Gear Ratio Calculator: Teeth, RPM, Torque and Speed

Mechanical and vehicle gearing tool

Gear Ratio Calculator

Calculate a simple or compound gear ratio from tooth counts, RPM and torque, or calculate vehicle speed, engine RPM and the axle ratio required for a tire and transmission.

A compound train multiplies the ratio of each active stage.
External gears reverse direction at every mesh; an open chain or belt does not.

Stage 1
Stage 2
Stage 3
Use any torque unit consistently; output uses the same unit.
For an ideal calculation, enter 100%.

Use measured loaded diameter for the closest real-world estimate.
Use 1.00 when there is no reduction.
Use 0% for a locked converter or direct mechanical drive.

Results

Gear ratio formulas

  • One stage: ratio = driven teeth ÷ driver teeth.
  • Compound train: total ratio = stage 1 ratio × stage 2 ratio × stage 3 ratio.
  • Output RPM: input RPM ÷ total ratio.
  • Estimated output torque: input torque × total ratio × efficiency per stagenumber of stages.
  • Vehicle overall ratio: transmission ratio × transfer-case ratio × axle ratio.
  • Vehicle speed: wheel RPM × tire circumference × 60, converted to mph or km/h.
20 teeth
driver
→
60 teeth
driven

Checked examples

A 20-tooth driver and 60-tooth driven gear produce a 3:1 reduction. At 1,800 input RPM, output speed is 600 RPM. With 10 units of input torque and 95% stage efficiency, estimated output torque is 28.5 units.

For two stages of 20:60 and 15:45, the total reduction is 9:1. At 1,800 input RPM, the final shaft turns at 200 RPM. With 10 torque units and 95% efficiency at each stage, estimated output torque is 81.225 units.

Driver, driven and direction

The driver is attached to the power source. A ratio above 1 is a reduction: the output turns more slowly and ideal torque increases. A ratio below 1 is an overdrive. Two meshing external gears rotate in opposite directions; every additional external mesh reverses direction again. Open chains and timing belts normally keep both shafts turning in the same direction.

Vehicle gearing limits

The vehicle calculation assumes a fixed rolling diameter and steady ratios. Real RPM and speed can differ because of tire deflection and growth, tread wear, converter or clutch slip, transmission control, differential behavior, measurement error and speedometer calibration. Wheel-torque output is a simplified multiplication estimate and does not predict tractive force, acceleration, component strength or safe operating speed.

This tool does not design tooth geometry or verify module, diametral pitch, pressure angle, center distance, backlash, contact stress, lubrication, bearing loads or gear strength. Planetary, worm and epicyclic sets require their own kinematic models.

Related calculators

Compare tire dimensions with the Tire Size Calculator, check wheel position with the Wheel Offset Calculator, calculate engine size with the Engine Displacement Calculator, calculate chamber and piston geometry with the Compression Ratio Calculator, or convert shaft torque and RPM with the RPM to kW Calculator.