Gear Ratio & Speed Calculator
Calculates the output speed of a two-gear meshing pair given the driver and driven tooth counts and the input speed. Use it when selecting gear pairs for motors, gearboxes, or power-transmission drives. (For output torque, multiply input torque by the gear ratio R = drivenTeeth / driverTeeth and by mesh efficiency — see the explanation below.)
Last updated: May 2026
About this calculator
The gear ratio R of a meshing pair is the number of teeth on the driven gear divided by the number of teeth on the driver gear: R = drivenTeeth / driverTeeth. Output speed follows directly: n_out = n_in / R = n_in × (driverTeeth / drivenTeeth), which is exactly what this calculator returns. A ratio R > 1 is a speed reduction (and ideal torque multiplication); R < 1 is a speed increase (and ideal torque reduction). Energy conservation gives ideal output torque T_out = T_in × R; a real gear pair loses some energy to friction, so the actual output torque is T_out = T_in × R × η, where η is the mesh efficiency (typically 0.96–0.99 for well-lubricated spur gears, lower for worm or bevel gears at sharp axis angles). This calculator returns only the output speed (the most common engineering question for a meshing pair); compute output torque separately as T_in × R × η using the gear ratio R from the formula and your assumed efficiency.
How to use
Driver gear: 20 teeth; driven gear: 60 teeth; input speed: 1,500 RPM. Step 1 — gear ratio: R = drivenTeeth / driverTeeth = 60 / 20 = 3 (a 3:1 reduction). Step 2 — output speed: n_out = n_in × (driverTeeth / drivenTeeth) = 1,500 × (20/60) = 500 RPM. ✓ The calculator returns 500.00 RPM. To compute the corresponding output torque outside this calc: if input torque is 10 Nm and mesh efficiency is 98 %, ideal T_out = 10 × 3 = 30 Nm; real T_out = 30 × 0.98 = 29.4 Nm. Now reverse the gears (driver = 60, driven = 20, n_in = 1500): R = 20/60 = 0.333 (a 1:3 step-up), n_out = 1500 × 3 = 4500 RPM, and torque drops to a third of input.
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.