providing PASS/CAUTION/FAIL verdicts with safety factor visualization — eliminating manual calculation errors.