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Wind Turbine Power Calculator

Calculate the theoretical and actual power output of a wind turbine using the wind power equation. Enter rotor radius, wind speed, and power coefficient.

Reviewed by Christopher FloiedPublished Updated

This free online wind turbine power calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.

Range: 0.1 – 100

Unit: m

Radius of the turbine rotor (blade length) in metres

Range: 0.1 – 50

Unit: m/s

Average wind speed at hub height in metres per second

Range: 0.01 – 0.593

Fraction of wind energy captured (Betz limit = 0.593, typical = 0.35-0.45)

Results

Swept Area

5026.5 m²

Power Output

1231.5 kW

How to Use This Calculator

1

Enter your input values

Fill in all required input fields for the Wind Turbine Power Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.

2

Review your inputs

Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.

3

Read the results

The Wind Turbine Power Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.

4

Explore parameter sensitivity

Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.

When to Use This Calculator

  • •Use the Wind Turbine Power Calculator when you need accurate results quickly without the risk of manual computation errors or unit conversion mistakes.
  • •Use it to verify calculations made by hand or in spreadsheets — an independent check can catch errors before they lead to costly decisions.
  • •Use it to explore how changing input parameters affects the output — a quick way to develop intuition and identify the most influential variables.
  • •Use it when collaborating with others to ensure everyone is working from the same numbers and applying the same assumptions.

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About Wind Turbine Power Calculator

The Wind Turbine Power Calculator computes the mechanical power available from a horizontal-axis wind turbine using the fundamental wind power equation. Wind energy is proportional to the cube of wind speed, meaning that a small increase in wind speed produces a dramatic increase in power output. The calculator uses standard sea-level air density and lets you specify the rotor radius, wind speed, and power coefficient. The power coefficient represents the fraction of the total kinetic energy in the wind that the turbine can actually capture. The theoretical maximum, known as the Betz limit, is approximately 59.3%. Real turbines typically achieve 35-45%. This tool is useful for preliminary site assessments, educational purposes, and comparing turbine designs.

The Math Behind It

Wind carries kinetic energy proportional to the mass of air passing through a given area and the square of its velocity. The power in the wind passing through a circular area A at speed v is P_wind = 0.5 * rho * A * v^3, where rho is air density (1.225 kg/m^3 at sea level and 15 degrees C). The cubic relationship between wind speed and power is the most important fact in wind energy. Doubling the wind speed increases available power by a factor of eight. This is why site selection with consistently strong winds is critical and why small differences in average wind speed between sites can make or break a project's economics. The Betz limit, derived by German physicist Albert Betz in 1919, proves that no wind turbine can capture more than 16/27 (approximately 59.3%) of the kinetic energy in the wind. This theoretical maximum arises because the turbine must allow some air to pass through; if it captured all the energy, the air would stop and no more could flow in. Real turbines have a power coefficient (Cp) that varies with wind speed, typically peaking at 0.35-0.45 for modern designs. Additional losses from the gearbox, generator, and power electronics further reduce the electrical output to roughly 25-35% of the total wind energy. Air density decreases with altitude and temperature. At 1,000 metres elevation, density drops to about 1.112 kg/m^3, reducing power by roughly 9%. Hot climates also see lower density. For precise calculations, adjust rho using the ideal gas law. The capacity factor of a wind turbine, typically 25-45% for onshore and 35-55% for offshore installations, represents the actual annual energy production divided by the theoretical maximum if the turbine ran at full power continuously.

Formula Reference

Wind Power Equation

P = 0.5 * ρ * A * v³ * Cp

Variables: ρ = air density (1.225 kg/m³ at sea level), A = πr² swept area, v = wind speed in m/s, Cp = power coefficient

Worked Examples

Example 1: Medium Onshore Turbine

A turbine with 40 m rotor radius operates at 10 m/s wind speed with Cp = 0.40.

Step 1:Swept area: A = π * 40² = 5,026.5 m²
Step 2:Power: P = 0.5 * 1.225 * 5026.5 * 10³ * 0.40 = 1,231,495 W
Step 3:Convert: 1,231,495 / 1000 = 1,231.5 kW

The turbine produces approximately 1,231.5 kW (1.23 MW).

Example 2: Small Residential Turbine

A small turbine with 2 m rotor radius in 6 m/s wind with Cp = 0.35.

Step 1:Swept area: A = π * 2² = 12.57 m²
Step 2:Power: P = 0.5 * 1.225 * 12.57 * 6³ * 0.35 = 581.3 W
Step 3:Convert: 581.3 / 1000 = 0.58 kW

The small turbine produces approximately 0.58 kW (580 W).

Common Mistakes & Tips

  • !Forgetting the cubic relationship: using v^2 instead of v^3, which vastly underestimates the sensitivity to wind speed.
  • !Setting the power coefficient above the Betz limit of 0.593, which is physically impossible.
  • !Using ground-level wind speed instead of hub-height wind speed. Wind speed increases with altitude, and turbine hubs are typically 60-120 m above ground.
  • !Ignoring the effect of altitude on air density. At high-elevation sites, air is less dense and power output drops proportionally.

Related Concepts

Solar Panel Energy

Calculates energy output from photovoltaic panels, the other dominant renewable electricity source.

Betz Limit

The theoretical maximum fraction of wind energy (59.3%) that any turbine can extract, derived from conservation of mass and energy.

Used in These Calculators

Calculators that build on or apply the concepts from this page:

Solar Panel Energy Calculator

Frequently Asked Questions

What is the Betz limit?

The Betz limit is the theoretical maximum power coefficient of 16/27 (about 0.593). It means no wind turbine can capture more than 59.3% of the kinetic energy in the wind, regardless of design.

Why does doubling wind speed increase power eightfold?

Power is proportional to the cube of wind speed (v^3). Doubling v means 2^3 = 8 times the power. This cubic relationship is why wind farm siting focuses intensely on average wind speed.

How do I find the wind speed at hub height?

Use the wind shear power law: v_hub = v_ref * (h_hub / h_ref)^alpha, where alpha is typically 0.14 for open terrain. Wind resource maps from national meteorological agencies also provide hub-height estimates.

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