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Cycling Speed & Power Estimator
Convert watts to speed (or back) from a physics model.
The physics
Riding power has to overcome three forces, all calculated at your speed: gravity on a gradient, rolling resistance from the tyres, and aerodynamic drag — which grows with the square of your speed through the air. The wheel power needed is the sum of those forces times your speed, then divided by drivetrain efficiency to get the power you actually put into the pedals.
The inputs that matter most
CdA (your drag area, around 0.32 m² in the drops) dominates on the flat and downhill; Crr (rolling resistance, ~0.004–0.006 on good tarmac) matters at all speeds; total weight dominates on climbs. A headwind is added to your ground speed before the drag term, so even modest wind costs a lot of watts.
Power → Speed vs Speed → Power
Going from speed to power is direct. Going the other way has no neat closed form — drag makes it non-linear — so the calculator binary-searches for the speed at which the required power matches your input. Treat results as a flat-road, steady-state estimate; real rides have corners, gusts, and acceleration the model ignores.
Questions
What does it account for?
The three forces that slow a cyclist: aerodynamic drag (from your CdA and air density), rolling resistance (from tyres and surface), and gravity on any gradient. It also applies a drivetrain efficiency loss.
What CdA should I use?
CdA is your drag area in m². Rough guides: ~0.4 sitting up, ~0.32 on the hoods, ~0.27 in the drops, and ~0.22 or lower in an aero tuck or TT position. The defaults give a sensible starting point.
Why is the math approximate?
Aero drag rises with the cube of speed, so solving speed from power needs iteration, and real-world wind, road surface, and position vary. Treat the output as a well-grounded estimate, not a wind-tunnel figure.