Cycling Power-Speed Calculator
Enter your power output, total weight, CdA, and gradient. It solves the cycling power equation and returns your expected speed. Same physics as Best Bike Split. No subscription.
How the calculation works
Your speed at a given power comes down to three forces: aerodynamic drag, rolling resistance, and gravity. The calculator finds the velocity v where:
P = Faero × v + Froll × v + Fgrav × v where: Faero = 0.5 × ρ × CdA × v² (air resistance) Froll = Crr × m × g × cos(θ) (rolling resistance) Fgrav = m × g × sin(θ) (gravity component) ρ = air density (kg/m³), adjusted for altitude θ = arctan(gradient / 100)
Air density uses the barometric formula: ρ = 1.225 × e(-0.0001184 × altitude). At 2,000 m that's roughly ρ = 0.999 kg/m³, about 18% lower than sea level. That's why the same watts produce more speed at altitude.
The equation is cubic in v, so the calculator uses Newton-Raphson to solve it numerically. It converges in 3–5 iterations.
Typical CdA values
| Position | CdA (m²) |
|---|---|
| Upright / city bike | 0.45–0.55 |
| Road bike, hoods | 0.36–0.42 |
| Road bike, drops | 0.30–0.36 |
| Road bike, aggressive drops | 0.26–0.32 |
| Time trial / triathlon | 0.20–0.26 |
| World-class TT position | 0.18–0.21 |
Use the CdA Estimator to get a field-test value specific to your position.
