Site units convert road speed (mph / km/h) and measured tire sizes (in / cm). Tire-code width stays in millimeters and rim code stays in inches. Shaft speeds use rpm; torque uses N·m.
How to use this gear ratio calculator
Choose a mechanical gear train, known shaft speeds, or a vehicle task. Vehicle modes use separate transmission and final-drive ratios, plus measured rollout or nominal tire dimensions.
How the calculation works
For a vehicle, wheel RPM = engine RPM / (transmission ratio × final-drive ratio). Speed in km/h = wheel RPM × rolling circumference in meters × 60 / 1000. Reverse this equation to find engine RPM or final drive. Tire-code nominal diameter in mm = rim inches × 25.4 + 2 × section width mm × aspect percent / 100; nominal circumference is π × diameter. Measured loaded rollout avoids assuming that nominal geometry equals the traveled distance.
For one external gear pair, ratio = driven teeth ÷ driver teeth. Output speed = input speed ÷ ratio. A 20-tooth driver turning a 60-tooth gear therefore gives a 3:1 reduction.
For a compound train, multiply the stage ratios. Each intermediate shaft carries the previous driven gear and the next driver; they rotate together. The breakdown shows speed after each stage.
Ideal output torque = input torque × overall ratio. The estimate with losses multiplies this by overall efficiency ÷ 100. Efficiency reduces transmitted torque in this model, not the tooth-determined speed ratio.
Each external mesh reverses direction. An odd number of stages reverses the output; an even number preserves its direction. A simple idler changes direction but cancels out of the tooth ratio between the first and last gear.
Worked example
A 20-tooth driver and 60-tooth driven gear give 3:1. At 1,200 rpm, output speed is 400 rpm. Add a compound 15-tooth to 45-tooth stage: the overall ratio is 9:1 and output is about 133.33 rpm. With 10 N·m input and 90% total efficiency, output torque is 81 N·m.
Limits and assumptions
Mechanical mode covers up to three external gear pairs, not planetary or internal arrangements. Vehicle speed is theoretical, without clutch, torque-converter or tire slip; tire-code geometry is nominal, not loaded rollout. No fitment, gear-strength, tire-rating or safe-speed assessment.
Frequently asked questions
How can I measure rolling circumference?
On level ground, mark the tire and ground, roll through one full revolution, then measure the distance between ground marks. Use representative loading and avoid slip. Tire-code estimates do not account for load, inflation, tread wear or real rolling behavior.
Which gear is the driver?
The driver supplies motion to that stage. The driven gear receives it. Reversing these inputs reverses the ratio.
Is 3:1 a reduction or an increase?
With the input-to-output speed convention used here, 3:1 means the output turns at one third of input speed.
How do I enter a compound gear train?
Choose two or three stages and enter each meshing pair. The next driver must be on the same shaft as the previous driven gear.
Can this calculate car speed from a final-drive ratio?
Yes. Choose a Vehicle mode, enter the selected transmission gear and final-drive ratio, and use measured tire rolling circumference, outside diameter, or tire-code dimensions. Solve road speed, engine RPM or final-drive ratio.
References
Michelin: tire markings and dimension codes
Wikipedia: gear trains, speed ratios and mechanical advantage