How to Calculate Gear Ratio: Formulas, RPM, and Gearbox Math

A gear ratio measures the mechanical relationship between two or more meshed gears in a gear train. It defines how input speed and torque transfer from a drive gear (connected to the motor) to a driven gear (connected to the output load).

THE GEAR RATIO FORMULA

To calculate the gear ratio of a single pair of gears, divide the number of teeth on the driven gear by the number of teeth on the drive gear: Gear Ratio = Output Teeth (Driven) ÷ Input Teeth (Drive).

WORKED EXAMPLE: If a 60-tooth driven gear is powered by a 20-tooth drive gear, the calculation is 60 ÷ 20 = 3. This gives a 3:1 gear ratio, meaning the drive gear turns 3 times for every single turn of the driven gear.

CALCULATING OUTPUT RPM & VEHICLE SPEED

Gear ratios directly alter output speed (RPM) and torque. Reducing output speed multiplies output torque by the same factor.

• Output RPM Formula: Output RPM = Input RPM ÷ Gear Ratio • Example Calculation: A motor spinning at 3,000 RPM into a 5:1 reduction gearbox outputs 600 RPM (3,000 ÷ 5). • Transmission Speed: To calculate road speed, multiply transmission gear ratio by final drive ratio to find total wheel RPM.

COMPOUND GEAR TRAINS

In multi-stage gearboxes with multiple gear sets, multiply individual stage ratios together to get the total reduction: Total Ratio = Stage 1 Ratio × Stage 2 Ratio × Stage 3 Ratio.

If Stage 1 is 4:1 and Stage 2 is 3:1, the total gearbox reduction is 12:1 (4 × 3). A motor spinning at 2,400 RPM through this gearbox results in an output speed of 200 RPM with 12 times the motor torque.