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SeriesCalc

⚙️ Gear Ratio Calculator

Calculate the gear ratio, output speed, and output torque of a simple gear train.

Inputs

RPM

Results

Gear Ratio (GR)0.00 : 1
Driven Gear Speed (RPM₂)0.00 RPM
Driven Gear Torque (τ₂)0.00 lbf·ft

Gear Train Process

N₁N₂

Calculator Description

The gear ratio is the ratio of teeth (or diameters) between two meshing gears, and it determines how rotational speed and torque are converted. A gear train is one of the most fundamental elements of machine design, trading speed for force (and vice versa) while transmitting power.

What this calculator finds

From the number of teeth on the driving and driven gears, and the input speed (RPM) and torque, it calculates the gear ratio, the output speed, and the output torque.

Why it matters

  • Selecting tooth counts to hit target speed and torque in reducers and gearboxes
  • Matching motor ratings (rated RPM and torque) to load requirements
  • Comparing the speed-versus-force trade-off in bicycle or vehicle drivetrains

Formula

Gear Ratio Formulas

The gear ratio is the driven gear's teeth divided by the driving gear's teeth. Output speed is inversely proportional to the ratio, while torque is directly proportional to it (conservation of energy).

GR=N2N1GR = \dfrac{N_2}{N_1}
RPM2=RPM1GRRPM_2 = \dfrac{RPM_1}{GR}
τ2=τ1×GR\tau_2 = \tau_1 \times GR
  • N₁ — Driving gear teeth
  • N₂ — Driven gear teeth
  • GR — Gear ratio (dimensionless)
  • RPM₁, RPM₂ — Driving / driven gear speed [rpm]
  • τ₁, τ₂ — Driving / driven gear torque [N·m]

How the formula works

  • GR > 1 (reduction): the driven gear is larger, so speed decreases and torque increases.
  • GR < 1 (overdrive): the driven gear is smaller, so speed increases and torque decreases.
  • Ideally input power equals output power, so speed and torque change in opposite directions.

Worked example

With N₁ = 20 driving teeth and N₂ = 60 driven teeth, GR = 60/20 = 3. If the input is 1500 rpm at 10 N·m, the output becomes 1500/3 = 500 rpm at 10 × 3 = 30 N·m.

Useful Tips

Practical tips

  • For large reductions, use a multi-stage gear train — the total ratio is the product of each stage's ratio.
  • Two meshing gears must share the same module (or diametral pitch) to engage properly.

Limitations & cautions

  • These formulas assume an ideal train with no friction or losses; real output torque is reduced by gear efficiency (typically 95–99% per stage).
  • Backlash, heat, wear and misalignment are not accounted for and require separate consideration in precision design.