Cycling Speed from Cadence Calculator
Calculate your bicycle speed from pedaling cadence, wheel circumference, front chainring size, and rear sprocket size.
What this calculator is doing
Cycling cadence describes how many complete pedal revolutions a cyclist makes each minute and is normally expressed in revolutions per minute (RPM). Together with the selected bicycle gear and wheel circumference, cadence determines the theoretical speed of the bicycle.
The front chainring and rear sprocket determine the bicycle gear ratio:
\[ G = \frac{N_f}{N_r} \]
where \(N_f\) is the number of teeth on the front chainring and \(N_r\) is the number of teeth on the rear sprocket.
For every complete revolution of the pedals, the rear wheel rotates \(G\) times. If the wheel circumference is \(C\), the distance travelled during one pedal revolution is:
\[ d = C \cdot G \]
If the rider pedals at a cadence of \(n\) revolutions per minute, the bicycle travels a distance of:
\[ d_{\mathrm{minute}} = n \cdot C \cdot G \]
Converting this distance from metres per minute to kilometres per hour gives the bicycle speed:
\[ v = \frac{n \cdot C \cdot G \cdot 60}{1000} \]
where \(v\) is the bicycle speed in km/h, \(n\) is cadence in RPM, \(C\) is wheel circumference in metres, and \(G\) is the gear ratio.
A larger front chainring or a smaller rear sprocket produces a higher gear ratio and therefore a higher bicycle speed at the same cadence. Conversely, selecting an easier gear reduces speed while allowing the same cadence to be maintained.
The calculated value represents theoretical bicycle speed and assumes that the wheel rolls without slipping. Actual speed can differ slightly because of tire deformation, tire pressure, wheel circumference, and measurement tolerances.
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