Bike power to speed.

Worked example

A 100 kg rider and bike, Crr 0.005, CdA 0.6 m², 95% drivetrain, no wind. At 25 km/h (6.94 m/s) on the flat: air drag is ½ × 1.225 × 6.94³ × 0.6 = 123 W, rolling resistance is 6.94 × 100 × 9.8 × 0.005 = 34 W, so 157 W at the wheel and 165 W at the pedals. Solving the other way, 150 W at the pedals holds 24.1 km/h on the flat but only 7.9 km/h up a 6% grade. A 10 km/h tailwind lifts the flat speed to 30.5 km/h and a 10 km/h headwind cuts it to 18.4 km/h. Adding a 250 W motor and 120 W of pedalling on that 6% grade gives 18.0 km/h.

How it works

At steady speed, wheel power = air drag + rolling resistance + climbing. Air drag is ½ × air density × (air speed)² × ground speed × CdA. Rolling resistance is speed × mass × g × cos(grade angle) × Crr. Climbing is speed × mass × g × sin(grade angle). Pedal power is wheel power divided by drivetrain efficiency. Air density is 1.225 kg/m³ and g is 9.8 m/s².

The page solves for the speed where those three add up to the power you enter, by bisection. For an e-bike, pedal watts are multiplied by drivetrain efficiency and motor watts are taken as delivered at the wheel (motor and battery losses are not modelled).

Limits. Rolling resistance is held constant although it rises with speed; CdA and Crr are inputs and vary a lot between riders and tires; acceleration is zero. Treat results as a guide, good to roughly the accuracy of your inputs.

Sources and basis (opened 2026-10-08): Wikipedia, Bicycle performance, Power required section (the air drag, rolling resistance and climbing power formulas, total power divided by drivetrain efficiency; air density 1.225 kg/m³; low-speed rolling resistance coefficients of 0.003 to 0.006 for a variety of tires, rising about 50% at 10 m/s) and Mechanical efficiency section (drivetrain transmission 1–7% lower with derailleur gearing).

FAQ

How fast will 150 watts go on a bike?

With these defaults (100 kg total, Crr 0.005, CdA 0.6, 95% drivetrain) about 24.1 km/h on the flat, 7.9 km/h up a 6% grade, and 30.5 km/h with a 10 km/h tailwind.

Why does speed barely rise when I add watts on the flat?

Air drag grows with the cube of speed, so each extra km/h costs more power. On a steep climb, climbing power dominates and speed is closer to proportional to power divided by mass.

What CdA and Crr should I use?

The cited page gives low-speed Crr of 0.003 to 0.006 for a variety of tires. CdA is rider and position specific; 0.6 is a common assumption for an upright commuter, not a published standard.

Can I use it for an e-bike?

Yes. Enter your pedal watts and the motor power delivered at the wheel. Motor and battery efficiency are not modelled, and many e-bikes cut assist above a set speed.

How accurate is it?

It is only as accurate as the inputs. It ignores acceleration, braking, gusts and rolling resistance rising with speed, so expect differences of several percent on real rides.