Worm Gear Calculator

Pick the thread starts, module and wheel teeth. Get the ratio, lead angle, all dimensions, efficiency, whether the drive is self-locking, and the forces on the bearings.

Worm thread starts
T
Axial module · DIN 780
m mm
q = d₁/m
Usual range 8 – 16. Smaller q gives a steeper thread and higher efficiency, but a thinner, weaker worm.
Materials and lubrication
RPM
kW
Pressure angle 20° (normal). The worm drives the wheel.
Worm turns, wheel follows

Dimensions

DimensionWormWheel

How it is calculated

Cylindrical worm drive with a 90° shaft angle, after DIN 3975. m is the axial module of the worm (equal to the transverse module of the wheel), z₁ the thread starts, z₂ the wheel teeth, q the diameter factor, αn = 20°, μ the friction coefficient.

Ratio i = z₂ / z₁ Worm pitch Ø d₁ = q · m Wheel pitch Ø d₂ = z₂ · m Center distance a = (d₁ + d₂) / 2 Lead angle γ = atan(z₁ / q) Axial pitch px = π · m Lead pz = π · m · z₁ Tip / root da = d + 2m, df = d − 2.4m Sliding speed vs = π · d₁ · n₁ / (60 000 · cos γ) Friction angle ρ' = atan(μ / cos αn) Efficiency η = tan γ / tan(γ + ρ') worm drives Back-drive η' = tan(γ − ρ') / tan γ wheel drives; self-locking when γ ≤ ρ' Output torque T₂ = T₁ · i · η

Friction for hardened steel on bronze comes from a typical curve of μ against sliding speed for a well-lubricated drive (about 0.08 at 0.1 m/s, 0.045 at 1 m/s, 0.025 at 5 m/s). Cast iron runs about 30% higher, plastic wheels are set to 0.10. The self-locking check uses static friction (about 0.11 for steel on bronze), because a drive only locks while it stands still. Running efficiency uses the friction at the actual sliding speed. Worm length and wheel face width use common design rules; check the gear maker's data.