About this site

bikegearing.com computes bicycle gearing from stated definitions. This page says how, so you can check the figures rather than trust them.

Who writes this

This site is written and maintained by Dennis Edinburgh, who is responsible for every figure on it and answers the correction address below.

The background is ordinary: mountain biking in spare time, and keeping the family's bikes serviced and repaired for cycling trips to the Lake District — several riders on several different bikes, with different wheel sizes and different crank lengths, which is where gearing stops being abstract: crank length is the one of those that gear inches cannot see. The working background is motors in industrial applications, driving belts, pulleys, gears and chains, which run on much the same ratio arithmetic a bicycle does.

That background is offered as where the habit of showing the working comes from, not as a reason to trust the figures — none of it is a credential, and none of it is something you can check from where you are sitting. Plenty of sites in this corner of the internet open with a paragraph of unverifiable background and leave it standing as the argument; this one would rather be judged on what you can actually check, which is the rest of this page: whether the relations are stated, whether the arithmetic follows from them, and whether the limitations further down are ones a less careful site would have left out.

What this site is

Four calculators, one per named computation: gear inches, gain ratio, speed at cadence, and the full gear table with gear range. Each has its own page because each is a different question, and a page that answers one question well is easier to check than a page that answers four.

The site exists because the gearing calculators already out there tend to answer a piece of the question and stop, and the intention here was the whole of the arithmetic on one site, with the derivation shown beside every figure. The whole of the arithmetic is a narrower promise than a complete guide to gearing, and a deliberate one: the two sections below on what these calculators deliberately do not do, and on where the figures stop being exact, are where that line is drawn.

How the figures are produced

Every result is computed from a relation written out on the page that uses it. Nothing is read from a stored rollout table. That matters because a rounded table is a cross-check, not a source: it can tell you a derivation is wrong, but a figure copied from one carries whatever rounding and whatever error the table already had, with no way to tell which.

Rolling circumference comes from ETRTO rim and tyre geometry rather than from a manufacturer's quoted figure. The wheel table is generated from two axes — bead seat diameter and nominal section width — rather than typed in, so a row cannot be individually wrong in a way the rest of the table hides. The derivation is stated in full on thegear inches page.

How the arithmetic is checked

The calculations are covered by an automated test suite that runs on every change. The acceptance figures in it are derived independently of the code from the defining relations, so a test agreeing with the implementation is not the implementation agreeing with itself.

The suite is also checked against deliberate faults: the arithmetic and the display logic are mutated one change at a time, and every mutation has to make the suite fail. A test that stays green against a broken function is not a test, however green the run looks, and this is how we find those.

What these calculators deliberately do not do

They do not tell you whether parts fit together. Shimano and SRAM publish authoritative compatibility information for their own components, free, and a third-party guess at it would be worse than their answer while looking just as confident. Gearing arithmetic is a computation with a right answer; compatibility is a manufacturer's specification, and we are not the manufacturer.

There is no advice layer. The site will tell you a gear is 32.4 gear inches; it will not tell you whether that is the right gear for you, because that depends on your legs, your terrain and your load, and none of those is a number this site has.

Where the figures stop being exact

Stated here rather than discovered by a reader who checks our working:

• The displayed chain does not always reproduce the displayed answer.Intermediate values are rounded for display, so recomputing by hand from the printed figures can land a digit out — 9.20 against a printed 9.19, for instance. The answer is computed at full precision and rounded once, at the end; the intermediates are shown to explain it, not to be multiplied together.
• The wheel data is bounded. Bead seat diameters 622, 584 and 559 mm, with nominal sections from 23 to 65 mm. Anything outside that is not yet covered rather than unavailable in principle.
• In miles-per-hour mode, development is still shown in metres. The unit toggle is scoped to speed only. It is a consequence of a deliberate decision to keep one conversion in one place, not an oversight.
• Duplicate-gear marks are a lower bound. On the gear table, the marks guarantee that every marked group really is within the tolerance — but grouping is anchored, so a genuine near-duplicate can sit just outside a group and go unmarked. The page says so where the marks appear.

Corrections

If a figure looks wrong, please say so: contact@bikegearing.com. It reaches Dennis Edinburgh directly. A wrong wheel row would corrupt three calculations at once, so a reported figure is checked against the standard rather than against our own table, and we will tell you what we found either way. More on what to include is on thecontact page.