SOLVETUTORMATH SOLVER

Instrument MI-11-015 · Sports

Bike Gear Calculator

Enter wheel diameter, chainring teeth and cog teeth and this instrument returns the figure in gear inches — one number that lets you compare any two setups directly.

Instrument MI-11-015
Sheet 1 OF 1
Rev A
Verified
Type 11 — Cycling SER. 2026-11015

Gear inches

79.412

gear inches = wheel diameter x (chainring teeth / cog teeth)

The working Every figure verified twice
  1. gearInches = 27·(50 ⁄ 17) = 79.412
Worksheet log
  1. No entries yet — change an input to log a scenario.

How this instrument works

Gear inches trace back to the high-wheel 'penny-farthing' bicycle, where the front wheel was driven directly by the pedals and its diameter alone told you how far one pedal turn carried the bike. Chain-driven bikes broke that direct link, so the gear-inch system was invented to restore a single comparable number: it multiplies the wheel's diameter by that ratio, giving the diameter an equivalent direct-drive wheel would need to produce the same effect.

The result is a wheel-independent way to compare gearing. A 50-tooth chainring on a 17-tooth cog means something different on a small-wheeled folding bike than on a 29-inch mountain bike, but converting both to gear inches puts them on the same scale, which is exactly why the system has stayed in use across more than a century of drivetrain changes.

A larger gear-inch number means a harder combination to turn: more distance covered per pedal revolution, at the cost of needing more force. A smaller number means an easier one that spins more freely but covers less ground per stroke. Road bikes commonly run somewhere in the 30s up past 100 gear inches across their full range; a mountain bike's lowest climbing option can drop well under 20.

Gin=Dwheel×TchainringTcogG_{\text{in}} = D_{\text{wheel}} \times \dfrac{T_{\text{chainring}}}{T_{\text{cog}}}
wheel diameter — in inches, including the tyre · chainring teeth — front sprocket tooth count · cog teeth — rear sprocket tooth count · the result is a wheel-independent number for comparing gearing across different bikes.
  • Enter Wheel diameter (in) — 27 is a long-standing approximation for a 700c road wheel with tyre fitted; measure your own wheel and tyre together for precision.
  • Enter Chainring teeth — the tooth count of the front chainring currently engaged.
  • Enter Cog teeth — the tooth count of the rear cog currently engaged.
  • Read Gear inches — the single comparable number for that specific gear combination.
  • All three inputs must be greater than zero, or the instrument will prompt for a valid value.

Worked example — a 50×17 gear on a 27-inch wheel

Enter 27 into Wheel diameter (in), 50 into Chainring teeth and 17 into Cog teeth — a road bike in its 50-tooth big chainring paired with a 17-tooth cog. Gear inches reads 79.412.

That comes from 27 × (50 ÷ 17) = 79.4117647..., rounded here to 79.412. Compare that against a smaller-wheeled bike running the exact same 50×17 combination — say a 24-inch wheel — and the gear-inch figure would drop to 24 × (50 ÷ 17) = 70.588, a genuinely easier setup despite identical chainring and cog, which is exactly the comparison gear inches exists to make possible.

Questions

What counts as a 'big' gear versus a 'small' one in gear inches?

There's no fixed cutoff, but as a rough guide, road cyclists commonly cruise in the 60s to 80s of gear inches on flat ground, push into the 90s and above for descents or sprinting, and drop into the 30s or 40s for steep climbs. Mountain bike granny gears built for very steep, technical climbing can fall well below 20.

How is gear inches different from gear ratio?

Gear ratio is just chainring teeth divided by cog teeth, a dimensionless number that ignores wheel size entirely. Gear inches multiplies that ratio by wheel diameter, so it captures how far the bike actually travels per pedal revolution — two bikes sharing an identical ratio but different wheel sizes will still show different gear inches, and therefore different real-world gearing.

How does this relate to the bike-cadence-and-speed-calculator instrument on this site?

That instrument takes gear ratio, cadence and wheel circumference and returns an actual speed in km/h at a given pedalling rate. This page instead returns gear inches, a wheel-independent comparison number that doesn't need a cadence input at all — use it to compare hardness across bikes, and the speed calculator to find out how fast a specific cadence in a specific setup will carry you.

Why is 27 inches the default wheel diameter for a road bike?

A 700c road wheel with a typical tyre fitted measures close to 27 inches in overall rolled diameter, which is why 27 became the traditional shorthand figure in gear-inch calculations even though the rim itself is labelled '700c'. Measuring your actual wheel and tyre combination will give a slightly different, more precise figure.

How does mountain bike gearing compare in gear inches?

A mountain bike's low climbing option, something like a 34-tooth chainring on an 11-tooth cog on a 29-inch wheel, comes to a fairly high 29 × (34 ÷ 11) = 89.636 gear inches — that particular combination is actually a taller gear, not a climbing one, illustrating why checking the actual figure matters more than assuming from the tooth counts alone.

References