liminfoWind Power Calculator
Free web tool: Wind Power Calculator
Swept Area
5026.5 m²
Betz Limit (Cp)
0.593
Power Output
1.83 MW
Power at Different Wind Speeds
| Wind Speed (m/s) | Power |
|---|---|
| 3 | 49.29 kW |
| 5 | 228.21 kW |
| 7 | 626.22 kW |
| 10 | 1.83 MW |
| 12 | 3.15 MW |
| 15 | 6.16 MW |
| 20 | 14.61 MW |
| 25 | 28.53 MW |
Formula: P = 0.5 × ρ × A × v³ × Cp. Betz limit Cp = 0.593 is the theoretical maximum efficiency.
About Wind Power Calculator
The Wind Power Calculator computes the theoretical maximum power output of a wind turbine using the fundamental wind power formula: P = 0.5 × ρ × A × v³ × Cp. The three primary inputs are wind speed (m/s), rotor diameter (m), and air density (kg/m³, defaulting to the sea-level standard of 1.225 kg/m³). The swept area A is automatically calculated as π × (d/2)², and the power coefficient Cp is fixed at 0.593 — the Betz limit, which represents the theoretical maximum fraction of wind kinetic energy that any turbine can extract.
The tool outputs four values: the swept area in m², the Betz limit coefficient (0.593), the calculated power output at the entered wind speed, and a multi-speed power table covering 8 standard wind speeds from 3 m/s to 25 m/s. Results are automatically scaled to the most appropriate unit: watts (W) for small values, kilowatts (kW) for moderate outputs, and megawatts (MW) for large turbines at high wind speeds. This makes it easy to compare small residential turbines to large utility-scale wind generators.
Wind energy engineers, renewable energy students, site developers, and enthusiasts use this calculator to estimate potential turbine output for feasibility studies, educational projects, and energy system modeling. Understanding how power scales with the cube of wind speed (v³) is crucial — doubling the wind speed increases power output by a factor of 8. The Betz limit reminds users that no turbine can exceed 59.3% efficiency regardless of design. All calculations run client-side in the browser with no server communication.
Key Features
- Uses the standard wind power formula P = 0.5 × ρ × A × v³ × Cp with Betz limit Cp = 0.593
- Three adjustable inputs: wind speed (m/s), rotor diameter (m), and air density (kg/m³)
- Automatic swept area calculation from rotor diameter using A = π × (d/2)²
- Power output auto-scaled to appropriate unit: W, kW, or MW based on calculated value
- Multi-speed power table covering 8 wind speeds (3, 5, 7, 10, 12, 15, 20, 25 m/s)
- Displays Betz limit coefficient (0.593) to educate users on theoretical maximum efficiency
- Air density input allows accurate calculations for high-altitude or non-standard conditions
- 100% client-side processing — no data ever sent to a server, works offline after page load
Frequently Asked Questions
What is the wind power formula?
The wind power formula is P = 0.5 × ρ × A × v³ × Cp, where P is the power output in watts, ρ (rho) is air density in kg/m³, A is the rotor swept area in m², v is wind speed in m/s, and Cp is the power coefficient (maximum 0.593, the Betz limit). The formula shows that power is proportional to the cube of wind speed — doubling the wind speed increases power by a factor of 8.
What is the Betz limit?
The Betz limit (Cp = 0.593, or 16/27) is the theoretical maximum fraction of kinetic energy that a wind turbine can extract from the wind. It was derived by German physicist Albert Betz in 1919. No turbine can exceed this limit because some wind must continue flowing through the rotor disc to maintain airflow. Real turbines typically achieve Cp values of 0.35–0.50, somewhat below the theoretical Betz limit.
Why does power increase with the cube of wind speed?
Wind power depends on both the kinetic energy of the air (which is proportional to v²) and the mass flow rate of air through the rotor (which is proportional to v). Multiplying these gives power proportional to v³. This cubic relationship has a dramatic practical implication: a site with average wind speed of 10 m/s produces 8 times more power than one with 5 m/s average wind, even though the speed is only doubled.
What is the swept area and how does it affect power?
The swept area (A) is the circular area covered by the rotating blades, calculated as A = π × (D/2)² where D is the rotor diameter. Power is directly proportional to swept area — doubling the rotor diameter quadruples the swept area and therefore quadruples the power output at the same wind speed. This is why large utility-scale turbines have rotor diameters of 100–200 meters.
Why does air density affect wind power output?
Air density (ρ) appears directly in the power formula — denser air contains more mass and therefore more kinetic energy per unit volume. At sea level, standard air density is 1.225 kg/m³. At high altitudes (e.g., 2,000 m), air density drops to about 1.007 kg/m³, reducing power output by approximately 18% compared to sea level at the same wind speed. Temperature also affects air density: colder air is denser and produces slightly more power.
How much power does a typical residential wind turbine produce?
A small residential wind turbine with a rotor diameter of 3–5 meters at a typical wind speed of 7–10 m/s produces roughly 1–5 kW. This is sufficient to supplement but not fully power an average home. Large utility-scale onshore turbines (80–100 m diameter) at wind speeds of 10–12 m/s can generate 2–3 MW each. Offshore turbines can exceed 10–15 MW with rotor diameters above 200 meters.
What wind speed is needed for viable wind energy generation?
Most wind turbines start generating power (cut-in speed) at around 3–4 m/s. Rated power is typically reached at 11–14 m/s. At wind speeds above 25 m/s (cut-out speed), turbines shut down to prevent mechanical damage. Sites with average annual wind speeds below 5 m/s are generally not economically viable for wind energy; sites with 7 m/s or higher are considered good. Class 4–7 wind resources (7–10+ m/s) are ideal.
What is the difference between theoretical and actual turbine output?
This calculator uses the Betz limit (Cp = 0.593) as the power coefficient, representing the theoretical maximum. Actual turbines have Cp values of 0.35–0.50 due to aerodynamic losses, mechanical friction, electrical conversion losses, wake effects, and blade imperfections. To estimate real-world output, multiply the calculated result by (actual Cp / 0.593). For example, a turbine with Cp = 0.44 produces about 74% of the Betz-limited theoretical maximum.