Gear Ratio Calculator
Use tooth counts from a simple gear pair to see the reduction or overdrive ratio, output shaft speed and torque multiplication.
How to use this calculator
- Count the teeth on the gear that receives input power and on the gear it directly drives. Do not substitute gear diameter unless both gears have the same tooth pitch and you only need an approximation.
- Enter input RPM to translate the tooth-count ratio into output-shaft speed. If you only need the ratio, the RPM value does not change the ratio itself.
- Enter input torque only when you want a torque estimate. Use an efficiency below 100% if you want to account for mechanical losses rather than reporting the ideal value.
- Interpret ratios above 1.00 as reductions in this calculator's convention: output speed falls and available output torque rises. Ratios below 1.00 act as overdrive.
- For compound gear trains, calculate each meshing stage separately or use the compound gear train calculator rather than multiplying random tooth counts from non-meshing gears.
Formula and assumptions
Gear ratio = driven teeth ÷ driving teeth. Output RPM = input RPM ÷ ratio. Approximate output torque = input torque × ratio × efficiency. The ratio is dimensionless; torque units stay the same as the input units when used consistently.
GIIRR calculates idealized geometry and kinematics. Friction, slip, compliance, tire deformation, manufacturing tolerances and control-system behavior can move real measurements away from the theoretical result.
Worked example
A 15-tooth driver turning a 45-tooth driven gear gives 45 ÷ 15 = 3.00, so the pair is a 3.00:1 reduction. At 3,000 rpm input, ideal output speed is 1,000 rpm. With 100 N·m input and 95% efficiency, estimated output torque is 100 × 3 × 0.95 = 285 N·m. The same ratio would apply at another RPM; only the resulting shaft speeds would change.
Frequently asked questions
Is a higher numerical ratio faster?
Usually no in the convention used here. A higher reduction ratio multiplies torque more but lowers output speed for the same input RPM.
Can I use sprocket teeth instead of gear teeth?
For a simple chain drive, the same tooth-count ratio applies. Use the sprocket calculator when you want chain-drive wording or before/after gearing comparisons.
Does gear diameter matter?
Tooth count is the preferred input for meshing gears. Pitch diameter is tied to tooth count and module or diametral pitch, while outside diameter is not a reliable substitute for an exact ratio.
Why is calculated torque higher while power is not?
A reduction trades rotational speed for torque. In an ideal system, power stays the same; in a real system, friction and other losses make output power slightly lower.
What efficiency should I enter?
Use a value supported by the gearbox, bearing and lubrication data for your system when accuracy matters. If you do not know it, treat any assumed percentage as a planning estimate rather than a measured fact.
For safety-critical, legal or fitment decisions, verify the result against manufacturer documentation and physical measurements.
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