Wind Turbine Power Calculator (with Betz Limit)
Estimate the power available from a wind turbine given rotor diameter and wind speed, including the theoretical Betz limit and a realistic output. Runs in your browser.
Power estimate
- Swept area
- 78.54 m²
- Power in the wind
- 48.11 kW
- Betz limit (max extractable, 59.3%)
- 28.51 kW
- Realistic output (Cp 40%)
- 19.24 kW
P = ½ · ρ · A · v³ with air density ρ = 1.225 kg/m³. No turbine can exceed the Betz limit of 16/27 ≈ 59.3% (Betz, 1919). Power scales with the cube of wind speed, so doubling the wind gives eight times the power.
About this tool
The power carried by the wind passing through a turbine's rotor is ½ × air density × swept area × wind speed cubed. This calculator computes that from the rotor diameter (which sets the swept area, π·r²) and the wind speed, and then shows how much of it a turbine could actually capture. No turbine can extract all the wind's energy: the Betz limit, derived by Albert Betz in 1919, proves the theoretical maximum is 16/27, about 59.3%, because the air must keep some velocity to flow out of the way. Real turbines reach a power coefficient (Cp) of roughly 35–45%, which you can set with the slider. The single most important takeaway the tool makes visible is the cube law — power scales with the cube of wind speed, so a site with twice the wind yields eight times the power, which is why turbine siting matters more than almost anything else. Air density is taken at sea level; high altitude or hot air reduces output. It is an idealized physics estimate, not a manufacturer's power curve. Everything runs in your browser.
How to use it
- Enter the rotor (blade) diameter in meters.
- Enter the wind speed in m/s or mph.
- Adjust the power coefficient (Cp) — 40% is typical for a good turbine.
- Compare the power in the wind, the Betz maximum, and the realistic output.
Frequently asked questions
- What is the Betz limit?
- The maximum fraction of the wind's kinetic energy any turbine can theoretically capture: 16/27, or about 59.3%, proven by Albert Betz in 1919. Beyond it, the slowed air would block incoming wind. It is a hard physical ceiling no design can beat.
- How is wind power calculated?
- Power in the wind = ½ × ρ × A × v³, where ρ is air density (1.225 kg/m³ at sea level), A is the rotor swept area (π × radius²), and v is wind speed. The extractable power is that value times the power coefficient (Cp), capped by the Betz limit.
- Why does wind speed matter so much more than rotor size?
- Power scales linearly with swept area but with the cube of wind speed. Doubling the diameter quadruples power (area ∝ r²), but doubling the wind speed multiplies power by eight. That cube law is why a windier site dramatically outperforms a calmer one.
- What is a realistic power coefficient (Cp)?
- Modern utility-scale turbines achieve a Cp around 0.35–0.45 across their operating range — below the 0.593 Betz limit due to aerodynamic, mechanical, and electrical losses. Small turbines are often lower. The slider lets you model your assumption.
- Does air density affect the result?
- Yes. This tool uses sea-level density (1.225 kg/m³). At higher altitude or in hot weather the air is thinner, reducing available power proportionally — a turbine at 2,000 m produces noticeably less than the same turbine at sea level in the same wind.
- Is this a manufacturer power curve?
- No. It is the idealized physics of available and extractable power. Real turbines have cut-in and cut-out speeds, rated-power plateaus, and efficiency that varies with wind — consult the manufacturer's power curve for actual output.