Gear Ratio Calculator

Gear Ratio is evaluated from Driver Gear Teeth, Driven Gear Teeth and Input Speed. The calculation reports Gear Ratio, Output Speed and Output Torque.

Results

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About the Gear Ratio Calculator

Gear Ratio is treated here as a quantitative relation between Driver Gear Teeth, Driven Gear Teeth, Input Speed and Input Torque and Gear Ratio, Output Speed, Output Torque and Power.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
GR = N_driven / N_driving = ω_in / ω_out
Output RPM = Input RPM / GR
Output Torque = Input Torque x GR
Power (kW) = Torque(N·m) x ω(rad/s) = T(ft·lb) x 1.35582 x 2piN/60
(1 ft·lb = 1.35582 N·m)

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

GR = N_driven / N_driving = ω_in / ω_out
Output RPM = Input RPM / GR
Output Torque = Input Torque x GR
Power (kW) = Torque(N·m) x ω(rad/s) = T(ft·lb) x 1.35582 x 2piN/60
(1 ft·lb = 1.35582 N·m)

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: Electric Motor Gear Reducer

Inputs

teeth_drive: 20 teeth_driven: 100 rpm_input: 1750 torque_input: 14.3
Gear Ratio: 5 :1. Output Speed: 350 RPM. Output Torque: 71.5 ft·lb. Power: 3.553 kW. Speed Multiplier: 0.2 x

With Driver Gear Teeth = 20, Driven Gear Teeth = 100, Input Speed = 1,750 and Input Torque = 14.3 as the stated inputs, the result is Gear Ratio = 5:1, Output Speed = 350 RPM and Output Torque = 71.5 ft·lb. Each value corresponds to the declared output fields.

Example 2: Ford F-150 Rear Axle

Inputs

rpm_input: 1800 torque_input: 400 gear_ratio_in: 3.73
Gear Ratio: 3.73 :1. Output Speed: 482.6 RPM. Output Torque: 1,492 ft·lb. Power: 102.226 kW. Speed Multiplier: 0.268 x

With Input Speed = 1,800, Input Torque = 400 and OR: Known Gear Ratio = 3.73 as the stated inputs, the result is Gear Ratio = 3.73:1, Output Speed = 482.6 RPM and Output Torque = 1,492 ft·lb. Each value corresponds to the declared output fields.

Example 3: Bicycle Gear Calculation

Inputs

teeth_drive: 50 teeth_driven: 14 rpm_input: 90 torque_input: 25
Gear Ratio: 0.28 :1. Output Speed: 321.4 RPM. Output Torque: 7 ft·lb. Power: 0.319 kW. Speed Multiplier: 3.571 x

With Driver Gear Teeth = 50, Driven Gear Teeth = 14, Input Speed = 90 and Input Torque = 25 as the stated inputs, the result is Gear Ratio = 0.28:1, Output Speed = 321.4 RPM and Output Torque = 7 ft·lb. Each value corresponds to the declared output fields.

Example 4: Wind Turbine Gearbox

Inputs

rpm_input: 15 torque_input: 800000 gear_ratio_in: 100
Gear Ratio: 100 :1. Output Speed: 0.2 RPM. Output Torque: 80,000,000 ft·lb. Power: 1,703.774 kW. Speed Multiplier: 0.01 x

With Input Speed = 15, Input Torque = 800,000 and OR: Known Gear Ratio = 100 as the stated inputs, the result is Gear Ratio = 100:1, Output Speed = 0.2 RPM and Output Torque = 80,000,000 ft·lb. Each value corresponds to the declared output fields.

Common Use Cases

  • Calculate output RPM after gear reduction
  • Find torque multiplication for a gear pair
  • Determine gear ratio needed for a target output speed