How It Is Calculated
The Bicycle Gear Ratio Calculator determines key metrics for your bike's gearing. The calculations are based on the number of teeth on the chainring and cog, wheel diameter, cadence, and drivetrain efficiency.
Gear Ratio
The gear ratio is the number of times the rear wheel turns for each pedal revolution. It is calculated as:
Gear ratio = C / R
where C is the number of teeth on the chainring and R is the number of teeth on the cog. The result is rounded to two decimal places.
Gear Inches
Gear inches represent the effective diameter of the wheel in terms of gearing. It is calculated as:
Gear inches = D × Gear ratio
where D is the wheel diameter in inches. The result is rounded to one decimal place.
Speed
The theoretical speed (in miles per hour) is calculated from the wheel circumference, gear ratio, and cadence. The formula is:
Theoretical speed = (D × π × Gear ratio × N × 60) / 63360
where N is the cadence in revolutions per minute, π is approximately 3.141592653589793, and 63360 converts inches per minute to miles per hour. The actual speed is then obtained by multiplying by the drivetrain efficiency E:
Speed = Theoretical speed × E
The final speed is rounded to one decimal place.
Skid Patches
For fixed-gear or single-speed bikes, skid patches indicate the number of distinct positions where the rear wheel can skid. It is calculated as:
Skid patches = R / gcd(C, R)
where gcd is the greatest common divisor of the chainring and cog teeth. The result is rounded down to the nearest whole number.
Assumptions
- Assumes a standard bicycle drivetrain with no slippage.
- Wheel diameter is measured including tire.
- Cadence is constant.
- Efficiency factor accounts for drivetrain losses.
- Typical values: chainring 32 teeth, cog 16 teeth, wheel diameter 27 inches, cadence 80 rpm, efficiency 0.98.
Worked Example
Using the default inputs: Chainring teeth = 32, Cog teeth = 16, Wheel diameter = 27 in, Cadence = 80 rpm, Drivetrain efficiency = 0.98.
- Gear ratio = 32 / 16 = 2.00
- Gear inches = 27 × 2.00 = 54.0 in
- Theoretical speed = (27 × 3.141592653589793 × 2 × 80 × 60) / 63360 ≈ 12.86 mph. Actual speed = 12.86 × 0.98 ≈ 12.6 mph
- gcd(32, 16) = 16, so skid patches = 16 / 16 = 1
Practical Tips
- For a comfortable cadence, adjust your gear ratio so that your speed matches your desired effort. A gear ratio around 2 (as in the example) is common for casual riding.
- Higher gear inches mean harder pedaling but more speed per revolution; lower gear inches make climbing easier.
- Skid patches are important for fixed-gear riders: more patches allow more skid positions, reducing uneven tire wear. If you have only one patch, consider changing your chainring or cog.
- If you are also calculating motor torque for an e-bike conversion, you might find the Motor Torque Calculator useful.
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