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Gear Ratio RPM Calculator

Calculate gear ratios, RPM changes, and mechanical advantage in gear systems

Calculate Gear Ratio and RPM

teeth

Number of teeth on the driving gear (power input)

teeth

Number of teeth on the driven gear (power output)

RPM

Revolutions per minute of the input gear

2.000:1

Ratio of input teeth to output teeth

Gear System Results

500.0
Output RPM
3000.0
Degrees per second
52.360
Radians per second
2.000:1
Gear Ratio
2.00x
Torque Multiplication
0.500x
Speed Multiplication

Formula used: Output RPM = Input RPM ÷ Gear Ratio

Gear Type: Reduction (Speed Reducer)

Calculation: 500.0 = 1000 ÷ 2.000

Gear System Analysis

🔧 Speed Reduction: This gear system reduces speed by 2.00x and increases torque by 2.00x

Example Calculation

Bicycle Gear System

Input gear (chainring): 52 teeth

Output gear (cassette cog): 11 teeth

Pedaling speed: 80 RPM

Gear ratio: 52 ÷ 11 = 4.73:1

Calculation

Output RPM = Input RPM ÷ Gear Ratio

Wheel RPM = 80 ÷ 4.73 = 16.9 RPM

Result: The rear wheel spins at 16.9 RPM

This is a high gear for fast cycling on flat terrain!

Common Gear Ratios

Bicycle high gear4.7:1
Car 1st gear3.5:1
Car 2nd gear2.1:1
Car 4th gear1:1
Car overdrive0.8:1
Clock mechanism12:1
Worm gear40:1

Key Formulas

Gear Ratio
Ratio = Input Teeth ÷ Output Teeth
Output RPM
Output RPM = Input RPM ÷ Gear Ratio
Torque Multiplication
Output Torque = Input Torque × Gear Ratio
RPM to rad/s
ω = RPM × (2π / 60)

Gear System Tips

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Higher gear ratio = more torque, less speed

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Lower gear ratio = less torque, more speed

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Power input = Power output (minus losses)

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Gear efficiency typically 95-98%

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Consider gear backlash in precision applications

Understanding Gear Ratios and RPM

What is a Gear Ratio?

A gear ratio is the relationship between the number of teeth on two meshing gears. It determines how much the output gear rotates for each rotation of the input gear, and directly affects both speed and torque transmission.

Speed vs. Torque Trade-off

  • •Reduction Gears (Ratio > 1): Reduce speed, increase torque - ideal for heavy loads
  • •Overdrive Gears (Ratio < 1): Increase speed, reduce torque - ideal for high-speed applications
  • •Direct Drive (Ratio = 1): No change in speed or torque

RPM Calculations

Basic Formula:

Output RPM = Input RPM ÷ Gear Ratio

Gear Ratio = Input Teeth ÷ Output Teeth


Angular Velocity Conversion:

ω (rad/s) = RPM × (2π / 60)

ω (deg/s) = RPM × 6

Applications

  • Automotive: Transmission systems for optimal power delivery
  • Bicycles: Different gear ratios for terrain and speed
  • Industrial: Motor speed reduction for machinery
  • Clocks: Precise time division through gear trains
  • Robotics: Servo motor control and positioning

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