Cycling Speed-to-Power Estimator
Estimate the power (watts) needed to hold a target cycling speed, split into rolling resistance, aerodynamic drag and climbing, using a physics-based model.
Formula: Power = Crr×mass×g×cos(θ)×v + mass×g×sin(θ)×v + 0.5×ρ×CdA×v³ (Martin et al., 1998 road-cycling power model)
Worked examples
- 30 km/h, 80 kg rider+bike, flat road, default CdA/Crr
A typical club-ride flat-road pace, where aerodynamic drag already dominates the power required.
- 20 km/h, 85 kg rider+bike, 6% climb
On a real climb, gravity overwhelmingly dominates the power required — aerodynamics barely matters at climbing speeds.
- 45 km/h, 75 kg rider+bike, flat road, aero position (lower CdA)
A time-trial-style scenario with a lower CdA (aero bars/position) — showing how much aerodynamics dominates at higher speed.
What this calculator does
This tool estimates the power, in watts, needed to hold a target cycling speed, and breaks that power down into its three physical components — rolling resistance, aerodynamic drag and (on a grade) climbing work. It's the reverse direction of this hub's power-to-weight calculator: instead of starting from a known power number, you start from a target speed and see what it would actually take to sustain it.
The physics model
The calculation follows the road-cycling power model validated by Martin, Milliken, Cobb, McFadden & Coggan in their 1998 paper "Validation of a Mathematical Model for Road Cycling Power" (Journal of Applied Biomechanics), the same model underlying most online cycling power calculators. Total power is the sum of three terms: rolling resistance (proportional to weight and a tire/road friction coefficient), gravity (proportional to weight and the sine of the road grade, zero on flat ground), and aerodynamic drag (proportional to your frontal-area drag coefficient, air density, and the cube of your speed).
Why aerodynamics dominates at speed, and gravity dominates on climbs
Aerodynamic power scales with the cube of speed — double your speed and drag power increases eightfold — which is why it quickly becomes the dominant cost at higher flat-road speeds. Gravity's power cost, by contrast, scales linearly with speed: on a climb, even a comparatively low speed requires substantial power simply to lift your body weight against the grade, and that gravitational cost swamps the (much lower at low speed) aerodynamic term. This is why aero equipment matters most for flat, fast riding, while weight matters most for climbing.
What CdA and Crr represent
CdA is your effective frontal area multiplied by your aerodynamic drag coefficient — a single number describing how "slippery" your body and bike position are. This tool defaults to 0.32 m², typical for a road cyclist riding with hands on the drops; an aggressive time-trial position can push CdA well below 0.25. Crr is the rolling-resistance coefficient between your tires and the road surface, defaulting to 0.005, typical for a good road tire on smooth asphalt — rougher surfaces or lower-quality tires push this higher.
What the model doesn't capture
This simplified model doesn't account for wind speed or direction (a headwind substantially increases effective aerodynamic power, a tailwind reduces it), drivetrain mechanical loss (typically 2–5% of power), or air density changes with altitude and temperature. Treat the output as a solid still-air, sea-level estimate rather than an exact real-world prediction — actual required power on any given ride will vary with conditions this model doesn't include.
Not medical advice
This is a physics-based training and pacing estimation tool, not medical or coaching advice. Build training intensity gradually and consult a coach or physician before undertaking demanding new training loads.
Frequently asked questions
- What assumptions does this model make?
- It models rolling resistance, aerodynamic drag and gravity (on a grade) from Martin et al.'s 1998 validated road-cycling power model. It doesn't model wind speed/direction, drivetrain loss (typically 2–5%) or altitude-adjusted air density, so treat the output as a solid estimate for still-air, sea-level conditions rather than an exact prediction.
- What is CdA and why does it matter so much?
- CdA is your effective frontal area times drag coefficient — essentially how aerodynamic your body and bike position are. Because aerodynamic power scales with the cube of speed, small CdA changes (an aero position, tighter clothing, a different bike) have an outsized effect at higher speeds, which is why time trialists obsess over it.
- Why does gravity dominate on climbs but aerodynamics dominate on the flat?
- Gravity's power cost scales with speed directly, while aerodynamic power scales with speed cubed — so at low climbing speeds, gravity's linear cost from lifting your weight against a grade outweighs drag, but at higher flat-road speeds, the cubic aerodynamic term quickly takes over.
- What CdA and rolling-resistance values should I use if I don't know mine?
- This tool defaults to CdA = 0.32 m² (a typical road cyclist riding in the drops) and Crr = 0.005 (a good road tire on smooth asphalt) — reasonable mid-range values for casual estimates. If you've had aero testing or know your tire's rated rolling resistance, override both for a more personalized estimate.
These calculators give general estimates from published formulas. They are not medical advice and do not account for your individual health; talk to a qualified professional before changing your diet or training.