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Gear Ratio, Torque & Output Speed Calculator

Gear trains transfer rotational power between rotating shafts, trading rotational speed for output torque according to the gear tooth ratio.

Number of teeth on input driving gear attached to motor shaft.

Number of teeth on output driven gear.

Rotational speed of motor input shaft (e.g. 1750 RPM 4-pole AC motor).

Torque delivered by driving motor in Newton-meters.

Mechanical mesh efficiency (Spur gear ≈ 95 - 98%; Planetary ≈ 90 - 95%; Worm gear ≈ 60 - 85%).

Calculated Result
4:1

Gear Ratio (Velocity Ratio)

Gear Ratio (i)

4:1 (Reduction (Speed Down, Torque Up))

Output Speed

437.5 RPM (Input: 1750 RPM)

Output Torque

95 N·m (Input: 25 N·m)

Input / Output Power

4.58 kW → 4.35 kW

Gearbox Efficiency

95%

Calculation Breakdown

  1. 1. Calculate Velocity RatioGear Ratio i = N_driven / N_driver = 72 / 18 = 4:1
  2. 2. Determine Output Shaft SpeedRPM_out = RPM_in / i = 1750 / 4 = 437.5 RPM
  3. 3. Determine Torque Multiplication with EfficiencyT_out = T_in · i · η = 25 N·m · 4 · 0.95 = 95 N·m

Input vs Output Comparison (4:1 Reduction)

Interactive visualization based on your current inputs

Value
0.04488131175Input Speed (RPM / 10)Output Speed (RPM / 10)Input Torque (N·m)Output Torque (N·m)ParameterValue

What Is the Gear Ratio, Torque & Output Speed Calculator?

A gear ratio expresses the mathematical relationship between the rotational speeds and torques of two meshing gears.

How Does the Gear Ratio, Torque & Output Speed Calculator Work?

Because interlocking gear teeth travel with identical linear pitch velocities, a gear with more teeth rotates slower with proportionately higher torque.

Gear Ratio, Torque & Output Speed Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

i = \frac{N_2}{N_1}, \quad \omega_{out} = \frac{\omega_{in}}{i}, \quad T_{out} = T_{in} \cdot i \cdot \eta, \quad P = \frac{2\pi \cdot N \cdot T}{60}

Gear ratio is driven teeth over driver teeth. Output speed is input speed divided by ratio. Output torque is input torque times ratio times efficiency.

How to Use the Gear Ratio, Torque & Output Speed Calculator

  1. Enter tooth counts for driver and driven gears.
  2. Specify input shaft speed in RPM and torque in N·m.
  3. Optionally adjust gearbox efficiency percentage.

Step-by-Step Example Calculation

4:1 Reduction Gearbox (18T to 72T, 95% Efficiency)

Input Values:

driverTeeth:18
drivenTeeth:72
inputSpeedRpm:1750
inputTorqueNm:25
efficiencyPercent:95
Worked Steps: Produces a 4:1 reduction: drops speed from 1,750 RPM to 437.5 RPM while multiplying torque from 25 N·m to 95 N·m.

Understanding Your Result

Gear Ratio (i): Velocity reduction or overdrive ratio.

Output Speed (RPM): Revolutions per minute of output shaft.

Output Torque (N·m): Delivered shaft turning force.

Power Conservation: Verification of mechanical kilowatt power throughput.

Factors That Affect the Result

  • Tooth count ratio (direct scaling) and gear train friction losses.

When Should You Use This Calculator?

  • Electric powertrain transmission design, robotics servo actuator sizing, winch winches, and machine drive engineering.

Assumptions & Limitations

  • Assumes rigid teeth with negligible backlash and constant input speed.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Standard machine design kinematic power transmission equations.

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