Bicycle Gear Ratio Calculator Formula

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

Use the Bicycle Gear Ratio Calculator

Formulas Used

Gear Ratio

ratio = gear_ratio

Development (per pedal turn)

development_m = gear_ratio * wheel_circumference_m

Speed at Cadence

speed_kmh = gear_ratio * wheel_circumference_m * cadence_rpm * 60 / 1000

Variables

VariableDescriptionDefault
chainring_teethFront Chainring Teeth50
cog_teethRear Cog Teeth17
wheel_circumference_mWheel Circumference(m)2.1
cadence_rpmPedaling Cadence(rpm)80
gear_ratioDerived value= chainring_teeth / cog_teethcalculated

How It Works

Bicycle Gear Ratios

The gear ratio determines how far the bike travels per pedal revolution and directly affects speed and effort.

Formula

Gear Ratio = Front Teeth / Rear Teeth

Development = Gear Ratio x Wheel Circumference

Speed = Development x Cadence x 60 / 1000

Higher ratios (big front, small rear) mean higher speed but more effort. Lower ratios (small front, big rear) are easier for climbing.

Worked Example

50-tooth chainring, 17-tooth rear cog, 2.1 m wheel, 80 rpm cadence.

chainring_teeth = 50cog_teeth = 17wheel_circumference_m = 2.1cadence_rpm = 80
  1. 01Gear ratio = 50 / 17 = 2.94
  2. 02Development = 2.94 x 2.1 = 6.18 m per pedal turn
  3. 03Speed = 6.18 x 80 x 60 / 1000 = 29.6 km/h

Ready to run the numbers?

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