Calculate worm gear output torque and speed from motor power, input rpm, reduction ratio and gear efficiency, or torque from tooth force and pitch radius.

Steady worm-gear reduction driven by the worm. Efficiency presets are typical values; use your gearbox rating if you have it.

Enter 30 for a 30:1 reduction.

Typical efficiencies; high ratios and single-start worms run lower.

Optional settings

Worm Gear Torque Formula

The following formula is used to calculate the Worm Gear Torque. 

Twg = L ร— r
  • Where Twg is the Worm Gear Torque (N-m)
  • L is the tangential tooth-load component (N), not the total contact force 
  • r is the radius of the pitch circle (m) 

Choose Torque from tooth force, Tangential tooth force or Pitch radius. Use the tangential component and pitch radius of the same gear: T = F ร— r. In Output torque from input power, nout = nin รท i, Pout = Pin ร— efficiency/100 and Tout = Pout รท (2ฯ€nout/60). The reduction ratio i = input speed/output speed is at least 1. Efficiency examples are not predictions; this is a forward steady-state estimate, not a strength, thermal, starting-torque or self-locking check.

Estimate Worm Gear Mesh Efficiency

Choose Mesh efficiency from geometry to estimate the tooth-mesh efficiency when the worm drives the wheel. Enter the worm lead angle ฮป, the normal pressure angle ฮฑn in degrees, and the dimensionless effective sliding friction coefficient ฮผ for the actual operating conditions. The editable 20ยฐ pressure angle is a typical value, not a measurement of your gears.

ฮท = tan ฮป ร— (cos ฮฑn โˆ’ ฮผ tan ฮป) รท (cos ฮฑn tan ฮป + ฮผ)

The calculator reports 100ฮท as a percentage, the complementary mesh-loss percentage, and the apparent sliding friction angle ฯ = atan(ฮผ รท cos ฮฑn). The equivalent efficiency expression is ฮท = tan ฮป รท tan(ฮป + ฯ). Use a lead angle greater than 0ยฐ and less than 90ยฐ, a normal pressure angle from 0ยฐ to less than 90ยฐ, and nonnegative ฮผ. The combination must give ฮป + ฯ < 90ยฐ for this positive forward-efficiency model.

This is a mesh estimate, not complete gearbox efficiency: bearings, seals and lubricant churning add losses. Friction varies with lubrication, surface finish, speed, load and temperature; use measured or manufacturer data rather than choosing ฮผ from materials alone. Sliding friction does not establish static self-locking, and a worm drive must not be relied on as a safety brake. The existing motor-power mode continues to use the overall efficiency you select or enter.

How to Calculate Worm Gear Torque?

The following two example problems outline how to calculate the Worm Gear Torque.

Example Problem #1:

  1. First, determine the tangential tooth load (N). In this example, it is 50 N.
  2. Next, determine the radius of the pitch circle (m). For this problem, the radius of the pitch circle (m) is calculated to be .23.
  3. Finally, calculate the Worm Gear Torque using the formula above: 

Twg = L * r

Inserting the values from above and solving the equation with the imputed values gives: 

Twg = 50 * .23 = 11.5 (N-m)

Example Problem #2: 

Using the same process as example problem 1, we first define the variables outlined by the formula. In this case, the values are:

tangential tooth load (N) = 1000

radius of the pitch circle (m) = .10

Entering these values yields:

Twg =1000 * .10 = 100 (N-m)