⚙️ Mechanical Design  ·  Gear Systems

Gear Ratio Calculator

Simple 2-gear & Multi-Stage compound systems, speed, torque & direction

🔵 Driver Gear (Input)
T
RPM
N·m
🟠 Driven Gear (Output)
T
mm
%
⚙️ Live Visualization
Ratio: 3.000
3.000
Gear Ratio
500.0
Output RPM
294.0
Output Torque N·m
3.00×
Mech. Advantage
0.333×
Speed Ratio
98.0%
Efficiency
📊 Detailed Analysis
ParameterValueType
📐 Formulas Used
Key Equations Loading…

Gear Ratio Calculator: Mechanical Design Guide

Gear ratio is a fundamental mechanical concept describing the relationship between the teeth counts of driver and driven gears. It directly affects output speed, torque and mechanical advantage. This calculator provides accurate results for spur, helical and planetary gear systems.

📋 How to Use This Calculator

  1. Select gear type, Simple (2 gears) or Multi-Stage compound system.
  2. Enter driver gear tooth count and input RPM.
  3. Fill in input torque (N·m), module (mm) and efficiency (%).
  4. Enter driven gear tooth count, output RPM, torque and gear ratio will be calculated instantly.

📐 Formula & Working Principle

Gear Ratio = Driven Gear Teeth ÷ Driver Gear Teeth. Output RPM = Input RPM ÷ Gear Ratio. Output Torque = Input Torque × Gear Ratio × Efficiency.

💡 Worked Example

Driver: 20 teeth, Input: 1000 RPM, 50 N·m. Driven: 60 teeth. Gear Ratio = 60÷20 = 3:1. Output RPM = 1000÷3 = 333 RPM. Output Torque = 50×3×0.98 = 147 N·m.

❓ Frequently Asked Questions (FAQ)

Q: What is the difference between gear ratio and speed ratio?

Gear ratio is calculated from tooth counts, while speed ratio is the ratio of actual measured RPMs. In an ideal system, both are equal.

Q: When are planetary gear systems used?

When a high reduction ratio is needed in a compact design, such as in automatic transmissions, robot joints and wind turbines.

Q: Why is gear efficiency never 100%?

Energy is lost due to friction, gear mesh losses and lubrication. Typical efficiency for steel spur gears is 95–99%.

Q: How do you calculate total ratio for a multi-stage gear train?

Multiply the ratio of each stage. Stage 1: 3:1, Stage 2: 4:1 → Total ratio = 3×4 = 12:1.

Q: What is module (m) in gear design?

Module = Reference Diameter ÷ Number of Teeth. It defines gear tooth size. Only gears with the same module can mesh together.