Cycling Power Calculator
Estimate the cycling power required to maintain a given speed by accounting for climbing, rolling resistance, aerodynamic drag, and wind.
What this calculator is doing
The power required to move a bicycle at a constant speed is mainly determined by three forces: gravity when riding on a slope, rolling resistance between the tires and road, and aerodynamic drag.
The total required mechanical power can be estimated as:
\[ P = P_{\mathrm{gravity}} + P_{\mathrm{rolling}} + P_{\mathrm{aero}} \]
The power required to overcome gravity is:
\[ P_{\mathrm{gravity}} = m g v \sin(\theta) \]
where \(m\) is the combined mass of the rider and bicycle, \(g\) is gravitational acceleration, \(v\) is bicycle speed, and \(\theta\) is the road angle.
Road gradient is usually specified as a percentage rather than an angle. The corresponding road angle can be calculated from:
\[ \theta = \arctan\left(\frac{G}{100}\right) \]
where \(G\) is the road gradient in percent.
Rolling resistance is caused mainly by tire deformation and interaction between the tires and road surface. The rolling resistance power is:
\[ P_{\mathrm{rolling}} = C_{rr} m g v \cos(\theta) \]
where \(C_{rr}\) is the coefficient of rolling resistance.
Aerodynamic drag becomes increasingly important as speed increases. The aerodynamic power is:
\[ P_{\mathrm{aero}} = \frac{1}{2} \rho C_d A v_{\mathrm{air}}^2 v \]
where \(\rho\) is air density, \(C_dA\) is the effective aerodynamic drag area, and \(v_{\mathrm{air}}\) is the bicycle's speed relative to the surrounding air.
With a headwind, the relative air speed is greater than the bicycle's ground speed:
\[ v_{\mathrm{air}} = v + v_{\mathrm{wind}} \]
A positive wind value therefore represents a headwind, while a negative value can be used to represent a tailwind.
This calculator estimates the mechanical power delivered to the bicycle. Actual power measured at the pedals may be slightly higher because some energy is lost in the bicycle drivetrain.
The result should be considered an engineering estimate. Real cycling power can also be affected by riding position, changing wind conditions, tire pressure, road surface, acceleration, drivetrain efficiency, and differences in air density.
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