Gear Ratio & Torque Calculator
Compute the output torque, gear ratio, and mechanical advantage of a gear pair given tooth counts, input torque, and efficiency. Use this when designing gearboxes, drivetrains, or any power transmission system.
About this calculator
The gear ratio of a pair of meshing gears is simply the ratio of tooth counts: GR = output teeth / input teeth. A ratio greater than 1 means the output gear is larger, producing torque multiplication (speed reduction). The output torque accounts for both the gear ratio and the mechanical efficiency of the gear mesh: T_out = T_in × (outputTeeth / inputTeeth) × (η / 100), where T_in is input torque (Nm) and η is efficiency (%). Output speed decreases in inverse proportion: n_out = n_in / GR. Efficiency losses arise from gear tooth sliding friction, bearing drag, and lubricant churning — typically 95–99% per stage for well-lubricated spur gears. Power is conserved (minus losses), so higher output torque always comes with proportionally lower output speed.
How to use
An electric motor delivers 50 Nm at 1,500 rpm through a gear pair with 20 input teeth and 60 output teeth, at 97% efficiency. Gear ratio = 60 / 20 = 3.0. Output torque = 50 × (60 / 20) × (97 / 100) = 50 × 3 × 0.97 = 145.5 Nm. Output speed = 1,500 / 3 = 500 rpm. The gearbox triples the torque from 50 Nm to 145.5 Nm while reducing speed from 1,500 to 500 rpm, with 3% of input power lost to friction.
Frequently asked questions
How do I calculate the gear ratio and what does it tell me about the drive system?
The gear ratio is the number of output teeth divided by the number of input teeth (GR = N_out / N_in). It tells you how much speed is reduced and how much torque is multiplied from input to output. A gear ratio of 4:1 means the output shaft turns four times slower than the input but carries four times the torque (before efficiency losses). Gear ratios above 1 are speed reducers used in most machinery to convert high-speed motor output into usable low-speed, high-torque drive. Ratios below 1 are overdrive arrangements that increase speed at the cost of torque.
Why does gear efficiency matter for output torque and power calculations?
No gear mesh is perfectly frictionless — some input power is always lost to sliding friction between tooth flanks, bearing friction, and lubricant viscosity. This efficiency loss means the actual output torque is always less than the theoretical (frictionless) value. For a single spur gear stage, efficiency is typically 97–99%; worm gears can be as low as 50% for high reduction ratios. When multiple gear stages are in series, efficiencies multiply together, so a three-stage gearbox at 97% per stage delivers only 0.97³ ≈ 91% of input power. Ignoring efficiency will cause you to undersize motors or overestimate available torque.
What is the relationship between gear ratio, output speed, and output torque?
Gear ratio, speed, and torque are linked by the conservation of power: P = T × ω (torque times angular velocity). If the gear ratio multiplies torque by a factor of GR, output speed must divide by the same factor to conserve power (minus efficiency losses). So output speed = input speed / GR, and output torque = input torque × GR × η. This inverse relationship means you cannot gain both speed and torque simultaneously from a passive gear system — you always trade one for the other. The efficiency factor η ensures the output power is always slightly less than the input power.