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⚙️ Gear Ratio Calculator

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)

Worked example: Driving gear 15 teeth, driven gear 60 teeth. GR = 60/15 = 4:1 reduction. Input shaft at 1,500 RPM → output at 375 RPM. Input torque 10 N·m → output torque 10 × 4 × 0.97 = 38.8 N·m.

Common gear-ratio applications

ApplicationTypical ratioNotes
Bicycle high gear1:1 to 3:1speed-up at wheel
Car final drive3:1 to 4.5:1engine RPM → wheel
Wind-turbine gearbox60:1 to 100:1step-up to generator
Worm-gear servo30:1 to 100:1high reduction
Planetary epicyclic3:1 to 12:1compact, coaxial

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.

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Standards & method

✓ Independently verified 12 July 2026
Basis
First principles
Method
Kinematics of a gear train. Two gears mesh only if they share the same module and pressure angle (ISO 53 / ISO 54).
Core formula
ratio = N_driven / N_driver  ·  torque multiplies by the ratio, speed divides by it
Why this matters
Gearing trades speed for torque — you cannot gain both. A 4:1 reduction gives 4× the torque at ¼ the speed. Idler gears reverse direction but do not change the ratio.
Independently verified
12 July 2026 — Formula re-derived from first principles and verified numerically against hand-computed reference cases, including edge cases and unit handling.

Results are for guidance. Verify against the current edition of the governing standard and have a qualified professional review before use in practice.