Bicycle cadence and speed:
turning wheel revolutions into km/h

Pedal turns are not wheel turns

Ask three cyclists how fast they are pedalling and you may get three different meanings. Cadence normally means crank revolutions per minute: how many times your feet go round. The road, though, only cares about the wheel. Each turn of the rear wheel lays down one wheel circumference of tarmac, and that is the only thing that sets your speed.

Between the two sits the drivetrain. With a bigger chainring or a smaller sprocket, one pedal turn spins the rear wheel more than once. That is why 90 rpm in a low gear is a gentle crawl and 90 rpm in a high gear is a fast descent-style effort. Cadence is a measure of effort rhythm; speed needs the gear and the wheel as well.

The conversion below works from the wheel's side, which is also what a wheel-mounted sensor reports. If you only have crank cadence, the later section shows how to get to wheel rpm first.

The wheel rpm to km/h formula

The equation is only unit bookkeeping. Distance per revolution times revolutions per minute gives distance per minute, and the two constants move that into the units riders quote. Because it is a straight product, doubling the rpm doubles the speed, and a wheel with a 5 % larger circumference goes 5 % faster at the same rpm.

Worked example: a 2.1 m wheel at 200 rpm

A typical 700c road wheel with a 25 mm tyre rolls about 2.1 m per turn. Suppose a wheel sensor shows 200 revolutions per minute over a flat stretch.

For a quick cross-check, 420 metres a minute is 7 metres every second. Seven metres per second times 3.6 is 25.2 km/h, which matches. In miles per hour the same ride is about 15.7 mph (25.2 ÷ 1.609).

Getting wheel rpm from pedal cadence

Say you ride a 50-tooth chainring with a 17-tooth sprocket at 90 crank rpm. The ratio is 50 ÷ 17 = 2.94, so the wheel turns about 264.7 times a minute. With the same 2.1 m circumference that is 2.1 × 264.7 × 60 ÷ 1000, or roughly 33.4 km/h.

Holding a fixed ratio of 2.5 (for example 50 ÷ 20) shows how each step in cadence moves the speedometer:

Measuring your wheel circumference

Tyre size labels are nominal, and real circumference changes with tyre width, pressure and rider weight. The most reliable method is a roll-out: mark the tyre and the floor, sit on the bike, roll forward one full turn and measure the distance between marks. Most computers accept a value in millimetres.

A rough alternative is circumference = π × the overall wheel diameter, where diameter includes the tyre. Manufacturer charts give a decent default, but the numbers can be a couple of percent off.

• A 2 % circumference error gives a 2 % speed error: 2.14 m instead of 2.10 m turns the 25.2 km/h example into 25.7 km/h.
• Fitting wider tyres raises the circumference slightly, so re-enter the value after a tyre change.
• Measuring a soft tyre while sitting on the bike gives a smaller, more realistic value than measuring it unloaded.

Using the formula to choose gears for a target speed

The relationship also works backwards, which is where it earns its keep on a training plan. Suppose you want to hold 30 km/h at a comfortable 90 crank rpm on a 2.1 m wheel. Rearranging gives wheel rpm = speed × 1000 ÷ (60 × circumference), so 30 × 1000 ÷ (60 × 2.1) = 238.1 wheel rpm. Dividing by cadence gives the gear ratio you need: 238.1 ÷ 90 = 2.65.

A 50-tooth chainring with a 19-tooth sprocket gives 50 ÷ 19 = 2.63, close enough that you would be riding almost exactly 30 km/h at 90 rpm. A 53 ÷ 20 gives 2.65 and is even closer. Working this way you can see that a cassette's neighbouring sprockets change speed by about 7 to 8 % per step at the same cadence, so each shift is worth roughly 2 km/h around 28 km/h.

On a climb the same maths explains why a compact crankset helps. Dropping to a ratio of 1.5 at 70 rpm gives 105 wheel rpm, which is 13.2 km/h on a 2.1 m wheel: slow, but with a cadence your legs can actually sustain.

Calibrating a sensor and trusting the number

A wheel sensor is only as good as the circumference programmed into it. After setting a new value, ride a measured stretch, such as a road with kilometre markers, and compare. If the head unit reports 5.0 km but the markers say 4.9, the circumference is about 2 % too large. Scale it down by the same proportion: 2.100 × 4.9 ÷ 5.0 = 2.058 m.

Pedal-cadence sensors are separate devices and do not know about speed at all. A computer that shows both needs two inputs, and the speed it displays always comes from the wheel or from GPS. This is the reason a cadence sensor on its own can never give you speed, and the reason the gear ratio is needed in the conversion above.

When the number and the road disagree

The formula describes a rolling wheel. Coasting down a hill, the wheel still turns, so computed speed stays valid, but pedal cadence drops to zero while the road speed climbs. That is a reminder that you should always start from wheel data when you want speed.

GPS speed and wheel-sensor speed will also differ a little: GPS smooths positions and can lag at the start of a ride, while a wheel sensor depends on a correct circumference. Disagreement beyond roughly 1 to 2 % usually points to a wrong circumference setting. For a trip-level figure, divide distance by moving time instead, which an average-speed calculation does for you.

Finally, none of this tells you about power or effort. Two riders can both show 25.2 km/h, one with a tailwind at an easy 70 rpm and the other into a headwind grinding at 95 rpm.