Last updated: 2026-05-25

Gear Ratio

The gear ratio tells you how many times the driven gear rotates for every one rotation of the drive gear. Seeing it as a fraction — 53/13 rather than 4.0769 — makes it immediately comparable to other gears without mental arithmetic.

How to use

1. Enter the drive (input) teeth — the number of teeth on the gear that delivers power (chainring, motor gear, driving pulley).
2. Enter the driven (output) teeth — the number of teeth on the gear that receives power (cassette cog, wheel gear, driven pulley).
3. Read the Gear ratio as an exact fraction and the Ratio (decimal) for numeric comparison.

The formula

The fraction is shown in its original form (not reduced), because a 53/13 and a 52/12 are meaningfully different even though both approximate 4:1. The decimal is rounded to four places.

Interpreting the ratio

A ratio greater than 1 is called overdrive or speed-up; a ratio less than 1 is a reduction or mechanical advantage.

Cycling application

Road cyclists describe gears as chainring/cog combinations: a 53/11 is a very high gear (fast flat riding), while 34/32 is a very low climbing gear. The gear ratio determines rollout — how far the bike travels per crank revolution — when combined with the wheel diameter.

Example: 50-tooth chainring, 17-tooth cassette cog → ratio = 50/17 ≈ 2.94. For every full crank rotation, the rear wheel turns 2.94 times. With a 700×23 mm wheel (circumference ≈ 2.096 m), rollout = $2.94 \times 2.096 \approx 6.16$ m per pedal stroke.

Automotive and mechanical application

In transmissions, gear ratios above 1 (first gear, reverse) give torque multiplication at the cost of speed. Overdrive gears (ratio < 1) increase speed at the cost of torque. A typical automotive gearbox might have ratios like:

Compound gear trains

When two or more gear pairs are arranged in series (the driven gear of the first pair drives the second), multiply their individual ratios:

Example: Stage 1 is 40/10 (ratio 4), Stage 2 is 20/60 (ratio 1/3). Total = $4 \times \frac{1}{3} = \frac{4}{3}$.