Bike gearing calculator

Wheel size comes from the ETRTO size printed on the tyre (e.g. 28-622 is a 700 × 28): the circumference is π × (bead-seat diameter + 2 × tyre width), Sheldon Brown’s approximation that a tyre is as tall as it is wide. If you have measured the rollout (mark the tyre, roll one turn with you sitting on the bike, measure), type it in — it beats any formula.

Gear inches = diameter of the drive wheel in inches × chainring ÷ cog (the old penny-farthing measure). Development (or rollout) = metres travelled per crank turn.

Gain ratio is Sheldon Brown’s: (wheel radius ÷ crank length) × (chainring ÷ cog) — how far the bike moves for each unit the pedal moves, so it also accounts for crank length. A gain ratio of 4 means the bike moves 4 mm per mm of pedal travel.

Speed = development × cadence; the Speed tab draws speed against cadence for every gear and tabulates 60–120 rpm.

Cross-chaining: on a double, the big ring with the two biggest cogs and the small ring with the two smallest are struck through (on a triple, three each side). They work, but the chain runs at its steepest angle — more friction, noise and wear — and there is nearly always the same gear on the other ring.

Compare adds drivetrain B on the same scale, with the steps (% jump to the next easier gear) of each cassette or hub and a table of lowest and top gear, range, distinct gears (non-cross-chained gears at least 3% apart) and the mean and largest step.

Chain length uses Park Tool’s formula, L = 2C + F/4 + R/4 + 1 inches (C the chainstay in inches, F the biggest ring, R the biggest cog), rounded to the nearest inch; an inch is two links.