Work out the gear ratio of a pair of gears and see the output speed and torque. Enter the number of teeth on each gear, the input speed and torque, and an efficiency. Free, private, and runs entirely in your browser.
The gear ratio is the number of teeth on the driven gear divided by the number of teeth on the driver. Output speed is the input speed divided by the ratio, and output torque is the input torque times the ratio times the efficiency.
What does a 3:1 ratio mean? The driver turns three times for every turn of the driven gear, so the output turns slower with about three times the torque.
Does efficiency matter? Yes. Real gear sets lose a little energy to friction, so the torque is a bit lower than the ideal value.
A 20-tooth driver turns a 60-tooth gear. The ratio is 60 ÷ 20 = 3:1. With 1,800 RPM at 10 N·m in, the output is 1,800 ÷ 3 = 600 RPM and, at 100% efficiency, 10 × 3 = 30 N·m.
How do I find the gear ratio of a train? Multiply the ratio of each pair. Idler gears change direction but not the ratio.
What does a ratio below 1 do? It is an overdrive: the output spins faster than the input, with less torque.
Gears are ancient. The Antikythera mechanism, built in the 2nd century BC, used a train of gears to model the movements of the Sun, Moon and planets. The mathematics of gear ratios is simply the proportion of teeth, which makes it a long-standing tool in clocks, vehicles and machinery.
Use this calculator for bicycles, robotics, motors and machinery, or to choose a gearbox for a target speed. For a motor at 3,000 RPM driving a 5:1 reducer, the output is 600 RPM. Combine it with the torque to horsepower calculator to check power.
What is the mechanical advantage of a gear pair? Equal to the gear ratio when friction is ignored, since torque is multiplied by the ratio.
Does the tooth count change the direction? Two meshing external gears rotate in opposite directions regardless of the ratio.