What is the Betz limit for wind turbines?

The Betz limit states that no wind turbine can capture more than 59.3% of the kinetic energy in the wind. This corresponds to a maximum power coefficient Cp of 0.593. Real commercial turbines typically operate with Cp values between 0.35 and 0.5 at their optimal wind speeds.

Why does wind speed matter so much for wind power?

Wind power scales with the cube of wind speed (v³). This means that if wind speed doubles, the theoretical power increases by a factor of eight. Small changes in average wind speed therefore have a very large impact on annual energy production and project economics.

What is capacity factor in wind energy?

Capacity factor is the ratio of actual energy produced over a period to the energy that would be produced if the turbine ran at its rated power 100% of the time. It is usually expressed as a percentage. Modern onshore wind farms often have capacity factors between 25% and 45%, while good offshore sites can exceed 50%.

How many homes can a wind turbine power?

The number of homes powered is calculated by dividing the turbine's annual energy production by the average household electricity use. For example, if a turbine produces 10,000,000 kWh per year and the average home uses 10,000 kWh per year, it can power about 1,000 homes. The calculator lets you adjust the average household consumption to match your country or region.

Wind Turbine Power Calculator

Estimate theoretical wind power, turbine electrical output, annual energy production, and number of homes powered using rotor size, wind speed, and efficiency.

Wind Turbine Power & Energy Calculator

Presets:

Rotor & Wind

Input mode

Diameter Radius

Rotor diameter

Unit

Wind speed

Unit

Air density ρ (kg/m³)

≈1.225 at sea level, 15°C

Environment

Efficiency & Capacity

Power coefficient Cp (Betz limit 0.593)

0.45

Modern turbines typically 0.35–0.50 at optimal speed.

Drivetrain & generator efficiency η

0.90

Includes gearbox, generator, and electrical losses.

Turbine rated power

In kW (e.g., 3000 = 3 MW)

Capacity factor (%)

Typical: onshore 25–45%, offshore 40–60%

Avg. household use (kWh/year)

US ≈10,000; EU often 3,000–5,000

Hours per year

8760 = 24×365

Results

Instantaneous Power at Given Wind Speed

Rotor swept area A: –
Wind speed (normalized): –
Theoretical wind power P_wind: –
Mechanical power at rotor P_rotor: –
Electrical power output P_elec: –

Annual Energy & Homes Powered

Rated power: –
Capacity factor: –
Annual energy E: –
Homes powered (approx.): –

How this wind turbine power calculator works

This calculator combines the fundamental wind power equation with realistic efficiency factors used by turbine manufacturers and energy agencies. It lets you:

Estimate the instantaneous power at a given wind speed.
Estimate annual energy production from rated power and capacity factor.
Convert that energy into an approximate number of households powered.

1. Power available in the wind

The kinetic power in the wind flowing through the rotor area is:

\( P_{\text{wind}} = \tfrac{1}{2}\,\rho\,A\,v^3 \)

\( \rho \) = air density (kg/m³)
\( A \) = rotor swept area (m²) = \( \pi r^2 \)
\( v \) = wind speed (m/s)

Note the cube of wind speed: if wind speed doubles, theoretical power increases by a factor of 8.

2. Rotor swept area from diameter or radius

You can enter either rotor diameter or radius. The calculator converts to radius in meters and computes:

\( r = \frac{D}{2} \quad\Rightarrow\quad A = \pi r^2 \)

3. Betz limit and power coefficient \( C_p \)

No turbine can extract all the power in the wind. The Betz limit shows that the maximum fraction is 59.3%, so:

\( C_{p,\text{max}} = 0.593 \)

Real turbines have a power coefficient \( C_p \) that varies with wind speed and blade design. Typical peak values:

Small turbines: \( C_p \approx 0.25–0.4 \)
Modern utility-scale onshore: \( C_p \approx 0.4–0.5 \)
Offshore: similar or slightly higher at optimal speeds

The mechanical power at the rotor is:

\( P_{\text{rotor}} = C_p \, P_{\text{wind}} = C_p \,\tfrac{1}{2}\,\rho\,A\,v^3 \)

4. Drivetrain and generator efficiency

Gearbox, generator, and electrical components introduce additional losses. We model them with an overall efficiency \( \eta \) (typically 0.85–0.95 for large turbines):

\( P_{\text{elec}} = \eta \, P_{\text{rotor}} = C_p \,\eta\,\tfrac{1}{2}\,\rho\,A\,v^3 \)

The sliders for \( C_p \) and \( \eta \) let you explore the impact of design improvements and losses on electrical output.

