Worm Gear Ratio & Output Torque Calculator
Work out the gear ratio, output torque, output speed, efficiency and whether a worm gearset is self-locking — all in one tool. Built for valve worm gearbox selection: a self-locking worm holds the valve in position with no power, which is exactly why quarter-turn and multi-turn valve actuators use them.
Worm gear formulas
λ is the worm lead angle, μ the coefficient of friction (lubricated ≈ 0.03–0.05). Efficiency is applied once; do not also divide input torque by η.
Typical worm-gear efficiency by ratio
| Ratio (approx) | Worm | Typical efficiency | Self-locking? |
|---|---|---|---|
| 5:1 | multi-start, high lead | 90–95% | No |
| 10–20:1 | multi-start | 80–90% | No |
| 20–40:1 | 1–2 start | 65–80% | Usually |
| 40–75:1 | single start, low lead | 50–65% | Yes |
| >75:1 | single start | 30–50% | Yes |
Valve worm actuators are conservatively rated ~40–60% efficient. Higher ratio = more output torque and more turns to operate.
Frequently Asked Questions
How do you calculate worm gear ratio?
Divide the number of teeth on the worm wheel by the number of starts (threads) on the worm: ratio = wheel teeth / worm starts. A 40-tooth wheel with a 2-start worm gives a 20:1 reduction.
How do you calculate worm gear output torque?
Multiply the input torque by the ratio and the efficiency: T_out = T_in × i × η. Efficiency is applied only once. For example, 10 N·m input at 20:1 and 70% efficiency gives 140 N·m output.
Are worm gears self-locking?
A worm gear is self-locking when its lead angle is smaller than the friction angle (arctan of the friction coefficient), roughly when the lead angle is below ~5°. Single-start, high-ratio worms self-lock and hold position with no power; multi-start, low-ratio worms generally do not.
What efficiency do worm gears have?
Efficiency falls as ratio rises: about 90–95% at 5:1 down to 30–50% above 75:1. Valve worm gearboxes are usually rated around 40–60%. Enter the lead angle to compute it precisely.
How do I size a worm gearbox for a valve?
Take the valve’s total operating torque (seating + packing + dynamic), apply a safety factor of at least 20%, then divide by the gearbox efficiency to get the required output torque. Choose the lowest standard ratio whose rated output torque meets it.
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