Wind Speed Frequency Distribution Calculator
Compute the Weibull probability distribution of wind speeds at turbine hub height to estimate how many hours per year a site experiences any given wind speed. Essential for wind resource assessment and annual energy production forecasting.
Last updated: September 2026
Formula below · 2 sources (energy.gov, Wikipedia) · Updated Sep 2026
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About this calculator
Wind speed distributions are well described by the two-parameter Weibull function. The probability density at a given wind speed v is: f(v) = (k/c) × (v/c)^(k−1) × exp(−(v/c)^k), where k is the dimensionless shape factor and c is the scale parameter, related to the mean speed by c = mean / Γ(1 + 1/k) (for k = 2, c ≈ 1.128 × mean). This calculator also adjusts for hub height using the power law: v_hub = v_ref × (hubHeight / measurementHeight)^0.2. Multiplying the probability density by 8760 hours/year gives the expected annual hours in a 1 m/s-wide bin centred on the target wind speed. The shape factor k typically ranges from 1.5 (highly variable wind) to 3.0 (steady trade winds), with k ≈ 2 (Rayleigh distribution) being a common default. Accurate Weibull fitting is the foundation of all bankable wind resource assessments.
How to use
Given: averageWindSpeed = 7 m/s, k = 2, targetWindSpeed = 8 m/s, measurementHeight = 10 m, hubHeight = 80 m. Step 1 – Hub-height mean: 7 × (80/10)^0.2 = 7 × 1.516 ≈ 10.61 m/s. Step 2 – Scale parameter: c = 10.61 / Γ(1.5) = 10.61 / 0.8862 ≈ 11.97 m/s. Step 3 – Speed ratio: 8 / 11.97 ≈ 0.668. Step 4 – Weibull density: (2/11.97) × 0.668 × exp(−0.668²) ≈ 0.1671 × 0.668 × 0.640 ≈ 0.0714 per m/s. Step 5 – Annual hours: 0.0714 × 8760 ≈ 626 hours/year with the 80 m hub wind between about 7.5 and 8.5 m/s.
Frequently asked questions
What Weibull shape factor k should I use if I have no site data?
If you lack measured wind data, a shape factor of k = 2 (the Rayleigh distribution) is the most widely used default and is recommended by the IEC 61400-1 standard for initial assessments. Values of k between 1.8 and 2.2 are appropriate for most mid-latitude temperate sites. Coastal and trade-wind sites often have higher k values (2.5–3.0), indicating steadier winds and a narrower speed distribution. If you have even a month of anemometer data, fitting k using maximum likelihood estimation will significantly improve forecast accuracy. Global wind atlases such as the Global Wind Atlas (DTU) also provide pre-computed k values at a 250 m resolution.
Why is the Weibull distribution used for wind speed analysis?
The Weibull distribution is used because it is a flexible two-parameter family that empirically fits measured wind speed histograms very well across a wide range of climates. Unlike a normal distribution, it is defined only for non-negative values (wind speed cannot be negative) and can represent both peaked, steady distributions (high k) and broad, gusty ones (low k). Since wind power scales with the cube of speed, the shape of the distribution matters enormously — a site with the same mean speed but lower k (more hours at very low and very high speeds) can produce more annual energy than a steady site. This makes Weibull parameterisation essential for reliable AEP calculations.
How does hub height affect annual energy production estimates?
Wind speed increases with height above ground due to surface friction, a phenomenon called wind shear. Even a modest height increase can significantly raise energy yield because power scales with speed cubed. Going from a 30 m hub to an 80 m hub at a site with a standard shear exponent of 0.2 increases mean wind speed by about (80/30)^0.2 ≈ 20%, which translates to roughly (1.20)³ ≈ 73% more available power. This is why modern utility turbines use hub heights of 80–150 m. The calculator applies the power-law correction so that the Weibull frequency reflects wind conditions at the actual operating height rather than the measurement mast height.