How do I calculate gear ratio?

Divide the number of teeth on the driven (output) gear by the teeth on the driving (input) gear. Example: 60 teeth ÷ 20 teeth = 3:1 ratio.

What does a 3:1 gear ratio mean?

A 3:1 ratio means the input shaft rotates 3 times for every 1 rotation of the output shaft. Speed is reduced by 3×, but torque is increased by 3×.

How does gear ratio affect torque?

Gear ratio multiplies torque. A 4:1 ratio increases output torque by 4× (minus efficiency losses). This is why trucks use high ratios for towing power.

How do I calculate compound gear ratio?

Multiply the individual ratios together. Example: First stage 3:1 × Second stage 2:1 = Overall 6:1 ratio.

What's the difference between gear ratio and speed ratio?

They're reciprocals. Gear ratio = Driven/Driving teeth. Speed ratio = Input speed/Output speed. A 3:1 gear ratio gives a 3:1 speed reduction.

How do I calculate sprocket ratio for a bicycle?

Divide rear sprocket teeth by front chainring teeth. Example: 28-tooth rear ÷ 42-tooth front = 0.67 ratio (higher gear). Lower ratios = harder pedaling, faster speed.

What gear ratio is best for speed vs torque?

Lower ratios (0.5:1 to 1:1) favor top speed. Higher ratios (3:1 to 5:1) favor torque/acceleration. Most vehicles use multiple ratios for different situations.

How do pulley ratios work?

Same as gears: Output pulley diameter ÷ Input pulley diameter = ratio. Alternatively, use pitch diameters or count grooves for timing pulleys.

Gear Ratio Calculator

Our gear ratio calculator helps engineers, mechanics, and hobbyists design and analyze gear systems. Calculate the ratio between driving and driven gears, determine output RPM and torque, and analyze compound gear trains. Essential for automotive transmissions, bicycles, robotics, and industrial machinery.

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calendar_today Updated: April 2025

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Driving Gear

teeth

Driven Gear

teeth

Input Speed

RPM

Input Torque

N·m

Efficiency: 98%

Gear Ratio

3.00 : 1

Reduction (Speed ↓, Torque ↑)

Output Speed

333.33

RPM

Output Torque

29.40

N·m

Multiplication

Speed Reduction -66.67%

Torque Multiplier ×3.00

Formula

Ratio = Driven ÷ Driving = 45 ÷ 15 = 3.00

Input Values

Calculate

Gear Ratio & Output

Required Teeth

Compound Ratio

Driving Gear (Input)

teeth

Driven Gear (Output)

teeth

Input Speed

RPM

Input Torque

N·m

auto_awesome AI Analysis

Enter your values and calculate to receive AI-powered insights about your results.

settings Common Gear Ratios

Bicycle (Low) 1:1

Bicycle (High) 3:1

Car 1st Gear 3.5:1

Car Final Drive 3-4:1

balance Trade-offs

⬆️ Higher ratio = More torque, Less speed
⬇️ Lower ratio = Less torque, More speed

How to Use This Calculator

Select Mode

Choose to calculate ratio, find teeth, or analyze compound gears

Enter Teeth Count

Input the number of teeth on driving and driven gears

Add Speed/Torque

Enter input RPM and torque for output calculations

View Results

See gear ratio, output speed, and torque multiplication

The Formula

Gear ratio is the ratio of driven gear teeth to driving gear teeth. A ratio greater than 1 reduces speed but increases torque (reduction gear). A ratio less than 1 increases speed but reduces torque (overdrive).

Gear Ratio = Driven Teeth ÷ Driving Teeth

lightbulb Variables Explained

GR Gear Ratio (dimensionless)
N₁ Number of teeth on driving gear (input)
N₂ Number of teeth on driven gear (output)
ω₂ Output speed = Input speed ÷ Gear Ratio
T₂ Output torque = Input torque × Gear Ratio

tips_and_updates Pro Tips

Gear ratio > 1 = speed reduction, torque increase (most common)

Gear ratio < 1 = speed increase, torque reduction (overdrive)

Compound gear trains multiply individual ratios together

For chains/belts, use sprocket/pulley teeth or diameters

Efficiency losses: ~2% per gear mesh, ~3-5% for chains

Bicycle: larger rear sprocket = easier pedaling, lower speed

Car final drive ratios typically range from 2.5:1 to 4.5:1

Gear ratios determine how speed and torque are transferred between rotating shafts. A higher ratio means more torque but less speed, which is ideal for starting heavy loads. A lower ratio means more speed but less torque, which is ideal for high-speed operation.

Gear ratios are used in automotive transmissions, bicycles, industrial machinery, robotics, and power tools. Understanding ratios helps in selecting the right gears for your speed and torque requirements.