Gear Ratio Calculator

Calculate gear ratio, output RPM, speed multiplier and torque multiplier for a pair of gears. Keep nav & footer includes — no existing functions removed.

Inputs

The gear attached to the input shaft (driving gear).
The gear being driven (output gear).
If provided, the calculator will compute output RPM.
If provided, the calculator will estimate output torque (ignoring losses).

Note: Results assume ideal (lossless) gears. For real systems, include gearbox efficiency (multiply torque by η and divide speed by η where appropriate).

Gear Ratio — Explanation, Formulas and Use Cases

A gear ratio describes the relationship between two meshing gears: how many times the driver gear must rotate for the driven gear to complete one rotation. Gear ratios are fundamental to mechanical design because they determine the speed and torque relationship between input and output shafts. In simple terms, gears can be used to increase torque (mechanical advantage) at the expense of speed, or vice versa.

Basic definitions and intuition

The simplest way to think about a gear pair is to compare the number of teeth on each gear. If the driver (input) has 20 teeth and the driven (output) has 40 teeth, the gear ratio is 40/20 = 2. This means the driven gear turns at half the speed of the driver but with twice the torque (ignoring losses). Conversely, a small driven gear with fewer teeth than the driver produces higher output speed but reduced torque.

Common applications

Gear ratios appear in countless mechanical systems: bicycle drivetrains, automotive transmissions, electric motor gearboxes, industrial conveyors, robotics, clocks, and power tools. For example:

  • Bicycles: The combination of chainrings and cogs yields effective gear ratios to match cadence and terrain.
  • Vehicles: Transmission gearsets provide multiple gear ratios so the engine can operate efficiently across speeds and loads.
  • Robotics: Gearboxes trade motor speed for torque to move arms and grippers precisely under load.

How to compute gear ratio and what it tells you

The calculation is straightforward: Gear Ratio = Driven Teeth ÷ Driver Teeth. If you know the input RPM, the output RPM follows from simple proportionality: output RPM = input RPM × (driver teeth / driven teeth). For torque, the ideal (lossless) relation is output torque = input torque × gear ratio. Because real gears have friction and efficiency losses, actual torque may be slightly lower — typical efficiencies range from 90% to 98% for well-lubricated, properly aligned gear pairs.

Compound gears and reduction stages

Most practical gearboxes use multiple stages or compound gears. The overall gear ratio is the product of the individual stage ratios. For instance, a two-stage gearbox with stage ratios 3:1 and 4:1 yields an overall ratio of 12:1. This compounding enables very large reductions or increases in speed while keeping each stage within practical size limits.

Selecting a gear ratio

Choosing the correct ratio requires considering the application's torque and speed requirements. For high torque applications (lifting, heavy transport), choose a higher reduction ratio. For high-speed needs (rotary tools, fans), favor ratios that preserve speed. In electric motor applications, match the motor's best-efficiency operating RPM to the machine's required output RPM via an appropriate gear ratio and, where necessary, add a gearbox efficiency correction.

Practical considerations and caveats

When using gear ratios in design, remember:

  • Real systems have losses — include gearbox efficiency in torque and power calculations.
  • Large ratios imply larger gear sizes or more stages; check packaging and weight.
  • Tooth form, module (or diametral pitch), and material determine load capacity and life.
  • Backlash and precision requirements may influence gear choice and assembly methods.

Examples

Example 1: A motor spins at 3,000 RPM and drives a 15-tooth pinion that meshes with a 45-tooth gear. Gear ratio = 45/15 = 3 → output RPM = 3,000 × (15/45) = 1,000 RPM. Output torque is ideally three times the motor torque.

Example 2: Bicycle gearing often uses a small front chainring and a large rear cog for climbing (high ratio for torque) and the opposite for sprinting (low ratio for speed).

Conclusion

Gear ratios are a simple yet powerful concept enabling designers to tailor speed and torque for any mechanical system. This Gear Ratio Calculator helps you quickly evaluate basic pairings and estimate output RPM and torque for design checks and educational use. Always validate critical designs with detailed strength, lubrication, and thermal analysis when moving from concept to production.