Wind Turbine Output Calculator

Frequently Asked Questions

How is wind turbine power calculated?

P = ½ × ρ × A × v³ × Cp, where ρ is air density (~1.225 kg/m³), A is swept area (πr²), v is wind speed, and Cp is the power coefficient (max 0.59 Betz; ~0.35–0.45 real), times drivetrain efficiency.

Why does wind speed matter so much?

Power scales with the cube of speed: doubling wind speed gives 8× the power. Site wind quality dominates output - a small speed gain beats a bigger rotor.

What is the Betz limit?

No turbine can extract more than 59.3% of the wind's kinetic energy (Betz's law); real turbines reach ~35–45%, which is the Cp the calculator uses.

How do I estimate annual energy?

Instantaneous power at average wind overstates output; apply a capacity factor (~20–35% for small turbines) to get realistic annual kWh.

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Estimates for informational purposes only.

Important Disclaimer: Estimates for informational purposes only.

This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.

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How This Calculator Works

The kinetic power available in moving air is P = ½ · ρ · A · v³, where ρ is air density (≈ 1.225 kg/m³ at sea level), A is the swept area of the rotor (A = π · r²), and v is wind speed in m/s. A turbine cannot capture all of it: the Betz limit caps any rotor at 59.3%, and real rotors achieve a power coefficient Cp of about 0.30–0.45. Generator and drivetrain losses trim further, so electrical output = ½ ρ A v³ × Cp × efficiency. Energy over time is then estimated with a capacity factor that averages the variability of real wind.

Worked Example

A small turbine with a 1.5 m blade has swept area A = π × 1.5² ≈ 7.07 m². In a 6 m/s wind at sea level: Pwind = 0.5 × 1.225 × 7.07 × 6³ = 0.5 × 1.225 × 7.07 × 216 ≈ 935 W in the wind. With Cp = 0.35 and 90% drivetrain efficiency: 935 × 0.35 × 0.90 ≈ 295 W electrical. At a 25% capacity factor that is 0.295 × 8,760 × 0.25 ≈ 646 kWh per year - modest, and a stark illustration of the v³ term: doubling wind speed to 12 m/s would multiply raw power eightfold.

Real-World Use

Use this to scope a residential or off-grid micro-wind project, compare rotor sizes, or reality-check a manufacturer's rated-power claim (always note the wind speed that rating assumes - often an optimistic 11–12 m/s). Because power scales with the cube of wind speed and the square of radius, site wind resource matters far more than turbine size: a slightly windier tower placement beats a bigger rotor in a poor location.

Common Mistakes

Using average wind speed in v³ directly. Because the relationship is cubic, the cube of the average underestimates true energy - a proper estimate integrates the wind speed distribution. This tool gives an instructive approximation, not a bankable yield.

Ignoring air density. High altitude and hot air reduce ρ and therefore output; cold dense winter air produces more.

Forgetting cut-in and cut-out speeds. Turbines produce nothing below cut-in (~3 m/s) and shut down above cut-out (~25 m/s).

Trusting nameplate kW without the assumed wind speed and capacity factor.

Limitations

This is a steady-state, single-wind-speed model. Real annual energy depends on the full Weibull wind-speed distribution at hub height, turbulence, the turbine's power curve, tower shadow, and downtime - a proper assessment uses site anemometry over a year. Treat the annual figure as an order-of-magnitude guide that the capacity factor crudely corrects for variability. For grid or financed projects, use measured site data and the manufacturer's certified power curve.

Wind Turbine Output Calculator

Frequently Asked Questions

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