Gear Ratio, Torque and Speed Calculator
See what a gearbox does to motor speed and torque, with the power in and out.
Gearbox
Ratio is input turns per output turn, so 20 means 20:1 reduction. Enter a value below 1 for a speed increaser. Typical efficiency is roughly 95–98% for a spur or planetary stage and 50–90% for worm gears; check the gearbox datasheet.
Ratio from tooth counts
How it works
A reduction gearbox trades speed for torque. The output turns slower than the input by the gear ratio, and the torque rises by the same ratio, reduced by losses in the gears and bearings. Power is torque times speed, so power out is power in multiplied by the efficiency.
output torque = input torque × ratio × efficiency
ratio = driven teeth / driver teeth
power (hp) = torque (lb·ft) × RPM / 5252
power (kW) = torque (N·m) × RPM × 2π / 60 / 1000
Worked example
A 1750 RPM motor delivers 5 lb·ft into a 20:1 gearbox that is 90% efficient.
- Output speed = 1750 / 20 = 87.5 RPM.
- Output torque = 5 × 20 × 0.90 = 90 lb·ft.
- Input power = 5 × 1750 / 5252 = 1.67 hp. Output power = 90 × 87.5 / 5252 = 1.50 hp, which is 90% of the input.
Common questions
Does torque always go up through a gearbox?
Only for a reduction (ratio above 1). A speed increaser raises speed and lowers torque. In both cases the output cannot carry more power than goes in.
Is the output torque the rated torque of the gearbox?
No. This is the torque you would get from the stated input. The gearbox itself has a rated output torque and a service factor; make sure the result stays within them.
Calculations are provided for convenience and education. Verify results against manufacturer ratings before relying on them for design or sizing.