5. Annual energy and capacity factor

Instantaneous power at one wind speed does not tell you annual production. Instead, we use the turbine's rated power and an assumed capacity factor:

\( E_{\text{year}} = P_{\text{rated}} \times \text{CF} \times \text{hours\_per\_year} \)

\( P_{\text{rated}} \) in kW (e.g., 3000 kW = 3 MW)
CF = capacity factor (0–1)
hours_per_year = usually 8760

Capacity factor captures the effect of wind variability, cut-in/cut-out speeds, and downtime. Typical values:

Older onshore sites: 20–30%
Modern onshore wind farms: 30–45%
Good offshore projects: 45–60% or more

6. Homes powered

To estimate how many homes a turbine can power, we divide annual energy by average household consumption:

\( \text{Homes} \approx \dfrac{E_{\text{year}}}{E_{\text{home}}} \)

\( E_{\text{year}} \) = annual turbine energy (kWh/year)
\( E_{\text{home}} \) = average household use (kWh/year)

The default 10,000 kWh/year is close to the US average. You can change this to match your country.

Typical example: 3 MW onshore turbine

As a sanity check, consider a 3 MW onshore turbine with a 120 m rotor diameter, average wind speed of 8 m/s, \( C_p = 0.45 \), \( \eta = 0.9 \), and capacity factor 35%:

Rotor area \( A \approx 11{,}310 \,\text{m}^2 \)
Instantaneous electrical power at 8 m/s ≈ 2.5–3 MW (near rated)
Annual energy \( E_{\text{year}} \approx 3{,}000 \times 0.35 \times 8{,}760 \approx 9.2 \,\text{GWh} \)
At 10,000 kWh/home/year, that’s ≈ 920 homes powered on average

Limitations and good practice

This tool uses a single average wind speed and a single capacity factor. Detailed assessments use full wind speed distributions (e.g., Weibull) and turbine power curves.
Air density varies with altitude, temperature, and humidity. For precise work, use site-specific meteorological data.
Always compare results with manufacturer power curves and certified performance data when evaluating real projects.

Frequently asked questions

How do you calculate wind turbine power?

We start from the physical power in the wind, \( P_{\text{wind}} = \tfrac{1}{2}\rho A v^3 \), then apply a power coefficient \( C_p \) (limited by the Betz limit) and an overall efficiency \( \eta \) for mechanical and electrical losses: \( P_{\text{elec}} = C_p \eta \tfrac{1}{2}\rho A v^3 \). The calculator handles unit conversions and these multipliers for you.

What is the Betz limit?

The Betz limit is a theoretical result showing that no wind turbine can capture more than 59.3% of the kinetic energy in the wind. It arises from conservation of mass and momentum in the air stream. In practice, modern turbines reach peak \( C_p \) values around 0.45–0.5 at their optimal operating point.

Why does wind speed matter so much?

Because power scales with the cube of wind speed, small changes in average wind speed have a huge impact on energy yield. For example, increasing average wind speed from 7 m/s to 8 m/s increases theoretical power by about 50%. That’s why careful site assessment and hub-height wind measurements are critical.

What is a good capacity factor for a wind farm?

It depends on location and technology. Older onshore projects might have 20–30% capacity factors, while modern onshore wind farms in good sites often reach 30–45%. Offshore projects, with stronger and more consistent winds, can exceed 50%. The calculator lets you test different assumptions quickly.

Can this calculator replace a professional energy assessment?

No. It is an educational and preliminary sizing tool. Professional assessments use long-term wind measurements, turbulence and shear analysis, detailed turbine power curves, wake effects, and probabilistic models. Use this calculator for understanding orders of magnitude and exploring scenarios, not for final investment decisions.