Gear Ratio & RPM Calculator

The Formula

Gear ratios trade speed for torque (or vice versa). A ratio greater than 1 reduces speed and multiplies torque; a ratio less than 1 increases speed and reduces torque. Output Torque = Input Torque × Gear RatioThe ratio of the number of teeth on two meshing gears. Determines torque multiplication and speed reduction in mechanical systems. × Efficiency.

Variable Definitions

How to Use This Calculator

1. 1

   Select the calculation mode: output RPM, gear ratio, or required input RPM.

2. 2

   Enter the known values (input RPM, output RPM, or gear ratio).

3. 3

   Optionally enter input torque to calculate output torque.

4. 4

   View output speed, torque, and gear type classification.

5. 5

   Use the result to select an appropriate gearbox for your application.

Common Applications

• Designing mechanical systems like conveyor drives, winches, or mixers by calculating the gear reduction needed to match motor speed to load requirements
• Determining output torque and speed for automotive transmissions, differentials, or industrial gearboxes
• Selecting the appropriate gearbox stage count (single vs multi-stage) for applications requiring specific speed reduction ratios

Gear ratio — larger driven gear turns slower but with more torque

Understanding the Concept

Gear systems are mechanical force multipliers — they trade speed for torque or torque for speed. A 3:1 reduction gear reduces output speed by 3x but multiplies torque by approximately 3x (minus losses). This is why gearboxes are used on electric motors to match high motor speeds to low-speed, high-torque applications like conveyors, winches, and vehicle drivetrains. Compound gear trains (multiple gear stages) multiply the ratios of each stage. Real-world example: an electric motor running at 1,800 RPM driving a conveyor that needs to operate at 60 RPM. The required gear ratio is 1,800 ÷ 60 = 30:1. A single-stage gearbox is usually limited to about 10:1, so this would need a two-stage gearbox (for example, 6:1 first stage times 5:1 second stage = 30:1). If the motor delivers 50 N·m of torque, the output torque is 50 times 30 times 0.95 = 1,425 N·m — enough to move the conveyor belt with heavy loads. In a vehicle transmission, the gearbox provides multiple ratios for different driving conditions. First gear might be 3.5:1 for maximum torque during acceleration, while fifth gear might be 0.75:1 overdrive for fuel-efficient highway cruising. The differential adds a final reduction of about 3:1 to 4:1, so the overall ratio from engine to wheels in first gear is roughly 10.5:1 to 14:1.

Frequently Asked Questions

Sources & References