Where wind power comes from
Wind is moving air, and moving air carries kinetic energy. A turbine slows the air down as it passes through the rotor and turns part of that energy into electricity. How much depends above all on the area swept by the blades and on the wind speed, cubed.
The formula
P = ½ × ρ × A × v³ × Cp
- ρ: air density, 1.225 kg/m³ at sea level
- A: swept area = π × (diameter ÷ 2)²
- v: wind speed
- Cp: power coefficient, the share of the wind’s energy actually captured
The Betz limit
No turbine can capture more than 59.3% of the wind’s energy, because the air must keep moving to leave the rotor. This is the Betz limit. Large utility turbines reach about 45% to 50%; small home turbines usually 25% to 35% once generator and inverter losses are counted.
Worked example
A small turbine with a 10 ft (3.05 m) rotor, in a 12 mph (5.4 m/s) wind, at 30% efficiency:
- Swept area = 7.3 m²
- Power ≈ 0.5 × 1.225 × 7.3 × 5.36³ × 0.30 ≈ 207 W
- The wind passing through the rotor carries about 690 W; the Betz limit would allow at most 409 W.
Yearly energy
Wind speed varies all the time, and because power follows the cube of speed, gusty hours contribute far more than calm ones. The calculator assumes a Rayleigh distribution of wind speeds around your average, for which the average of v³ is about 1.91 times the cube of the average speed. With a 12 mph average, the estimate is about 3,460 kWh a year, worth about $589 at $0.17 per kWh.
Treat this as an upper bound: real turbines stop below their cut-in speed (often 6 to 8 mph), cap their output at the rated power in strong winds and lose energy to turbulence. Real-world capacity factors for small turbines are often 10% to 20%.
Why height and site matter
- Doubling the wind speed multiplies the power by eight.
- Wind is slower and more turbulent near the ground and behind trees and buildings. A common rule is to put the rotor at least 30 ft above anything within 300 ft.
- An average of at least 10 to 12 mph at hub height is usually needed for a home turbine to make sense.
Is it worth it?
In most suburban yards, solar panels produce more energy per dollar with fewer permits and no moving parts. Small wind can make sense on open rural land, on coasts and plains, or off-grid in winter when solar output is low. Check local zoning, height limits and utility interconnection rules before buying.