Wind Turbine Power Calculator
m
m/s
0.40
0.35
Power Output3,078.8 W
Swept Area12.566 m²
Available Wind Power7,696.9 W
Annual Energy9,439 kWh/yr
The Wind Turbine Power Calculator estimates the electrical power a turbine can produce from its rotor size and the wind speed. Because power scales with the cube of wind speed, small changes in wind have a huge effect on output. It also reports the swept area, the total power in the wind, and an annual energy estimate using a capacity factor.
Formula
P = 0.5·ρ·A·v³·Cp, where A = π·r²
- P
- Captured electrical power in watts
- ρ
- Air density, 1.225 kg/m³ at sea level
- A
- Rotor swept area in square metres
- v
- Wind speed in metres per second
- Cp
- Power coefficient (max 0.593, the Betz limit)
How it works
- Enter the blade (rotor) radius in metres and the wind speed in m/s; the swept area is π·r².
- The total power in the wind is 0.5·ρ·A·v³ using air density ρ = 1.225 kg/m³, and the turbine captures a fraction of it set by the power coefficient Cp.
- A capacity-factor slider scales the rated power into a realistic annual energy figure in kWh per year (power × 8760 hours × capacity factor ÷ 1000).
Worked example
A small turbine with a 2 m blade radius in a 10 m/s wind at Cp = 0.4.
- Swept area = π × 2² ≈ 12.566 m².
- Available power = 0.5 × 1.225 × 12.566 × 10³ ≈ 7696.9 W.
- Captured power = 7696.9 × 0.4 ≈ 3078.8 W.
About 3078.8 W of output (from roughly 7696.9 W available in the wind).
Frequently asked questions
- What is the Betz limit?
- The Betz limit is the theoretical maximum fraction of wind kinetic energy a turbine can capture, equal to 0.593 (59.3%). Real turbines reach a power coefficient of roughly 0.35 to 0.45, and the calculator flags any Cp above 0.593.
- Why does doubling the wind speed do so much?
- Power depends on wind speed cubed, so doubling the wind speed multiplies the available power by eight. This is why turbine siting and average wind speed dominate energy yield.
- What is a capacity factor?
- A capacity factor is the ratio of actual annual energy to the energy if the turbine ran at full rated power all year. Onshore turbines typically sit around 0.25 to 0.45 because the wind is not always blowing at rated speed.