Capacity Factor vs. Hub Height Calculator
Wind speed rises with height above the ground because friction from terrain and vegetation slows air near the surface — a phenomenon called wind shear. Because turbine power scales with the cube of wind speed, even a modest speed gain from a taller tower translates into a much larger increase in available power density and, ultimately, capacity factor. This calculator applies the wind shear power law to extrapolate your reference wind speed up to your target hub height, then reports the resulting power density increase factor. Pair the result with our Wind Power Density Calculator to convert that speed into watts per swept area, and our Wind Turbine Output Calculator to turn it into instantaneous power.
Wind speed measured at the reference height, typically from a meteorological station or anemometer.
10m is the standard meteorological measurement height.
Modern utility-scale onshore turbines typically use 80-120m hub heights.
0.143 (1/7 power law) is a standard simplified value. Typical range is 0.10 for smooth/open terrain (including offshore) to 0.25+ for rough or forested terrain.
reference wind speed (m/s) × (target hub height (m) ÷ reference height (m))^wind shear exponent
(wind speed at hub height (m/s) ÷ reference wind speed (m/s))^3 — the cube law
Results update live as you type. For planning and field-check estimates — always verify against applicable standards and equipment ratings.
How we calculate this →Raising a turbine from a 10m reference height to a 100m hub height increases wind speed from 6.5 m/s to about 9.0 m/s in this example -- a 39% speed increase that translates into nearly a 2.7x increase in available power density, thanks to the cube law. This is exactly why modern wind turbines keep growing taller: every additional meter of hub height captures faster, more consistent wind that was previously out of reach near the ground, where friction from terrain and vegetation slows air movement.
How capacity factor vs. hub height is calculated
This calculator extrapolates a measured wind speed up to a turbine's hub height and quantifies the resulting power density gain, tying four inputs together: the reference wind speed, the reference height it was measured at, the target hub height, and the wind shear exponent (alpha). Two quantities tie the calculation together.
Wind Speed at Hub Height (m/s) = Reference Wind Speed (m/s) × (Target Hub Height (m) ÷ Reference Height (m))^Wind Shear Exponent. Friction from the ground, vegetation, and buildings slows air movement near the surface, so wind speed increases with height — a phenomenon known as wind shear. The power law captures this relationship: the ratio of heights raised to the wind shear exponent gives the speed-up factor, which multiplied by the reference wind speed yields the wind speed at the target height. At the defaults (6.5 m/s at 10m, 100m hub height, alpha 0.143), that is 6.5 × (100 ÷ 10)^0.143 = 6.5 × 10^0.143 = 6.5 × 1.39 = 9.0 m/s.
Power Density Increase Factor (x) = (Wind Speed at Hub Height (m/s) ÷ Reference Wind Speed (m/s))^3. The power available in moving air scales with the cube of wind speed — doubling wind speed yields eight times the power density. This cube-law relationship is why even modest wind shear-driven speed gains from added height produce substantial increases in available power density, and ultimately capacity factor. At the defaults, that is (9.0 ÷ 6.5)^3 = (1.39)^3 = 2.7x.
Two notes on the model. First, the wind shear exponent (alpha) is site-specific: smooth terrain like open water or flat grassland has a lower exponent (around 0.10), while rough terrain with trees, buildings, or hills has a higher exponent (0.20-0.25+), meaning wind speed increases more dramatically with height in rougher terrain. The 0.143 (1/7 power law) default is a widely used simplified value, not a measured site characteristic. Second, this calculator reports the power density increase factor — the relative multiplier on available wind power — not the capacity factor itself, which also depends on the turbine's power curve, cut-in and cut-out speeds, rated power, air density, and wake losses from neighboring turbines. For project financing, validate against a full site-specific wind resource assessment. Data sources: wind shear exponent (power law) methodology from IEC 61400 wind turbine design standards and NREL wind resource assessment guidelines; wind speed extrapolation formulas from meteorological standards and wind energy engineering references; power density cube-law relationship from wind physics and turbine power curve analysis; hub height and tower cost data from utility-scale wind project case studies and manufacturer specifications; terrain-specific wind shear exponents from wind resource assessment databases and field measurement studies. Verification: with defaults (6.5 m/s at 10m, 100m hub height, alpha 0.143), Wind Speed at Hub Height = 9.0 m/s, Power Density Increase Factor = 2.7x.