Bike Gear Ratio Calculator

Compute bicycle gear ratio, gear inches, metres of development, and gain ratio from chainring, cog, wheel size, and crank length.

Inputs

Number of teeth on the front chainring.

Number of teeth on the selected rear sprocket.

Effective rolling diameter incl. tyre. 700×25c ≈ 668 mm; 26″ MTB ≈ 660 mm; 650b ≈ 632 mm.

Crank arm length, used for gain ratio. Common: 165–175 mm.

Pedalling cadence used to estimate road speed.

Result

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How to use this calculator

  • Enter the front chainring and rear cog tooth counts for the gear you want to analyse.
  • Enter the wheel-plus-tyre diameter in mm (use the common presets in the hint).
  • Enter the crank length for the gain-ratio calculation.
  • Optionally set a cadence to estimate road speed; read gear inches, ratio, development, and gain ratio.

About this calculator

Cyclists compare gears using several related measures, and this calculator reports all of them from your chainring teeth, rear cog teeth, wheel size, and crank length. The gear ratio is simply chainring divided by cog — how many wheel turns you get per pedal stroke. Gear inches, a measure inherited from the penny-farthing era, expresses that as the diameter of an equivalent direct-drive wheel; bigger numbers mean a harder, faster gear. Development (or rollout) is the distance the bike travels per complete pedal revolution. Gain ratio, devised by Sheldon Brown, refines gear inches by also accounting for crank length, making it the most accurate way to compare effort across bikes with different cranks. Enter a cadence and the tool also estimates your road speed in that gear.

How it works — the formula

Gear ratio = Chainring ÷ Cog Gear inches = Ratio × (Wheel Ø mm ÷ 25.4) Development = Gear inches × π × 0.0254 (m/rev) Gain ratio = (Wheel radius ÷ Crank length) × Ratio Speed (km/h) = Development × Cadence × 60 ÷ 1000

All measures start from the chainring-to-cog ratio. Gear inches scales it by wheel size; development converts that to distance; gain ratio reweights it by crank leverage.

Sources: Sheldon Brown — Gain Ratios · Sheldon Brown — Gear-inch & development theory

Worked examples

Example 1
50T / 17T, 700×25c (668 mm), 170 mm crank
Inputs:
chainring=50, cog=17, wheel=668, crank=170
Output:
77.3″ gear, 6.17 m development, gain 5.78
Example 2
53T / 12T, 700c
Inputs:
chainring=53, cog=12, wheel=668
Output:
ratio 4.42, 116.2″ gear inches
Example 3
34T / 28T compact climbing, 700c
Inputs:
chainring=34, cog=28, wheel=668
Output:
ratio 1.21, 31.9″ gear inches

Limitations

  • Wheel diameter must include the tyre for accurate gear inches.
  • Speed estimate assumes continuous pedalling at the entered cadence.
  • Does not model drivetrain losses or chainline cross-chaining.

Geometric gearing values; real speed also depends on rider power, wind, and gradient.

Frequently asked

What is the difference between gear inches and gain ratio?+
Gear inches measures a gear as the diameter of an equivalent old high-wheel bicycle wheel, ignoring crank length. Gain ratio (Sheldon Brown) divides the wheel radius by the crank length before multiplying by the gear ratio, so it captures the true mechanical advantage at the pedal. Gain ratio is better for comparing bikes with different cranks.
How do I calculate gear ratio?+
Divide the number of chainring teeth by the number of rear cog teeth. A 50-tooth chainring with a 17-tooth cog gives 50 ÷ 17 ≈ 2.94, meaning the wheel turns 2.94 times per pedal stroke.
What is development (rollout)?+
Development is how far the bike rolls forward for one full turn of the pedals. It equals gear inches × π converted to metres. A 77-inch gear has a development of about 6.17 metres per pedal revolution.
What wheel diameter should I enter?+
Use the effective rolling diameter including the tyre. Common values: a 700×25c road wheel is about 668 mm, a 26-inch mountain-bike wheel about 660 mm, and 650b (27.5″) about 632 mm. Larger tyres add a few mm.
Why does crank length matter?+
Longer cranks give more leverage at the pedal, effectively making a given gear feel easier. Gear inches ignores this, but gain ratio includes it — so two riders with the same gear inches but different crank lengths actually experience different efforts.
How is the speed estimate calculated?+
Speed = development (metres per pedal revolution) × cadence (revolutions per minute) × 60 ÷ 1000 for km/h. At 90 rpm in a 6.17 m gear, that is about 33 km/h (≈ 21 mph). It assumes no freewheeling.

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