Cycling Speed from Power Calculator (Watts to km/h on Hills and Flat)
How fast you will ride on a given gradient for the power you can hold, from your weight, rolling resistance and aerodynamics, and how long a climb will take.
Results
The dashed line marks the value you entered.
What this tool does
Pedal power goes into three things: lifting you and the bike (weight × gradient), rolling resistance and air, and the air term grows with the cube of speed. That makes the speed the root of a cubic equation, solved here exactly rather than by trial and error. On a steep climb nearly all the power goes into gravity, so time depends on watts per kilogram; on the flat, aerodynamics dominates, which is why a good position beats a light bike. Air density, a headwind and drafting are the main errors, so treat the answer as a plan.
Formula
η P = ½ ρ CdA v³ + m g (sin θ + Crr cos θ) v — the cubic is solved exactly for v
Variables
| Symbol | Meaning | Unit |
|---|---|---|
p | Power you can hold | W |
m | Rider, bike and kit together | kg |
gr | Road gradient (negative downhill) | % |
crr | Rolling resistance coefficient | — |
cd | Drag area CdA | m² |
rh | Air density | kg/m³ |
ef | Drivetrain efficiency | % |
ds | Length of the climb or ride | km |
V | Speed you will ride | km/h |
TM | Time for that length | min |
VAM | Climbing rate (VAM) | m/h |
AS | Share of power spent on air resistance | % |
Worked example
- Power you can hold200 W
- Rider, bike and kit together80 kg
- Road gradient (negative downhill)3 %
- Rolling resistance coefficient0.005
- Drag area CdA0.32 m²
- Air density1.225 kg/m³
- Drivetrain efficiency97 %
- Length of the climb or ride10 km
- Speed you will ride20.6 km/h
- Time for that length29.1 min
- Climbing rate (VAM)618 m/h
- Share of power spent on air resistance19 %
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.