Gear inches calculator

Work out gear inches from your chainring, cog and tyre — derived from ETRTO geometry, not copied from a rollout table.

Wheel and tyre

Chainring20 to 70 teeth

Rear cog9 to 52 teeth

—gear inches

Ratio: —
Wheel diameter: — mm

Source for 700 × 28c (28-622): ETRTO 28-622 — the designation on the tyre sidewall. Wheel diameter is derived from it, not tabulated — bead-seat diameter plus twice the nominal section width: $d = b + 2 s$

26.7 in: your wheel, 700 × 28c (28-622), geared 50 × 11
121.3 in: the direct-drive wheel that gives the same gear, pedals fixed to the hub

Both machines are drawn to one scale, from the same computation as the answer above — the chainring and cog included, at the ½-inch pitch every bicycle chain uses. The drawing zooms as you change the gear; the proportions never do. The dashed circle at the hub is the pedal circle, 172.5 mm cranks. No penny-farthing was ever built this big: leg length capped them around 60 inches, which is precisely why gears were invented. The big wheel is what this gear means, not a machine that existed — and the trailing wheel is a proportion rather than a computed length.

50 ÷ 11 = 4.55: turns of the rear wheel for one turn of the pedals
4.55 × 26.7 in = 121.3: gear inches — the ratio applied to the wheel it drives

A worked example, drawn to one scale: a 50-tooth chainring driving a 11-tooth cog. Every tooth is counted out, both sprockets are at their true pitch radius — half an inch of chain per tooth — and the centres sit a real 15.7-inch chainstay apart. That size difference is the ratio. This one keeps its numbers whatever you type above; the drawing beside the answer is the one that follows the form.

What gear inches means

Gear inches is the diameter, in inches, of a wheel that a direct-drive bicycle — a penny-farthing, with the pedals fixed straight to the hub — would need in order to give you the same gear. It is one number that folds the chainring, the cog and the wheel together, which is why it survived the century that made it obsolete as a description of actual machinery.

The drawing beside your answer above is this sentence made literal: your bicycle, and the direct-drive machine whose front wheel is your gear in inches, to one scale.

Multiply the wheel’s diameter, in inches, by the ratio of chainring teeth to cog teeth:

G = \frac{d}{25.4 mm} \times \frac{n_{c}}{n_{s}}

where $G$ is gear inches, $d$ the wheel diameter in millimetres, $n_{c}$ the chainring teeth and $n_{s}$ the rear cog teeth. The inch is exactly 25.4 mm by the 1959 international yard-and-pound agreement, so that divisor is a definition rather than a measurement.

Where our wheel diameter comes from

Every incumbent quietly picks a wheel figure without saying which. We derive ours, and state the relation:

d = b + 2 s

for a bead-seat diameter $b$ and a nominal section width $s$ — both printed on your tyre’s sidewall. A tyre marked 28-622 has $b = 622 mm$ and $s = 28 mm$ , so

d = 622 + 56 = 678 mm, \frac{d}{25.4} = 26.69 in

622 + 2 × 28 = 678 mm: bead seat, plus one section width at each end

Your wheel in section, to scale. The inner circle is the rim's bead seat — b, the number after the slash on your tyre — and the coloured band is the tyre, exactly one nominal section width s thick. Because the band sits at both ends of the span, s is counted twice, which is the whole of d = b + 2s. The band looks thin because it is: 28 mm on a 622 mm rim is about of the radius, and drawing it fatter to make room for the label would make the picture disagree with the arithmetic. Spoke count and hub size are drawn for recognition only and are not computed from anything.

The rolling circumference follows from the same diameter, which is why no circumference figure is stored anywhere on this site:

C = π d

This differs from common rollout tables, and we would rather say so than hide it. Published tables usually give 700 × 28c a circumference of 2136 mm; the derivation above gives 2130.0 mm. There are at least two candidate explanations and we have not established which dominates. The first is that the relation above assumes the tyre’s section height equals its nominal width — an aspect ratio of about 1, which is an approximation. The second is nominal-versus-actual width: a 28c tyre measures 29–30 mm on a modern 19–21 mm internal rim, and 2136 mm implies a section of about 29 mm. The 2136 figure’s own provenance is not stated anywhere we could find.

If you want the more accurate answer for your own wheel, measure a rollout: mark the tyre, roll the bike one full revolution with your weight on it, and measure the distance.

Reading the number

Higher is harder. A 50 × 11 on 700 × 28c is about 121 gear inches — a gear you would push downhill; a 34 × 34 on the same wheel is about 27, which is the one you want on a wall. Most riders find the gear they actually live in sits somewhere between 60 and 80 — but that band is editorial judgement about riders, not a measurement, and no derivation produces either number.

The range this calculator accepts is not a range we picked either. Its ends fall out of the declared limits on the three fields. The softest gear is the smallest chainring on the largest cog, turning the smallest wheel:

G_{min} = \frac{d_{min}}{25.4 mm} \times \frac{n_{c,min}}{n_{s,max}}

and the hardest is the same relation with every term at its other extreme:

G_{max} = \frac{d_{max}}{25.4 mm} \times \frac{n_{c,max}}{n_{s,min}}

Both are the relation from the top of this page, evaluated at the field limits rather than at anything you typed — so nothing the form will accept falls outside them, and no bound is stated anywhere as a figure of its own. Adding a wheel widens the range; it does not require a new number to be written down and kept in step.

Gear inches ignores crank length, which is the one thing it genuinely gets wrong: a longer crank is a longer lever, and two riders on identical gear inches with different cranks are not pushing the same gear. Gain ratio accounts for that, and it is the next calculator on this site.

How this page is produced

Method: Every figure this calculator produces is computed from the relation stated on this page — nothing is read from a stored rollout table, and the relation is written out so you can check the result rather than trust it. Where a number in the surrounding prose is editorial judgement rather than a derivation, the page says so where it appears.
Wheel data: Rolling circumference is derived from ETRTO rim and tyre geometry, not from a manufacturer's quoted figure. The derivation is stated on the gear inches page.
Verification: The arithmetic is checked against acceptance vectors derived independently of the code, in an automated test suite that runs on every change.
Last reviewed: 10 September 2026
Corrections: Found a figure that looks wrong? Tell us and we will check it against the standard and say what we found.