What is a gear ratio?

Gear ratio (i) is the ratio of angular velocities between input and output shafts. It equals the ratio of teeth counts i = Z2/Z1 or speed ratio i = n1/n2. A ratio greater than 1 means speed reduction (torque multiplication).

How do I calculate multi-stage gear ratio?

For a multi-stage gear train, the total ratio is the product of individual stage ratios: i_total = i1 × i2 × i3 × ... For example, two stages with i=3 and i=4 give i_total = 12.

What is the difference between gear ratio and speed ratio?

They express the same relationship differently. Gear ratio i = Z_driven/Z_driver = n_input/n_output. Speed ratio is the inverse: output_speed/input_speed = 1/i. Both describe the same gear mesh.

What is a typical gear ratio range for single stage?

Single-stage spur gears typically achieve ratios of 1:1 to 6:1. Helical gears can go to 10:1. For higher ratios, use multi-stage (e.g., two-stage gearbox: up to 36:1) or worm gears (5:1 to 100:1).

How does gear ratio affect torque?

Torque is multiplied by the gear ratio (minus losses): T_output = T_input × i × η. A 3:1 reduction triples the torque while reducing speed by 3. This is the fundamental trade-off in gear systems.

Free Engineering Tool #086

Gear Ratio Calculator

Calculate gear transmission ratio from speeds, teeth count, or diameters. Supports multi-stage gear trains with up to 5 stages. i = Z₂/Z₁ = n₁/n₂.

i = Z₂/Z₁ Multi-Stage Speed & Torque

Results

Total Gear Ratio

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Output Speed

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Output Torque (η≈97%/stage)

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Per-Stage Ratios

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Gear Mesh (First Stage)

Single-Stage Gear Ratio

Multi-Stage Total Ratio

Output Torque

Where η is efficiency per stage (typically 97–99% for spur gears).

Example — Two-Stage Gearbox

Given: Stage 1: Z₁=18, Z₂=72; Stage 2: Z₁=20, Z₂=60; Input = 1500 RPM, 15 kW

i₁ = 72/18 = 4.0, i₂ = 60/20 = 3.0

i_total = 4.0 × 3.0 = 12.0

n_out = 1500 / 12 = 125 RPM

T_out = 9549 × 15 / 125 × 0.97² = 1080 N·m

Gear Ratio Calculator | Multi-Stage | Free Online Tool

Published by Nikolai Shelkovenko on February 15, 2026 February 15, 2026

Results

Single-Stage Gear Ratio

Multi-Stage Total Ratio

Output Torque