Bicycle Gain Ratio Calculator

The traditional 'gear inches' figure (wheel diameter in inches × chainring teeth ÷ rear cog teeth) compares gears by how far the wheel travels per pedal revolution, but it silently assumes every bike has the same crank length. Sheldon Brown's gain ratio fixes that by using a radius ratio instead of raw wheel size: gain ratio = (wheel radius ÷ crank length) × (chainring teeth ÷ rear cog teeth). A shorter crank on the same gearing and wheel gives a higher gain ratio, since a rider's foot travels a shorter arc for the same wheel rotation, effectively raising the mechanical leverage of that gear.

Gain ratio is a pure, unitless ratio — it comes out identical whether wheel diameter and crank length are both measured in millimeters or both in inches, as long as they're consistent, which this calculator's single unit toggle guarantees automatically. Gear inches is still reported alongside it for comparison, converting wheel diameter to inches internally regardless of which unit system is active, since that older figure is conventionally always expressed in inches.

Practically: for every unit of distance the pedal travels around its circular path, the bike moves forward that distance multiplied by the gain ratio — so a gain ratio of 6 means one full crank revolution (about 2π × crank length of pedal travel) moves the bike roughly 6 times that distance.