Gear Ratio Calculator — RPM & Torque
Calculate gear ratio, output RPM, torque ratio, and speed reduction for gear trains.
What Is the Gear Ratio Calculator — RPM & Torque?
The Gear Ratio Calculator computes the gear ratio between meshed gears and determines output speed, torque, and mechanical advantage. Enter the number of teeth on each gear (or pitch diameter), input speed, and torque to analyze simple gear trains, compound gear trains, and belt-pulley systems.
Formula
How to Use
Enter the number of teeth on the driving gear and the driven gear. Optionally enter the input RPM and input torque. The calculator shows the gear ratio, output RPM, output torque, and the mechanical advantage. For multiple gear stages, chain the calculations together.
Example Calculation
Driver gear: 20 teeth at 1500 RPM. Driven gear: 60 teeth. Gear Ratio = 60/20 = 3:1. Output Speed = 1500 ÷ 3 = 500 RPM. If input torque = 10 N·m, output torque = 10 × 3 × 0.98 (efficiency) = 29.4 N·m.
Understanding Gear Ratio — RPM & Torque
Gear ratios are fundamental to mechanical engineering and power transmission systems. Gears transform speed and torque: a larger driven gear reduces speed while multiplying torque, and a smaller driven gear increases speed while reducing torque. This trade-off governs the design of automotive transmissions, industrial gearboxes, clocks, bicycles, and robotics.
The gear ratio is determined purely by the tooth counts (or diameters) of the meshing gears, regardless of material or tooth profile. When two gears mesh, the product of teeth and speed is constant: N₁ω₁ = N₂ω₂. This meshing condition ensures no slipping between properly manufactured gears.
Real gear systems also account for mechanical efficiency, which is typically 95–99% for well-lubricated spur gears but can be lower for worm gears or heavily loaded systems. When designing a gear train, engineers must also consider gear strength, contact ratio, backlash, and service life to ensure reliable operation.
Frequently Asked Questions
What does a gear ratio of 3:1 mean?
A 3:1 ratio means the driven gear rotates once for every three rotations of the driver gear. The driven gear spins at one-third the speed but generates three times the torque (less friction losses).
How do gear ratios affect torque?
Gear ratios trade speed for torque. A higher gear ratio (larger driven gear) increases output torque and decreases output speed. This is why low gears in a car provide more pulling force at lower speeds.
Can I use this for belt-and-pulley systems?
Yes. Belt and pulley systems follow the same principle: Ratio = Driven Pulley Diameter ÷ Driver Pulley Diameter (or teeth count for toothed belts).
What is a compound gear train?
A compound gear train has multiple gear pairs in series. The overall ratio is the product of individual stage ratios, allowing very high or very low final ratios in a compact space.
Is this calculator free?
Yes, completely free with no account required.