Gear Ratio Calculator
Find gear ratio, output speed and torque.
Teeth on the input (driver) gear.
Results update as you type.
How it works
A gear ratio describes how a pair of meshing gears trades rotational speed for turning force, and this gear ratio calculator returns that ratio along with the output speed and output torque from the teeth counts and input values you enter. When a small driving gear turns a larger driven gear, the output shaft spins slower but delivers more torque, which is exactly how a car climbs a hill or a winch lifts a heavy load. This relationship matters because almost every machine with rotating parts relies on it: gearboxes, bicycles, clocks, drills, wind turbines, and conveyor drives all pick tooth counts to hit a target speed or force. Getting the ratio right means the motor runs in its efficient range while the output does the work required, so a gear ratio calculator saves hours of trial and error at the design stage. The formula works because meshing gears share the same tooth size, so their tooth counts fix how their rotations relate. Speed drops in proportion to the ratio while torque climbs by the same factor, since the power passing through stays nearly constant. Mechanical engineers, machinists, robotics builders, and students all use a gear ratio calculator to size drivetrains quickly and correctly.
ratio = driven teeth ÷ driving teeth
The gear ratio equals the driven gear teeth divided by the driving gear teeth, because meshing gears must share the same tooth pitch, so tooth counts set how many turns of the driver produce one turn of the driven wheel. Output speed falls by that ratio while output torque rises by it, since power stays roughly constant and speed traded away returns as turning force.
Source:Standard mechanical engineering
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter driving gear teeth, driven gear teeth, input speed and input torque.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Gear ratio updates instantly as you type — no button to press.
Frequently asked questions
How is the gear ratio calculated?
The gear ratio is the number of teeth on the driven gear divided by the number of teeth on the driving gear. If the driven gear has 30 teeth and the driver has 10, the ratio is 3 to 1. This means the driving gear turns three times for every single turn of the driven gear, a reduction that trades speed for extra torque at the output shaft.
Why does output torque increase when speed drops?
Power equals torque multiplied by rotational speed, and an ideal gear pair passes power through with little loss. When the ratio lowers the output speed, torque must rise by the same factor to keep the product roughly constant. That is why a reduction gearbox gives a small motor enough turning force to move a heavy load, at the cost of the output turning more slowly than the input.
What is the difference between a driving and driven gear?
The driving gear, also called the driver, is the one connected to the power source such as a motor or pedal. The driven gear is the one it turns, connected to the load. The ratio between their teeth counts determines whether the setup increases speed or increases torque. Swapping which gear drives which inverts the ratio, turning a reduction into an overdrive and vice versa.
What does a gear ratio greater than one mean?
A ratio above one is a reduction: the output turns slower than the input but with more torque. A ratio below one is an overdrive, giving higher output speed but less torque. A ratio of exactly one passes speed and torque straight through unchanged. Choosing the number depends on whether your application needs more force, like a winch, or more speed, like a fan.
Can I chain multiple gear stages together?
Yes. When gears are arranged in stages, the total ratio is the product of each stage's individual ratio. Two 3-to-1 stages in series give an overall 9-to-1 reduction. Compound gear trains let designers reach very large ratios in a compact space without one enormous gear. Use this calculator stage by stage, then multiply the ratios together to find the complete drivetrain reduction.