Gear Ratio & Speed Calculator
Determine the gear ratio, output shaft speed, and torque multiplication of any meshing gear pair. Use it when designing drivetrains, gearboxes, or motor-to-wheel power transmissions.
About this calculator
A gear system transmits rotational motion by meshing teeth between a driver and driven gear. The gear ratio (GR) is defined as GR = outputTeeth / inputTeeth. Output speed is calculated as: outputSpeed = inputSpeed × inputTeeth / outputTeeth. When a gear ratio is greater than 1, speed is reduced and torque is multiplied; when less than 1, speed increases and torque decreases. Output torque is given by: outputTorque = inputTorque × GR × efficiency, where efficiency accounts for friction losses in the mesh (typically 0.95–0.99 for spur gears). These relationships come directly from the conservation of power: power in equals power out minus losses.
How to use
Suppose a motor spins at 1,200 rpm with 10 N·m of torque. The drive gear has 20 teeth and the driven gear has 60 teeth. Step 1 — Gear ratio: GR = 60 / 20 = 3.0. Step 2 — Output speed: outputSpeed = 1,200 × 20 / 60 = 400 rpm. Step 3 — Output torque (assuming 97% efficiency): outputTorque = 10 × 3.0 × 0.97 = 29.1 N·m. The driven shaft therefore rotates three times slower but delivers nearly three times the torque.
Frequently asked questions
What is a gear ratio and how does it affect speed and torque?
A gear ratio is the ratio of the number of teeth on the output gear to the number of teeth on the input gear. A ratio greater than 1 means the output shaft spins slower than the input shaft, but the torque is multiplied by the same factor. Conversely, a ratio less than 1 increases output speed while reducing torque. This trade-off is governed by conservation of power: ignoring losses, power in always equals power out.
How do I calculate output RPM from a gear ratio?
Output RPM is calculated by multiplying the input RPM by the number of input gear teeth and dividing by the number of output gear teeth: outputSpeed = inputSpeed × inputTeeth / outputTeeth. For example, an input of 3,000 rpm through a 15-tooth driver into a 45-tooth driven gear yields 3,000 × 15 / 45 = 1,000 rpm. This formula applies equally to compound gear trains by multiplying ratios in series.
Why does gear efficiency matter when calculating output torque?
No gear mesh is perfectly frictionless; sliding contact between teeth converts a small fraction of input power to heat. Gear efficiency (typically 95–99% for spur gears, lower for worm gears) quantifies that loss. When you multiply the theoretical torque by efficiency you get the actual torque available at the output shaft. Ignoring efficiency can lead to undersized components that overheat or fail prematurely under load.