How the calculator works
Riding at a steady speed, the power you put into the pedals, minus about 2.5% lost in the chain, equals the power needed to push through three forces:
- Air drag: ½ × air density × CdA × speed². It grows with the square of speed, so it dominates on flat roads and descents.
- Rolling resistance: Crr × total weight × g. About 0.004 for a road tyre on smooth asphalt, twice that on rough roads.
- Gravity: total weight × g × the sine of the road angle. Zero on the flat, the biggest force on any real climb.
Multiply the sum by speed to get watts. The calculator works backwards from your power to the one speed where they balance. It leaves out wind and the energy to speed up your wheels, so it describes steady riding on a calm day.
What the numbers tell you
On the flat, most of your power goes into the air, which is why getting lower on the bike gains more than losing a few kilograms. Switch from hoods to drops in the calculator and 200 W goes from about 32 to 34 km/h. On a climb the split flips: past 6% or so, most of your watts go into lifting you and the bike, and power-to-weight is what counts. For climbs, the climbing time calculator uses the same model to predict your time and VAM.
Frequently asked questions
How fast is 200 watts on a bike?
On a flat road in still air, a 75 kg rider on a 9 kg bike riding 200 W goes about 34 km/h (21 mph) in the drops and about 32 km/h (20 mph) on the hoods, at 20 °C near sea level. Wind, rough roads or a more upright position bring that down.
How many watts does it take to ride at 30 km/h or 20 mph?
For a 75 kg rider on a 9 kg bike on a flat road with no wind, about 145 W in the drops holds 30 km/h, and about 170 W holds 20 mph (32 km/h). Riding 40 km/h takes about 310 W, because air drag rises with the square of speed and the power to overcome it with the cube.
Why does weight matter so little on the flat?
On a flat road your weight only adds rolling resistance, while air drag takes over 80% of your power at 30 km/h or more. In the calculator, adding 5 kg to a rider holding 250 W costs about 0.1 km/h on the flat but about 0.7 km/h on a 6% climb, where most of the power goes into lifting you.
How accurate is a power-to-speed calculator?
The physics is well tested: Martin and colleagues (1998) found this model predicted measured road power closely. The uncertainty is in the inputs. Your real drag area (CdA) can differ from the typical value for your position by 10% or more, and any wind changes the answer, so treat the result as a good estimate for a calm day.
What CdA should I use?
Typical drag areas are about 0.35–0.40 m² sitting up on the hoods, 0.30–0.35 m² in the drops and 0.25–0.30 m² on aero bars, with elite time-trialists near 0.20–0.22 m². The calculator uses 0.38, 0.32 and 0.27. Field testing or a wind tunnel can measure yours.
Sources
- Martin et al. (1998), Validation of a mathematical model for road cycling power, Journal of Applied Biomechanics
- Best Bike Split: CdA explained, with typical values by position
- Engineering ToolBox: rolling resistance coefficients
- Zwift Insider: rolling resistance (Crr) by tyre and surface
Air density uses the standard atmosphere for pressure at your altitude and the ideal-gas law for temperature.