Math
Gear Ratio Calculator
Compute gear ratio, output RPM, torque multiplication, and vehicle road speed. Two-gear, multi-stage, and full drivetrain modes.
Gear Ratio Calculator
Driving gear meshes with driven gear. Ratio = driven / driving.
Teeth on the input (driver) gear. Must be greater than zero.
Teeth on the output (driven) gear.
Rotational speed of the driving gear.
Leave blank to skip torque calculation.
Gear ratio
3.00 : 1
Speed reduction (torque multiplication). Output turns slower than input.
Input speed
1,500 RPM
Output speed
500 RPM
Input torque
100 N m
Output torque
300 N m
Mechanical advantage
3
Frequently Asked Questions about the Gear Ratio Calculator
How do you calculate a gear ratio?
Divide the number of teeth on the driven gear by the number on the driving gear. A 36-tooth driven gear meshing with a 12-tooth driver gives a 3.00 : 1 ratio, meaning the input turns three times for every one turn of the output.
What does a gear ratio of 3:1 actually do?
A 3:1 reduction cuts output speed to one third of input speed and multiplies torque by three (minus friction losses). At 1500 input RPM you get 500 output RPM, and 100 N m of input torque becomes 300 N m at the output.
How do you calculate vehicle speed from gear ratios?
Wheel RPM equals engine RPM divided by the product of the transmission ratio and final drive (differential) ratio. Multiply wheel RPM by tire circumference (pi times diameter in inches), then divide by 1056 to get miles per hour. The 1056 constant comes from 5280 feet per mile times 12 inches per foot divided by 60 minutes per hour.
How does a multi-stage gear train ratio work?
Total ratio is the product of each stage ratio. Two stages of 3:1 and 2:1 in series give an overall 6:1 reduction. The same multiplication applies to torque: input torque is multiplied by the total ratio, and output speed is divided by it.
What is mechanical advantage in a gear ratio?
Mechanical advantage equals the gear ratio itself (ignoring friction). A 4:1 reduction gives a mechanical advantage of 4, so 25 N m of input torque produces 100 N m at the output while the output spins four times slower than the input.