Gear Ratio Calculator
Work out the gear ratio between two meshed gears from their tooth counts, and see the resulting output speed and torque if you know the input.
Gear ratio result
The physics behind gear ratios
Two meshed gears are really a pair of wheels-and-axles working together: their teeth interlock so the linear speed at the point where they touch must match. Since that point traces a bigger circle on the larger gear, the larger gear must turn proportionally slower — exactly in the ratio of its tooth count to the smaller gear’s.
The same ratio runs the torque relationship in reverse: whatever speed advantage the smaller gear has, the larger gear gets back as extra turning force. This is why a bicycle’s lowest gear (a big rear sprocket paired with a small chainring) makes climbing easier at the cost of pedaling speed, and why a car’s first gear multiplies engine torque to get a heavy vehicle moving from a stop.
Frequently Asked Questions
How is gear ratio calculated?
Gear ratio is the driven gear's tooth count divided by the driver gear's tooth count. A 40-tooth gear driven by a 10-tooth gear gives a 4:1 ratio — the driven gear has 4 times as many teeth, so it turns 4 times slower but with 4 times the torque (ignoring friction).
Why does a higher gear ratio mean lower speed but more torque?
Meshed gears turn at a rate set by their tooth counts passing each other at the same speed, so a bigger driven gear must turn slower to keep pace tooth-for-tooth with the smaller driver. Because power (roughly torque × speed) is conserved in an ideal gear pair, whatever speed you give up you get back as torque — that's why a low gear helps a vehicle climb a hill at the cost of top speed.
What is a speed increaser, and when would I want one?
A gear ratio below 1 (a smaller driven gear on a larger driver) increases output speed at the cost of torque — an overdrive gear in a car transmission or the small rear sprocket on a bicycle for a top-speed gear. This calculator flags any ratio under 1 as a speed increaser rather than a speed reducer.
Does this calculator include friction losses in a real gearbox?
No — this is the ideal, frictionless torque and speed relationship. A real gear train loses a few percent of power to friction and meshing losses at each stage, so actual output torque will be slightly lower than the ideal figure shown here, especially through a gear train with several stages.
Educational estimate only, based on ideal (frictionless) gear mechanics. Real gearboxes lose some power to friction at each meshing stage.