Case 1
- Air density
- 1.225kg/m³
- Rotor swept area
- 100m²
- Wind speed
- 12m/s
- Power coefficient Cp
- 0.4
42,336.00W
Open with these valuesWind Turbine Power Calculator
42,336.00W
Result: 42,336.00 WWind power rises with the cube of the wind speed, so doubling the wind gives eight times the output. A 100 m² rotor at 12 m/s with a power coefficient of 0.4 delivers about 42.3 kW. No rotor can pass 16/27 of the wind's power — the Betz limit, roughly 0.593.
The numbers at a glance
Held fixed: Air density 1.225 kg/m³, Rotor swept area 100.0 m², Wind speed 12.0 m/s.
| Power coefficient Cp | Result (W) |
|---|---|
| 0.300 | 31,752.00 |
| 0.350 | 37,044.00 |
| 0.400Your value | 42,336.00 |
| 0.450 | 47,628.00 |
| 0.500 | 52,920.00 |
Worked examples
Case 2
- Air density
- 1.2kg/m³
- Rotor swept area
- 50m²
- Wind speed
- 8m/s
- Power coefficient Cp
- 0.45
6,912.00W
Open with these valuesCase 3
- Air density
- 1.225kg/m³
- Rotor swept area
- 100m²
- Wind speed
- 12m/s
- Power coefficient Cp
- 0.593
62,763.12W
Open with these valuesHow it's calculated
P = ½ × ρ × A × v³ × Cp
- StepAir density: 1.225 kg/m³ at sea level and 15 °C, less at altitude.
- StepSwept area: π × r² for a rotor of radius r, in square metres.
- StepWind speed in m/s — divide km/h by 3.6 — and it enters cubed.
- ResultPower coefficient: 0.35 to 0.45 in practice, never above 0.593.
Reference table
| Density, area, speed, Cp | What it shows | Power |
|---|---|---|
| 1.225, 100, 0, 0.4 | No wind, no power | 0 |
| 2, 1, 1, 0.5 | Unit check: one square metre at 1 m/s | 0.5 |
| 1.225, 1, 10, 0.5 | One square metre at 10 m/s | 306.25 |
| 1.2, 50, 8, 0.45 | Small turbine on a warm day | 6912 |
| 1.225, 100, 12, 0.4 | Realistic rotor and coefficient | 42336 |
| 1.225, 100, 12, 0.593 | Same rotor at the Betz limit | 62763.12 |
Questions
How do I calculate wind turbine power?
Use the wind power equation P = ½ × ρ × A × v³ × Cp. Multiply half the air density by the swept area, the cube of the wind speed and the power coefficient. With kg/m³, m² and m/s the answer is in watts — 1.225, 100 m², 12 m/s and 0.4 come to about 42.3 kW.
What is the power coefficient Cp?
It is the fraction of the wind's power the turbine actually extracts, between 0 and 1. It can never exceed the Betz limit of 0.593, because the air has to keep moving to leave the rotor. Modern utility-scale turbines reach roughly 0.35 to 0.45 in practice.
What is the Betz limit?
It is the theoretical maximum share of the wind's kinetic energy a turbine can turn into mechanical power: 16/27, about 59.3 %. Albert Betz derived it in 1919 for any open-flow rotor, since slowing the air completely would stop the flow through it. It is a derived bound rather than a measurement, which is why the coefficient field here stops at 0.593.
Why does doubling the wind speed give eight times the power?
Because the wind speed enters cubed. Power scales with v³, so twice the speed is 2³ = 8 times the output and three times the speed is 27 times. That is why a few extra metres per second of average wind decide whether a site is worth building on.
Where does 1.225 kg/m³ come from?
It is the air density of the International Standard Atmosphere at sea level, 15 °C and 1013.25 hPa. Warmer air and higher ground are thinner, so the same rotor yields less; on a hot day at 1000 m you might use about 1.1 kg/m³ instead. The field is editable for exactly that reason.
Which units should I use?
SI throughout: kg/m³ for density, m² for the swept area and m/s for the wind speed, which gives power in watts. If your wind speed is in km/h, divide by 3.6 first. A thousand watts make one kilowatt, so 42336 W is 42.3 kW.
Sources and last check
Information, not professional advice.