Cycling Speed vs Power Calculator

Cycling speed vs power calculator

Ever wondered how many watts it takes to hold 35 km/h, or why a small climb feels so much harder than the flat? This calculator answers both using the standard cycling power model. Enter your weight, bike weight, the gradient, and a target speed, and it returns the power required plus a clear breakdown of where that power goes.

How the required power is calculated

Three resistive forces oppose your motion. The calculator computes each, multiplies by road speed to get power, and divides by drivetrain efficiency:

F_roll = Crr · m · g · cos(θ)        rolling resistance
F_grav = m · g · sin(θ)              gravity on the slope
F_aero = 0.5 · ρ · CdA · v²          aerodynamic drag
P = (F_roll + F_grav + F_aero) · v / 0.97

Here m is total mass, θ is the slope angle from the gradient, v is speed in metres per second, ρ is air density, Crr is rolling resistance, and CdA is your drag area. The defaults model good road tyres and a hoods riding position.

A practical comparison: flat vs climb

The same rider at the same speed on two different terrains shows the model at work.

For a 75 kg rider on an 8 kg bike (83 kg total) at 30 km/h (8.33 m/s) on the flat:

• Rolling resistance: 0.005 × 83 × 9.81 × 1.0 × 8.33 ≈ 34 W
• Aerodynamic drag: 0.5 × 1.225 × 0.32 × 8.33² × 8.33 ≈ 116 W
• Gravity: 0 W
• Total at pedals: approximately 155 W, or 1.87 W/kg

Now add a 6% gradient at the same speed:

• Rolling resistance: similar, about 34 W (cos of a small angle is close to 1)
• Aerodynamic drag: same 116 W (speed is unchanged)
• Gravity: 83 × 9.81 × sin(3.43°) × 8.33 ≈ 407 W
• Total at pedals: approximately 574 W, or 6.9 W/kg

Even world-class climbers cannot hold 6.9 W/kg for long at sustained effort, which is why steep climbs are ridden slowly — speed drops until the gravity term becomes affordable. Reducing mass is the fastest way to make steep climbs more manageable because the gravity term scales directly with total system weight.

The flat-road power curve, tabulated

Running the same 83 kg rider-plus-bike through the model at increasing flat speeds (defaults: Crr 0.005, CdA 0.32 m², sea-level air, 97% drivetrain) makes the cubic scaling visible:

Each additional 5 km/h costs more than the previous one — the last step from 40 to 45 km/h costs more than the entire power needed to ride at 25 km/h. This is the arithmetic behind drafting: sitting in a wheel typically spares a large slice of the aero term, which at 40 km/h is most of the total.

Air density is the quiet variable in the drag term. At around 2,000 m of altitude, ρ falls from 1.225 to roughly 1.0 kg/m³, and the same 40 km/h effort drops from ~324 W to ~274 W — why velodrome hour-record attempts favour altitude, and why the calculator’s sea-level default overstates the power needed for high-altitude riding. Heat and humidity nudge density too, but altitude is the dominant effect.

Using the breakdown to make training decisions

The power breakdown tells you where to focus improvement.

Primarily a flat rider? Aero drag dominates. A lower bar position, narrower elbows, a tighter-fitting jersey, and aero wheels each reduce CdA. Small CdA changes produce larger gains at high speed because power scales with the cube of velocity — a 5% CdA reduction saves more watts at 40 km/h than at 25 km/h.

Primarily a climber? Gravity dominates. Every kilogram removed from the rider or bike directly reduces the gravity term. Beyond weight, the only lever is power — raising FTP through structured training. Aerodynamics barely matters at climbing speeds.

Rolling terrain? All three forces matter. Rolling resistance from tyre choice and inflation pressure is often overlooked: high-quality road tyres at the right pressure can reduce Crr from 0.007 to 0.004, saving 20 to 30 watts at race effort.

Example and tips

Holding 32 km/h on the flat for a 75 kg rider on an 8 kg bike needs roughly 180 to 200 W, most of it fighting air. Add a 5% gradient at the same speed and gravity suddenly dominates, pushing the requirement well above threshold. To go faster on the flat, lower your CdA (aero position, tighter kit); to climb faster, reduce system weight or raise FTP. Both levers interact — a lighter and more aero rider needs less power for any given speed on any terrain.

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Sources and references

• Martin JC, Milliken DL, Cobb JE, McFadden KL, Coggan AR. Validation of a Mathematical Model for Road Cycling Power. Journal of Applied Biomechanics (1998) — the physics model (rolling, gravity, aerodynamic drag) this tool implements
• International Standard Atmosphere — sea-level air density (1.225 kg/m³) — the ρ default used in the drag term

Maintained by the Gera Tools editorial team. Defaults model good road tyres (Crr 0.005), a hoods position (CdA 0.32 m²), sea-level air, and 97% drivetrain efficiency in still air; real wind, surface, and position shift the result. Last reviewed 2026-07-02.