Gear Ratio Calculator
Calculate gear ratios, mechanical advantage, and speed/torque relationships
Calculation Mode
Gear Ratio Calculator
Number of teeth on the driving gear
Number of teeth on the driven gear
Example Calculation
Bicycle Gear System
Input (pedal): 42 teeth chainring
Output (wheel): 14 teeth rear sprocket
Gear ratio: 14 ÷ 42 = 0.33 (or 1:3)
Effect: Speed advantage - wheel turns 3x faster than pedals
Calculation Steps
1. Count teeth on input gear: 42
2. Count teeth on output gear: 14
3. Calculate ratio: 14 ÷ 42 = 0.33
4. Result: Every 1 pedal turn = 3 wheel turns
Gear System Types
Gear Reduction
More torque, less speed
Output gear larger than input
Gear Overdrive
More speed, less torque
Output gear smaller than input
Direct Drive
Same speed and torque
Gears are the same size
Gear Physics
Gear ratio = Output teeth / Input teeth
Speed ratio = Input RPM / Output RPM
Torque multiplication = Gear ratio
Power is conserved (ignoring friction)
Trade-off between speed and torque
Understanding Gear Ratios
What is a Gear Ratio?
A gear ratio is the relationship between the number of teeth on two gears that mesh together. It determines how much the speed and torque change as power is transmitted from the input gear (driving) to the output gear (driven).
How Gears Work
- •Gears transfer rotational motion and force
- •Teeth must be the same size to mesh properly
- •Speed and torque are inversely related
- •Power remains constant (minus friction)
Gear Ratio Formulas
Basic Gear Ratio
Ratio = Output Teeth / Input Teeth
Speed Relationship
Output RPM = Input RPM / Gear Ratio
Torque Relationship
Output Torque = Input Torque × Gear Ratio
Remember: Higher gear ratios provide more torque but less speed, while lower ratios provide more speed but less torque.
Real-World Applications
Bicycles
- • Low gear: High ratio for climbing hills
- • High gear: Low ratio for speed
- • Multiple gears for different conditions
- • Chain and sprocket system
Automobiles
- • Transmission gear ratios
- • Differential gearing
- • Engine to wheel power transfer
- • Automatic vs manual systems
Industrial
- • Motor speed reduction
- • Conveyor belt systems
- • Machine tool applications
- • Robotic actuators