Cycling Power Calculator (Watts Needed for a Speed)

How it works

P = [½ρ · CdA · (v + v_wind)² + m·g·cosθ·Crr + m·g·sinθ] × v ÷ (1 − 0.025) · ρ = 1.225 · e^(−altitude/8,434 m) · θ = arctan(grade)

A rider must overcome three forces: aerodynamic drag (which grows with the square of air speed, so it dominates on the flat above about 25 km/h), rolling resistance from the tyres (proportional to weight), and gravity on climbs (proportional to weight × gradient). Multiplying the total force by road speed gives power at the wheel, and a 2.5% drivetrain loss gives the power at the pedals that a power meter would read. CdA values for each position and Crr values for each surface are typical figures from field and wind-tunnel testing; your own numbers can differ by 10–20%.

Worked example

A 75 kg rider on a 9 kg bike rides 30 km/h (8.33 m/s) on the flat, on the hoods (CdA 0.32), with average tyres (Crr 0.005) at sea level: air drag = ½ × 1.225 × 0.32 × 8.33² × 8.33 = 113 W, rolling = 84 × 9.80665 × 0.005 × 8.33 = 34 W, so wheel power is 148 W and pedal power is 148 ÷ 0.975 = 152 W (2.02 W/kg).

Sources: Martin JC et al. (1998) Validation of a mathematical model for road cycling power. J Appl Biomech 14:276–291 · Wilson DG (2004) Bicycling Science, 3rd ed. MIT Press

Frequently asked questions