What is the Cycling Wattage Calculator?
This calculator estimates the mechanical power, in watts, a cyclist must produce to ride at a chosen speed. It models the three forces a rider must overcome: rolling resistance between the tyres and the road, aerodynamic drag against the air, and gravity when climbing a gradient. A drivetrain loss factor converts the power delivered to the wheel into the higher power you must produce at the pedals. It is a universal physics model and applies anywhere.
How to use it
Enter your total mass (rider plus bike and gear), your target speed in km/h, and the road grade as a percentage (use 0 for flat, negative for descents). The defaults for rolling resistance (Crr \(\approx 0.005\) for road tyres), aerodynamic drag area (CdA \(\approx 0.3\) m² for a road hoods position), air density (\(\rho = 1.225\) kg/m³ at sea level) and drivetrain loss (\(\approx 2\%\)) are reasonable for a road cyclist, but you can refine them. The result shows total pedal power plus a breakdown by force.
The formula explained
Power equals force times velocity. Rolling resistance force is \(C_{rr}\cdot m\cdot g\), aerodynamic drag force is \(0.5\cdot\rho\cdot C_dA\cdot v^{2}\), and climbing force is \(m\cdot g\cdot\text{grade}\). Multiplying each by speed \(v\) (in m/s) gives the power for each component. Note that aerodynamic power grows with the cube of speed, which is why going faster on the flat becomes so demanding.
$$P = \dfrac{\left(C_{rr}\,m\,g\,v\right) + \left(\tfrac{1}{2}\,\rho\,C_dA\,v^{3}\right) + \left(m\,g\,G\,v\right)}{1 - \dfrac{\text{Drivetrain Loss (\%)}}{100}}$$where
$$\left\{ \begin{aligned} v &= \dfrac{\text{Speed (km/h)}}{3.6}, \quad g = 9.8067 \\ m &= \text{Mass (kg)}, \quad G = \dfrac{\text{Grade (\%)}}{100} \\ C_{rr} &= \text{Crr}, \quad C_dA = \text{CdA} \\ \rho &= \text{Air Density} \end{aligned} \right.$$
Worked example
For a rider of 80 kg riding at 30 km/h (8.333 m/s) on flat ground with Crr 0.005, CdA 0.3, \(\rho\) 1.225 and g 9.8067: rolling \(= 0.005\cdot80\cdot9.8067\cdot8.333 \approx 32.69\) W; aero \(= 0.5\cdot1.225\cdot0.3\cdot8.333^{3} \approx 106.34\) W; gravity \(= 0\) W. Wheel power \(\approx 139.04\) W, and dividing by 0.98 for a 2% drivetrain loss gives about 141.9 W at the pedals.
FAQ
Why does the breakdown not include drivetrain loss? The three breakdown rows are wheel-side power; the headline total adds the drivetrain loss on top.
What CdA should I use? Roughly 0.4 upright, 0.3 on the hoods, 0.25 in the drops, and 0.20 or lower in a time-trial position.
Does wind matter? Yes — a headwind effectively raises the air speed in the aero term. This basic model assumes still air.
