Wind Turbine Power Calculator
Enter the air density, rotor swept area, wind speed, and power coefficient to get the turbine's power output in watts — and see why output climbs with the cube of wind speed.
The full wind power equation
Enter the four inputs and the wind turbine power calculator returns the available power (½ρAv³Cp) in watts, the standard model for turbine output.
Use SI units
Air density in kg/m³, swept area in m², and wind speed in m/s give power in watts — divide km/h by 3.6 to get m/s before you start.
How much power does a wind turbine produce?
The wind power equation
A wind turbine power calculator turns four measurements — the air density, the rotor swept area, the wind speed, and the power coefficient — into the mechanical power the turbine can deliver, in watts. The wind carries kinetic energy, and the rotor extracts a fraction of it as it flows through the swept disc. The power available scales with how dense the air is, how large an area the blades sweep, and — most dramatically — the cube of the wind speed, while the power coefficient (Cp) caps how much of that wind power the machine actually captures. It is the number behind turbine siting, sizing, and the energy yield estimates that decide whether a site is worth building on.
Enter the air density, swept area, wind speed, and power coefficient to get the turbine's power output in watts instantly.
The available power is half the air density multiplied by the swept area, the cube of the wind speed, and the power coefficient.
P = ½ × ρ × A × v³ × CpThe wind speed is cubed, so it dominates the result: a small change in wind speed produces a large change in power. The air density (ρ) and swept area (A) enter to the first power, so they scale the output in direct proportion. The power coefficient (Cp) is the share of the wind's power the turbine actually captures, and it can never exceed the Betz limit of 0.593. Use kilograms per cubic metre, square metres, and metres per second and the power comes back in watts.
Suppose a turbine has a 100 m² swept area in air of density 1.225 kg/m³, a wind speed of 12 m/s, and a power coefficient of 0.4.
Cube the wind speed
12³ = 1,728 — the cubed speed that drives the power.
Multiply the steady factors
½ × 1.225 × 100 × 0.4 = 24.5 — half the air density times the area times Cp.
Combine
24.5 × 1,728 = 42,336 W (about 42.3 kW) — the turbine's power output.
The headline number is the mechanical power available at the rotor for that wind speed, in watts. The single most important insight is that power scales with the cube of the wind speed: double the wind from 12 to 24 m/s and the power does not double — it rises eightfold, from 42,336 W to 338,688 W. That is why turbine siting obsesses over a few extra metres per second of average wind, and why a site with steady strong wind is worth far more than its wind-speed advantage alone suggests. The power coefficient sets the ceiling on efficiency: no turbine can capture more than the Betz limit of 0.593 (about 59.3 %) of the wind's power, because the air has to keep moving to leave the rotor. Real machines reach roughly 0.35 to 0.45. Air density and swept area matter too, but only in direct proportion — wind speed is the lever that moves the result the most.
The equation is the standard theoretical model, but a few practical points are worth keeping in mind.
Theoretical available power, not delivered electricity
This calculator gives the mechanical power available at the rotor for the power coefficient you enter. It does not subtract the mechanical and electrical losses in the gearbox, generator, and power electronics, so the electricity actually delivered to the grid is lower. Keep your units consistent — kilograms per cubic metre, square metres, and metres per second — or the watts will be wrong, and convert km/h to m/s by dividing by 3.6 before you enter the wind speed.