Bike Gear Ratio Calculator Formula

Understand the math behind the bike gear ratio calculator. Each variable explained with a worked example.

Use the Bike Gear Ratio Calculator

Formulas Used

Gear Ratio

ratio = round(gear_ratio * 100) / 100

Development

development = round(development_m * 100) / 100

Gear Inches

gear_inches = round(gear_ratio * wheel_diameter_mm / 25.4 * 100) / 100

Speed at 90 RPM

speed_at_90rpm = round(development_m * 90 * 60 / 1000 * 0.621371 * 100) / 100

Variables

VariableDescriptionDefault
chainring_teethChainring Teeth (front)(teeth)50
cog_teethCog Teeth (rear)(teeth)17
wheel_diameter_mmWheel Diameter(mm)700
gear_ratioDerived value= chainring_teeth / cog_teethcalculated
development_mDerived value= gear_ratio * wheel_diameter_mm * 3.14159 / 1000calculated

How It Works

How Bike Gear Ratios Work

Formula

Gear Ratio = Chainring Teeth / Cog Teeth

Development = Gear Ratio x Wheel Circumference

Development tells you how far the bike travels per pedal revolution. Higher gear ratios mean more distance per revolution but require more force.

Gear Inches

Gear inches is a traditional measure: Gear Inches = Gear Ratio x Wheel Diameter (inches).

Worked Example

A road bike with a 50-tooth chainring, 17-tooth rear cog, and 700mm wheels.

chainring_teeth = 50cog_teeth = 17wheel_diameter_mm = 700
  1. 01Gear ratio = 50 / 17 = 2.94
  2. 02Wheel circumference = 700 * 3.14159 = 2199 mm = 2.199 m
  3. 03Development = 2.94 * 2.199 = 6.47 m per pedal revolution
  4. 04At 90 RPM: 6.47 * 90 * 60 / 1000 = 34.93 km/h = 21.71 mph

Ready to run the numbers?

Open Bike Gear Ratio Calculator