Gear Transmission Calculator — Speed, Torque & Power
Enter the driver and driven tooth (or diameter) counts, input speed and torque, and efficiency to find the gear ratio, output speed, output torque and power lost to friction.
RPM
N·m
%
Ratio > 1 = speed reduction & torque multiplication; < 1 = overdrive
- 1
Gear ratio
N₂ ÷ N₁ = 60 ÷ 20 = 3Ratio > 1 means the output spins slower but with proportionally more torque. - 2
Output torque
T₁ × i × η = 50 × 3 × 0.97 = 145.50
How does this calculator work?
Gear ratio i = N₂/N₁. Output speed = input speed / i. Output torque = input torque × i × efficiency. Power in = T₁ × 2π × n₁/60; power out = power in × efficiency. Spur gears typically reach 97–99% efficiency; worm gears can be as low as 50%.
Formula
How this is calculated
A mechanical transmission changes speed and torque between a power source (motor, engine) and a load. The gear ratio i = N₂/N₁ is the ratio of driven teeth to driver teeth (or driven diameter to driver diameter for belt and chain drives). When i > 1 the output spins slower but with higher torque; when i < 1 the output spins faster at lower torque. Power is conserved except for friction losses captured by the efficiency η.
Output speed is n₂ = n₁/i and output torque is T₂ = T₁ × i × η, where η accounts for gear mesh friction, bearing drag and lubricant churning. Input and output power are P = T × ω = T × 2π × n/60, where n is in RPM. Typical efficiencies are 97–99% for spur and helical gears, 95–98% for chain drives, 90–95% for bevel gears, and 50–90% for worm gears depending on lead angle.
This calculator applies equally to gear pairs, chain-and-sprocket systems, and belt-and-pulley systems — substitute pitch diameters or sprocket tooth counts for N₁ and N₂ as appropriate. It assumes constant efficiency across the operating range and does not account for dynamic loading, inertia effects, or service-factor derating.
Frequently asked questions
The gear ratio is the number of output shaft rotations per input shaft rotation (or the inverse, depending on convention). A ratio of 3:1 means the output shaft turns once for every three input revolutions — it spins at one-third the speed but delivers three times the torque (less friction losses).
Use the pulley pitch diameters instead of tooth counts. Gear ratio = driven-pulley diameter / driver-pulley diameter. For a V-belt or flat belt, use the effective pitch diameter; for a synchronous (toothed) belt, use the sprocket tooth count.
The kinematic gear ratio (speed ratio) is set purely by geometry — tooth counts — and is independent of friction. Torque, however, is reduced by the efficiency factor because friction consumes part of the input torque. Power loss appears as heat in the gearbox.
Also known as
TG we-Calculate Editorial Team. (2026). Gear Transmission Calculator — Speed, Torque & Power [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/transmission-calculator
TG we-Calculate Editorial Team. "Gear Transmission Calculator — Speed, Torque & Power." TG we-Calculate. 2026. https://we-calculate.com/calculator/transmission-calculator.
TG we-Calculate Editorial Team, "Gear Transmission Calculator — Speed, Torque & Power," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/transmission-calculator
@misc{wecalculate_transmission_calculator, title = {Gear Transmission Calculator — Speed, Torque & Power}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/transmission-calculator}}, year = {2026}, note = {TG we-Calculate} }
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