Weibull Wind Distribution Calculator

Work out weibull wind distribution instantly with clear inputs, formula shown and shareable results.

About Weibull Wind Distribution Calculator

Wind speed distributions are described by a Weibull function with scale parameter c and shape parameter k, where k near 2 gives the Rayleigh distribution typical of temperate sites. Mean speed is c x gamma(1 + 1/k), and wind power density uses gamma(1 + 3/k) because power depends on the cube of speed.

Formulas

Weibull mean

Mean = c x gamma(1 + 1/k)

Power density

Power density = 0.5 x rho x c^3 x gamma(1 + 3/k)

Worked example

With the default values below, Weibull Wind Distribution Calculator returns Mean Wind Speed of 7.0898. Change any input above and every figure here is recalculated in your browser.

Inputs used

Weibull Scale Parameterminimum 0.01 m/s: 8 m/s
Weibull Shape Parameteraccepts 0.1–6: 2
Turbine Cut-In Speedminimum 0 m/s: 3 m/s
Turbine Cut-Out Speedminimum 0.1 m/s: 25 m/s

Results

Mean Wind Speed: 7.0898
Time Within Operating Range: 86.876%
Wind Power Density: 416.88
Operating Hours Per Year: 7,610

Step by step

1Values used
2Weibull mean
3Power density
4Mean Wind Speed= 7.0898
5Time Within Operating Range= 86.876
6Wind Power Density= 416.88
7Operating Hours Per Year= 7,610

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why not just use the mean wind speed?

Because power varies with the cube of speed, so the distribution matters more than the mean. Two sites with the same average can differ by 20% in energy if their shape parameters differ.

What does the shape parameter tell you?

Low k means highly variable wind with strong gusts and calms, typical of monsoon or thunderstorm-driven climates. High k means steady wind, as in trade wind regions, which is easier to harvest.