Calculate gear ratio, output RPM, and output torque from gear teeth
Mechanical Calculator
Gear ratio — Quick answer
Gear ratio is the ratio of teeth (or pitch diameter) between driven and driving gear. It determines speed reduction (or step-up) and torque multiplication.
GR = Ndriven / Ndriving = Ddriven / Ddriving ωout = ωin / GR Tout = Tin × GR × η (efficiency)
Standard / source: AGMA 2000 (gear quality); ISO 1328-1; BS 436.
Used for: Drivetrain design, robotics actuators, conveyor speed selection, wind/hydro gearboxes, watch movements, mechanical advantage in machine design.
⚙️ Gear Ratio Calculator
Formula
This calculator uses the standard gear ratio calculator formula:
Gear Ratio Formula
GR = T_driven / T_driver = N_input / N_output
Frequently Asked Questions
What is a gear ratio?⌄
A gear ratio is the ratio of the number of teeth on the driven gear to the number of teeth on the driver gear. GR = T_driven / T_driver.
How do I calculate output speed from gear ratio?⌄
Output RPM = Input RPM ÷ Gear Ratio. For example, if the gear ratio is 3:1 and input speed is 1,500 RPM, output speed = 500 RPM.
How does gear ratio affect torque?⌄
Output torque = Input torque × Gear Ratio. A higher gear ratio increases torque but reduces speed proportionally, assuming 100% efficiency.
What is a reduction gear ratio?⌄
A reduction gear ratio is greater than 1:1, meaning the output shaft rotates slower than the input but with more torque. Typical in gearboxes for motors.
What gear ratio is used in cars?⌄
Automotive transmissions use multiple gear ratios. Low gears (e.g. 3.5:1) give high torque for acceleration; high gears (e.g. 0.75:1) allow high-speed cruising with reduced fuel consumption.
How do I calculate compound gear ratios?⌄
For a gear train with multiple stages, multiply individual ratios: Total GR = GR1 × GR2 × GR3. For example, 2:1 × 3:1 = 6:1 overall reduction.
Need Advanced Calculations?
Use the full AI Calculator suite — 350+ precision engineering and science calculators with PDF report export.