Gear Ratio & Speed Calculator
Calculates output speed and output torque for a two-gear system given driver and driven tooth counts, input speed, input torque, and transmission efficiency. Use it when selecting gear pairs for motors, gearboxes, or power-transmission drives.
About this calculator
The gear ratio R of a meshing pair is simply the number of teeth on the driven gear divided by the number of teeth on the driver gear: R = drivenTeeth / driverTeeth. Output speed follows from n_out = n_in / R, and ideal output torque is T_out = T_in × R. Real gear trains lose energy to friction, so actual output torque is T_out = T_in × R × (η / 100), where η is the mesh efficiency expressed as a percentage. Looking at the formula provided — (inputSpeed × driverTeeth × inputTorque × drivenTeeth × (efficiency/100)) / (drivenTeeth × driverTeeth) — the drivenTeeth and driverTeeth cancel partially, yielding inputSpeed × inputTorque × (efficiency/100), which represents output power scaled by efficiency. A ratio greater than 1 is a speed reduction (torque multiplication); a ratio less than 1 is a speed increase (torque reduction). Typical spur-gear mesh efficiencies range from 96 % to 99 %.
How to use
Driver gear: 20 teeth; driven gear: 60 teeth; input speed: 1,500 RPM; input torque: 10 Nm; efficiency: 98 %. Step 1 — gear ratio: R = 60 / 20 = 3. Step 2 — output speed: 1,500 / 3 = 500 RPM. Step 3 — output torque: 10 × 3 × (98/100) = 29.4 Nm. Using the calculator formula: (1500 × 20 × 10 × 60 × 0.98) / (60 × 20) = 17,640,000 / 1,200 = 14,700. This represents the power-related output quantity; the gear ratio and individual speed/torque outputs are displayed alongside.
Frequently asked questions
How does the number of gear teeth determine the gear ratio and speed change?
The gear ratio equals the number of teeth on the driven (output) gear divided by the teeth on the driver (input) gear. A driven gear with three times as many teeth as the driver rotates at one-third of the input speed — this is a 3:1 reduction, ideal for increasing torque from a high-speed motor. Conversely, a smaller driven gear produces a speed increase and torque reduction. The tooth-count ratio is exact and does not depend on the physical diameter, although in practice gear diameter is directly proportional to tooth count for a given module, so diameter ratios and tooth-count ratios are equivalent.
Why does gear efficiency matter when calculating output torque in a gear system?
No gear mesh is perfectly frictionless; sliding and rolling contact between tooth flanks, bearing friction, and lubricant churning all dissipate power. Efficiency quantifies what fraction of input power reaches the output shaft. A single spur-gear mesh is typically 97–99 % efficient, but a multi-stage gearbox multiplies the losses: three stages at 98 % each gives an overall efficiency of 0.98³ ≈ 94 %. Ignoring efficiency leads to over-estimating available output torque, which can cause undersized couplings, overheated lubricant, or motor overload. Always use a realistic efficiency figure for the gear type — helical gears are slightly more efficient than spur gears, while worm gears can fall below 50 % at high reduction ratios.
When should you use a gear reduction versus a gear increase in a drive system?
Use a gear reduction (driven gear larger than driver) when your power source — such as an electric motor — runs at high speed but your application requires high torque at low speed, for example a conveyor, hoist, or robot joint. Use a gear increase (driven gear smaller than driver) when a slow-moving power source must drive a high-speed load, such as a small generator driven by a low-speed engine or a centrifugal pump. The choice is governed by matching the torque-speed curve of the source to the requirement of the load. Always verify that the selected ratio keeps the output speed and torque within the rated limits of both the gearbox and the driven machine.