Speed at cadence calculator

What speed at cadence means

A gear on its own says nothing about how fast you are going. It says how far you travel for each turn of the cranks. Add a cadence — how many times a minute you turn them — and the two together are a speed.

Turn the cranks once and the rear wheel turns as many times as the drivetrain ratio says: chainring teeth divided by cog teeth. Each of those wheel turns covers the tyre’s rolling circumference once. So the distance per crank revolution, which is called development, is the circumference multiplied by the ratio:

$$d=C\times \frac{n_{\text{c}}}{n_{\text{s}}}$$

and the speed is that distance repeated at whatever cadence you are pedalling, with the minutes turned into hours and the metres into kilometres:

$$v=\frac{dN\times 60}{1000}$$

Here $d$ is the development in metres, $C$ the rolling circumference, $n_{\text{c}}$ the chainring teeth, $n_{\text{s}}$ the rear cog teeth and $N$ the cadence in crank revolutions per minute.

The kilometres are the computed figure and the miles are converted from them. Everything on this site is worked out in metric and converted once, at the last step, for display. The mile is exactly 1.609344 km — 63360 inches of exactly 25.4 mm each, fixed by the 1959 international agreement — so that conversion is exact by definition and not a rounded factor. Switching the toggle changes how the answer is written down; it cannot change the answer.

It is a derived speed, not a measured one. It is what the gear covers if the wheel rolls without slipping and the cranks keep turning at exactly the cadence you entered. Nothing here knows about wind, gradient, drivetrain friction or the fact that nobody holds one cadence for an hour. Treat it as the speed that gear corresponds to, which is a real and useful thing to know, rather than as a prediction of your next ride.

Development, and why it is shown beside the speed

Development is the more fundamental of the two figures, and it is the one you can check. It is a distance you could mark on the ground: lift the rear wheel, turn the cranks through exactly one revolution, and the distance the tyre rolls is your development. On a 50 × 11 with a 700 × 28c tyre it is a little under ten metres.

9.68 m

development — the distance one turn of the cranks covers

4.55

wheel revolutions inside that distance

The speed depends on your cadence, and your cadence is a choice. Development does not — it is a property of the bike alone, so it is the figure to compare two setups with. Two bikes with the same development are the same gear, whatever either rider happens to be spinning at.

It is also the intermediate the speed is built from, which is why the page prints it rather than hiding it. If the speed looks wrong, development is where to look first: it is the number that carries the tyre and the tooth counts, and the cadence only scales it.

Where the rolling circumference comes from

The circumference is derived from the two ETRTO figures printed on your tyre’s sidewall, not tabulated: a bead-seat diameter $b$ and a nominal section width $s$ give a diameter of $b+2s$, and the circumference is that diameter multiplied by π.

$$C=\pi (b+2s)$$

This assumes the tyre’s section height equals its nominal width — an aspect ratio of about 1, which is an approximation rather than a measurement, and it is the same assumption behind every figure on this site. It matters more here than anywhere else on the site, because published rollout tables print a larger circumference for the same tyre than this derivation gives, and the speed follows the circumference exactly. The gear inches page states where the two differ and why.

If you want the accurate answer for your own wheel, measure a rollout: mark the valve’s position, roll the bike forward one wheel revolution with your weight on it, and mark it again. That distance is your real circumference, tyre pressure and rider weight included, and it is a better input than any sidewall figure. A rollout override is not on this page yet.