Physics

Gear Ratio Calculator

Calculate gear ratio, output RPM, and torque.

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THE NUMORIX GUIDE

How to use the Gear Ratio Calculator

Last reviewed September 14, 2026

What this calculator does

The engine defines gear ratio as R = N_driven / N_driver.

Formula and method

The engine defines gear ratio as R = N_driven / N_driver. It then uses output RPM = input RPM / R and ideal output torque = input torque x R.

Variables and inputs

Enter driven and driver tooth counts, input RPM, and input torque. The default pair is 48 driven teeth and 16 driver teeth with 3,000 input RPM and 100 torque units; only the two tooth counts are explicitly unit-checked by the UI.

Worked example

For N_driven = 48 and N_driver = 16: R = 48/16 = 3:1. With 3,000 input RPM and 100 torque units, output RPM = 3,000/3 = 1,000 RPM and ideal output torque = 100(3) = 300 torque units.

How to interpret the result

A ratio above 1 reduces output speed and increases ideal output torque by the same factor. The result expresses the kinematic and torque tradeoff for one ideal gear pair, not the complete performance of a gearbox.

Common mistakes to avoid

Keep driven and driver in the correct positions; reversing them reverses the ratio and speed result. Do not assume the unlabeled input torque is automatically lb-ft or N*m, and do not treat ideal torque multiplication as free power.

Assumptions and limitations

The engine assumes no friction, tooth slip, backlash, bearing loss, or gear-mesh efficiency, and it does not model gear diameter, pressure angle, multi-stage layouts, or tooth strength. The UI validates positive tooth counts but does not validate RPM or torque ranges.

Practical use and checks

The Gear Ratio Calculator compares driven and driver tooth counts, then estimates output speed and ideal torque. Enter 48 driven teeth, 16 driver teeth, 3,000 input RPM, and 100 torque units as a check. The ratio should be 3:1, output speed 1,000 RPM, and ideal output torque 300 units. The slower output and larger torque are the expected tradeoff for a reduction ratio, not a gain in power. Keep the roles straight: the driver is connected to the input, and the driven gear receives motion. Reversing the tooth counts changes the ratio and can turn a reduction into a speed increase. The calculator does not assign a torque unit, so carry lb-ft or N m explicitly and do not compare unlabeled results. It assumes one ideal gear pair with no friction, backlash, tooth slip, bearing loss, mesh efficiency, gear inertia, or strength limit. A zero tooth count is invalid, and a real gear train with several stages should multiply stage ratios while accounting for each loss. Use the output as a kinematic check, then inspect speed, torque, lubrication, tooth loading, and efficiency before selecting hardware or deciding whether a gearbox can deliver the required load.

Sources and references

COMMON QUESTIONS

Frequently asked questions

Which gear is the driver?

The driver is connected to the input and turns the driven gear. This calculator divides driven teeth by driver teeth, so a larger driven gear produces a ratio above 1.

Why is actual output torque lower than the estimate?

The engine uses an ideal ratio. Friction, gear-mesh losses, bearings, lubrication, and deformation reduce the torque delivered in a real mechanism.