Wind Turbine Power Output Calculator
Calculate wind turbine power using P = ½ρAv³ from blade diameter, wind speed, and air density.
Returns kilowatts and annual energy generation estimate.
Wind turbine power output is governed by a formula from fluid dynamics that relates power to the cube of wind speed — a relationship that makes wind resource quality critically important.
Wind power formula:
P = 0.5 × ρ × A × v³ × Cp
Variable definitions:
- P = Power output (watts)
- ρ (rho) = Air density — typically 1.225 kg/m³ at sea level, 15°C
- A = Rotor swept area = π × r² (where r = blade length in meters)
- v = Wind speed in m/s — this is the most critical variable
- Cp = Power coefficient (turbine efficiency)
The Betz limit: In 1919, physicist Albert Betz proved theoretically that no wind turbine can extract more than 59.3% of the wind’s kinetic energy (the “Betz limit”). Real turbines achieve 35–45% efficiency (Cp = 0.35–0.45) — about 75% of the theoretical maximum.
Why wind speed is everything: Power scales with v³, meaning wind speed is exponentially important.
- Wind at 8 m/s produces 8× more power than wind at 4 m/s
- Wind at 10 m/s produces 3.9× more power than wind at 7 m/s
- A 10% increase in wind speed yields a 33% increase in power output
Turbine size reference:
| Turbine Class | Rotor Diameter | Rated Power | Typical Use |
|---|---|---|---|
| Micro | 1–3 m | 0.1–1 kW | Off-grid, boats |
| Small residential | 3–10 m | 1–10 kW | Homes, farms |
| Medium commercial | 20–50 m | 100–500 kW | Small grids |
| Large utility | 80–130 m | 2–5 MW | Wind farms |
| Offshore giant | 130–220 m | 8–20 MW | Offshore farms |
Wind speed classes (Beaufort scale relevant range):
| m/s | mph | Description | Typical Power |
|---|---|---|---|
| 3–4 | 7–9 | Light breeze | Cut-in speed (turbine starts) |
| 5–7 | 11–16 | Gentle-moderate breeze | Low output |
| 8–11 | 18–25 | Fresh breeze | Good output |
| 12–15 | 27–34 | Strong breeze | High output |
| 15+ | 34+ | Near-gale | Rated/cut-out speed |
Most turbines reach their rated power at around 12–13 m/s and shut down above 25 m/s to prevent structural damage.
Worked example: A residential turbine with 5 m blade radius at 8 m/s wind speed:
- A = π × 5² = 78.5 m²
- P = 0.5 × 1.225 × 78.5 × 8³ × 0.40 = 9,797 W ≈ 9.8 kW