Cycling Speed from Power Calculator
Enter a steady power output and the physical conditions, and this tool solves for the ground speed that balances aerodynamic drag, rolling resistance and gradient. It compares scenarios — it does not predict a specific ride.
Model: Martin et al. (1998) road-cycling power • Checked 24 Aug 2026Enter power and conditions
| Speed | -- |
| Speed | -- |
| Pace | -- |
| Pace | -- |
How the speed is calculated
The tool uses the standard road-cycling power balance from Martin et al. (1998). At a steady speed, the power you put through the pedals must supply three resistances — rolling resistance, aerodynamic drag and the gravitational cost of the gradient — after drivetrain losses:
- P_total
- the steady power you enter, in watts
- C_rr
- rolling resistance coefficient (dimensionless)
- m
- total mass of rider, bike and kit, in kilograms
- g
- gravitational acceleration, 9.80665 m/s²
- θ
- road angle, atan(grade% / 100), in radians
- ρ
- air density, in kg/m³ (about 1.225 at sea level, 15 °C)
- CdA
- drag coefficient × frontal area, the effective aerodynamic area in m²
- v
- ground speed, the unknown solved for, in m/s
- v_wind
- headwind component in m/s (positive headwind, negative tailwind)
- η
- drivetrain efficiency, the fraction of pedal power reaching the wheel
For any non-negative headwind the required power rises monotonically with speed, so bisection on a single bracket is safe and converges to the unique solution. With a strong tailwind or a steep descent the power needed can fall to zero or below at low speed; in that case the tool reports a coasting note instead of forcing a number, because the model no longer describes a power-limited effort.
Worked example: 250 W on the flat
With the default assumptions — 80 kg total, CdA 0.30, Crr 0.004, ρ 1.225, η 0.975, no wind, 0% grade — the gradient term vanishes and the balance reduces to:
- Rolling:
0.004 × 80 × 9.80665 × v ≈ 3.14·vW - Aero:
½ × 1.225 × 0.30 × v³ ≈ 0.184·v³W - Set
(3.14·v + 0.184·v³) / 0.975 = 250and solve by bisection - Result:
v ≈ 10.47 m/s ≈ 37.7 km/h ≈ 23.4 mph
Notice that going from 250 W to 300 W (a 20% power increase) lifts speed only from about 37.7 to 40.3 km/h — roughly 7% — because aerodynamic drag scales with the cube of speed.
Speed at different power outputs (reference)
Flat road, default assumptions (80 kg total, CdA 0.30, Crr 0.004, ρ 1.225, η 0.975, no wind). Speed rises far more slowly than power — close to a cube-root relationship.
| Power | Speed (km/h) | Speed (mph) |
|---|
Accuracy notes and limits
±5–10% is realistic with estimated CdA and Crr, larger on windy days or unknown surfaces. CdA is the dominant unknown. This compares scenarios; it does not predict a specific ride. Real riding adds gusts, corners, gradient changes, drafting and position shifts that a steady-state balance cannot capture. Treat the output as an educational estimate, not a target. See our editorial policy.
Frequently asked questions
What CdA value should I use?
If you have not measured it, start from the guide values: about 0.40 upright, 0.30 on the drops, 0.25 in a committed aero position. Small changes matter — a 0.02 shift in CdA moves flat speed by roughly a kilometre per hour at typical power.
Why does more power barely raise my speed?
Aerodynamic drag grows with the cube of speed, so most of your power at road speeds is spent pushing air. Doubling speed needs roughly eight times the aero power, which is why speed responds so weakly to power once you are already moving quickly.
What happens on a steep descent or big tailwind?
The power needed to hold speed can drop to zero or below, meaning you would coast or need to brake rather than pedal. The tool detects this and shows a coasting note instead of an invented number.
Related tools and reading
FTP training zones calculator
Turn your Functional Threshold Power into the seven Coggan power zones as watt ranges.
Power-to-weight calculator
Convert power and body mass into watts per kilogram to compare with typical cycling tiers.
Sources
- Martin, J.C., Milliken, D.L., Cobb, J.E., McFadden, K.L. & Coggan, A.R. (1998). Validation of a Mathematical Model for Road Cycling Power. Journal of Applied Biomechanics, 14(3), 276–291. DOI 10.1123/jab.14.3.276 — the power-balance model used here.
- UCI technical regulations — referenced only for equipment and riding position, not for the physics of this estimate.