Estimating speed from power — and why CdA dominates
Given a rider’s power, mass, gradient and a few environmental numbers, a physics model can estimate cycling speed with useful accuracy. The interesting part is what the model reveals: at road speeds on the flat, aerodynamic drag — captured by a single number, CdA — is by far the biggest lever. Here is the model, the reason the aero term wins, and how much it really moves your speed.
Open the Cycling Speed from Power calculatorWant the numbers for your own setup? The Cycling Speed from Power calculator applies the model below and lets you change CdA, gradient, mass and air density to see how each one moves your speed.
The physical model behind speed from power
To move a bike, the rider’s power has to overcome three resistances — rolling resistance, aerodynamic drag and gravity on any slope — while some of it is lost in the drivetrain. The widely used road-cycling model from Martin and colleagues expresses this as a balance between the power at the wheel and the power dissipated by each force acting at speed v.
- P
- rider power at the pedals, in watts
- Crr
- coefficient of rolling resistance (tyre and surface)
- m
- total mass of rider plus bike and kit, in kilograms
- g
- gravitational acceleration, 9.80665 m/s²
- θ
- road angle, where θ = atan(grade)
- v
- ground speed of the bike, in metres per second
- ρ
- air density, in kg/m³ (falls with altitude and rising temperature)
- CdA
- drag area — drag coefficient multiplied by frontal area, in m²
- v_wind
- head/tail wind component along the road (positive into a headwind)
- η
- drivetrain efficiency, typically about 0.97–0.98
The three bracketed terms are, in order, rolling resistance, aerodynamic drag and the gravity term for climbing or descending. Because speed appears on both sides — and inside the aero term as a square — you cannot rearrange it neatly for v. Solvers step the speed up or down until the power required matches the power supplied, which is exactly what the calculator does numerically.
Why the aero term dominates at speed
Look at how each term scales with speed. Rolling resistance and the gravity term rise roughly in proportion to v — double the speed, double that power. The aerodynamic term is different: it contains v² multiplied by another v, so the power needed to push air aside grows with the cube of speed.
That cubic growth is the whole story. Going from 30 to 36 km/h — a 20% increase — needs roughly 1.2³ ≈ 1.73× the aerodynamic power, about a 73% jump, while rolling and gravity power rise only 20%. At typical road speeds on the flat, the aero term is already the largest slice of the total, and it becomes overwhelmingly so as speed climbs. On a steep climb, where speed is low, the picture flips: the gravity term dominates and aerodynamics barely matters.
What CdA is, and typical values
CdA is the single number that packages up how aerodynamic you are. It is the drag coefficient (how slippery your shape is) multiplied by your frontal area (how big a hole you punch in the air), and it has units of square metres. A smaller CdA means less drag for the same speed. Since your position on the bike changes frontal area dramatically, CdA is largely something you control — unlike power, which is limited by fitness.
| Position | Indicative CdA (m²) | Indicative flat speed at 250 W |
|---|---|---|
| Sitting upright, hands on tops | ~0.40 | ~35 km/h |
| On the drops | ~0.30 | ~39 km/h |
| Optimised aero / TT position | ~0.25 | ~42 km/h |
The speeds above assume the same 250 W, flat road, no wind, sea-level air density and typical rolling resistance — only the position changes. Dropping CdA from 0.40 to 0.25 buys several km/h for no extra effort, which is why time-triallists obsess over position, helmets and clothing. These are indicative numbers only; your real CdA depends on your body size, kit and bike.
Why does CdA dominate speed from power?
Because CdA sits inside the term that grows with the cube of speed, a percentage change in CdA produces a bigger speed gain than the same percentage change in power. Roughly, once the aero term dominates, speed scales with the cube root of the power-to-CdA ratio — so halving CdA has a similar effect to nearly doubling power, but is usually far easier to achieve. On the flat, at road speeds, no other input moves the answer as much. Weight, by contrast, barely registers on the flat and only becomes decisive when you point the road uphill.
Why the estimate has a ±5–10% error band
A speed-from-power figure is a model, not a measurement, and several inputs are educated guesses:
- CdA and Crr are estimated. Unless you have done wind-tunnel or field testing, these come from typical values that may be off by 10% or more for your setup.
- Air density varies. ρ drops with altitude and rising temperature, and a hot day at elevation can be 10–15% less dense than a cold day at sea level — directly changing the aero term.
- Wind is rarely steady. Real wind shifts in speed and direction, and yaw angle changes effective CdA, so a single v_wind value is only an approximation.
Stack these up and a realistic estimate carries a ±5–10% band. That is still plenty to compare scenarios — upright versus drops, sea level versus altitude — which is what the model is genuinely good at.
Treat any speed-from-power figure as a like-for-like comparison between setups, not a forecast of how fast a specific ride will go. It is not a betting aid or a performance guarantee, and it cannot account for everything a real road throws at you.
Frequently asked questions
Is more power or better aerodynamics faster?
On the flat at road speeds, aerodynamics usually wins. Because the aero term grows with the cube of speed, halving your drag saves far more than an equivalent percentage gain in power. On steep climbs, where speed is low, power-to-weight matters more.
What is a typical CdA for a road cyclist?
Roughly 0.40 m² sitting upright, about 0.30 m² on the drops, and around 0.25 m² or lower in an optimised aero position. These are indicative figures; real values depend on body size, kit and bike.
How accurate is a speed-from-power estimate?
Expect a ±5–10% error band. CdA and rolling resistance are estimated rather than measured, air density changes with altitude and temperature, and wind is rarely steady, so the model compares scenarios rather than predicting a specific ride.
Related tools and reading
Cycling Speed from Power calculator
Enter power, mass, gradient and CdA to estimate speed — and see how much each input moves the answer.
ToolPower-to-weight calculator
Work out your W/kg — the metric that matters most when the road tilts uphill.
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. Checked 24 Aug 2026.