Wind Turbine Calculator – Calculating Wind Turbine Power Output

This useful wind turbine calculator is specially designed to compute the power output of wind turbines using P = 0.5 × Air Density × Area × Wind Speed^3 × (Efficiency / 100) formula.

When you’re planning to install a wind turbine on your property. The calculator would take into account factors such as:

• Wind speed in your area
• Turbine blade length
• Air density
• Turbine efficiency

By inputting these parameters, you can obtain a realistic estimate of the power your turbine could generate, aiding in decision-making and project planning.

Wind Turbine Calculator

Blade Radius (m)	Wind Speed (m/s)	Air Density (kg/m³)	Cp	Ng	Nb	Power Output (kW)
2	5	1.225	0.4	0.95	0.95	0.183
2	6	1.225	0.4	0.95	0.95	0.288
2	7	1.225	0.4	0.95	0.95	0.415
5	8	1.225	0.42	0.96	0.96	10.261
5	9	1.225	0.42	0.96	0.96	12.726
5	10	1.225	0.42	0.96	0.96	15.292
10	12	1.2	0.45	0.97	0.97	193.271
10	13	1.2	0.45	0.97	0.97	221.762
10	14	1.2	0.45	0.97	0.97	251.776
20	15	1.18	0.48	0.98	0.98	1,060
20	16	1.18	0.48	0.98	0.98	1,220
20	17	1.18	0.48	0.98	0.98	1,392
40	15	1.18	0.48	0.98	0.98	5,283
40	16	1.18	0.48	0.98	0.98	6,073
40	17	1.18	0.48	0.98	0.98	6,900

Wind Turbine Calculation Formula

The fundamental equation for calculating wind turbine power output is:

P = 0.5 ρ A v³ Cp Ng Nb

Where:

• P = Power output (watts)
• ρ (rho) = Air density (kg/m³)
• A = Swept area of the turbine blades (m²)
• v = Wind speed (m/s)
• Cp = Power coefficient (efficiency)
• Ng = Generator efficiency
• Nb = Gearbox bearing efficiency

Suppose we have a wind turbine with a blade radius of 5 meters, operating in an area with an average wind speed of 7 m/s. Assuming standard air density (1.225 kg/m³), a power coefficient of 0.4, and generator and gearbox efficiencies of 0.95 each:

Calculate swept area: A = π r² = 3.14 5² ≈ 78.5 m²

Apply the formula: P = 0.5 1.225 78.5 7³ 0.4 0.95 0.95 ≈ 5,890 watts or 5.89 kW

How to Calculate Wind Turbine Power?

• Determine wind speed: Use local weather data or conduct on-site measurements.
• Calculate swept area: Measure the turbine blade length and use A = πr².
• Assess air density: This varies with altitude and temperature but is often approximated at 1.225 kg/m³ at sea level.
• Estimate efficiency factors: Research the specific turbine’s power coefficient and mechanical efficiencies.
• Apply the formula: Input all values into the equation mentioned earlier.

For a small turbine with 2-meter blades in a 6 m/s wind:

Wind speed = 6 m/s

Swept area = π * 2² = 12.57 m²

Air density = 1.225 kg/m³

Assume Cp = 0.35, Ng = 0.9, Nb = 0.95

P = 0.5 1.225 12.57 6³ 0.35 0.9 0.95 ≈ 413 watts

How to Calculate Wind Turbine Efficiency?

The efficiency of a wind turbine is typically expressed through its power coefficient (Cp). This coefficient represents the ratio of actual power extracted by the turbine to the total power available in the wind.

The formula for the power coefficient is:

Cp = P / (0.5 ρ A * v³)

Where:

• Cp = Power coefficient (efficiency)
• P = Actual power output of the turbine (watts)
• ρ (rho) = Air density (kg/m³)
• A = Swept area of the turbine blades (m²)
• v = Wind speed (m/s)

Betz Limit

It’s important to note that there’s a theoretical maximum to wind turbine efficiency, known as the Betz Limit. According to this principle, no wind turbine can convert more than 59.3% of the kinetic energy of the wind into mechanical energy turning a rotor.

In other words:

Cp(max) = 16/27 ≈ 0.593 or 59.3%

Let’s calculate the efficiency of a wind turbine given the following parameters:

• Actual power output (P) = 5,000 W
• Air density (ρ) = 1.225 kg/m³
• Blade radius (r) = 5 m
• Wind speed (v) = 8 m/s
• Calculate swept area: A = π r² = 3.14 5² = 78.5 m²

Apply the efficiency formula:

Cp = 5,000 / (0.5 1.225 78.5 * 8³)
Cp = 5,000 / 19,673.6
Cp ≈ 0.254 or 25.4%

This turbine is operating at about 25.4% efficiency, which is well below the Betz Limit but not unusual for real-world conditions.

What Size Wind Turbine is Needed to Power a House?

• Average household energy consumption
• Local wind conditions
• Available space
• Zoning regulations

For a typical American household consuming about 10,000 kWh annually, a rough estimate would be a 5-15 kW turbine, depending on wind resources.

With average wind speeds of 5 m/s and a capacity factor of 25%:

Daily energy requirement = 10,000 kWh / 365 days ≈ 27.4 kWh/day

Hourly power needed = 27.4 kWh / 24 hours ≈ 1.14 kW

Accounting for capacity factor: 1.14 kW / 0.25 = 4.56 kW

In this case, a 5 kW turbine might suffice, but local conditions could necessitate a larger system.

How Much Power Does a 500W Wind Turbine Produce?

Assume a 500W turbine with 1.5-meter blades, rated at 12 m/s wind speed:

At rated speed (12 m/s): 500W (as designed)

At 6 m/s (half rated speed): P = 500W * (6/12)³ ≈ 62.5W (due to cubic relationship)

Annual energy production (AEP) estimation: Assume average wind speed of 5 m/s

Capacity factor ≈ 15% AEP = 500W 24 hours 365 days * 0.15 ≈ 657 kWh

How Much Power Can One Wind Turbine Generate?

A large offshore wind turbine with 80-meter blades:

Swept area = π 80² = 20,106 m²*

Rated wind speed = 15 m/s

Assuming Cp = 0.45, Ng = 0.98, Nb = 0.97

P = 0.5 1.225 20,106 15³ 0.45 0.98 0.97 ≈ 12 MW

The power generation capacity of a single wind turbine varies dramatically based on its size and design. Modern utility-scale turbines can generate several megawatts, while small residential turbines might produce a few kilowatts.

Sources / References

• U.S. Department of Energy: Wind Energy Technologies Office
• National Renewable Energy Laboratory: Wind Research
• American Wind Energy Association: Resources

Related Tools: