Wind Speed Probability Calculator

Model wind behavior with robust distribution metrics quickly. Compare speed bands, thresholds, and energy expectations. Turn site inputs into clear engineering probability insights today.

Input Parameters

Distribution Model

Shape Factor k

Scale Factor c (m/s)

Target Wind Speed v (m/s)

Lower Interval Speed (m/s)

Upper Interval Speed (m/s)

Operating Threshold (m/s)

Air Density (kg/m³)

Rotor Swept Area (m²)

Analysis Hours

Reset

Example Data Table

Scenario	Model	k	c (m/s)	Target v (m/s)	Band (m/s)	Threshold (m/s)	Hours
Coastal wind farm	Weibull	2.10	9.20	12.00	8 - 14	4.00	8760
Inland ridge	Weibull	1.85	7.60	10.00	6 - 11	3.50	4380
Preliminary site review	Rayleigh	2.00	8.00	9.00	5 - 10	3.00	2160

Formula Used

Weibull probability density: f(v) = (k / c) × (v / c)^k−1 × e^{−(v/c)^k}

Cumulative probability: F(v) = 1 − e^{−(v/c)^k}

Exceedance probability: P(V > v) = e^{−(v/c)^k}

Interval probability: P(v₁ < V < v₂) = e^{−(v₁/c)^k} − e^{−(v₂/c)^k}

Mean wind speed: v̄ = c × Γ(1 + 1/k)

Variance: σ² = c² × [Γ(1 + 2/k) − Γ²(1 + 1/k)]

Wind power density: WPD = 0.5 × ρ × c³ × Γ(1 + 3/k)

Expected rotor power: P = WPD × A

Rayleigh model: use k = 2 for a simplified special Weibull case.

How to Use This Calculator

Select Weibull for flexible site fitting or Rayleigh for quick screening.
Enter the shape factor, scale factor, and target wind speed.
Provide a speed interval to estimate occurrence within a band.
Add operating threshold, air density, rotor area, and analysis hours.
Press Calculate Probability to display results above the form.
Use CSV for spreadsheet review or PDF for reporting and documentation.

Frequently Asked Questions

1. What does the shape factor mean?

The shape factor describes spread. Lower values indicate more variable wind behavior, while higher values indicate tighter clustering around the typical site speed.

2. When should I use the Rayleigh model?

Use Rayleigh when measured site data is limited and you want a quick first estimate. It assumes a shape factor of two.

3. What is exceedance probability?

Exceedance probability is the chance that wind speed will be greater than your selected target speed. It is useful for cut-in or survivability checks.

4. Why is interval probability important?

It shows how often wind falls inside a working band. That helps estimate turbine operating time, load exposure, and dispatch expectations.

5. Does expected rotor power equal electrical output?

No. It estimates available wind power across swept area. Real electrical output depends on turbine efficiency, controls, losses, and power curve limits.

6. Which units should I use?

Use meters per second for speed, kilograms per cubic meter for air density, square meters for rotor area, and hours for duration.

7. Can I use this for annual energy studies?

Yes, as a screening tool. For bankable energy studies, combine measured data, long-term correction, turbine power curves, and site losses.

8. Why do results change strongly with scale factor?

Scale factor controls the characteristic speed of the wind regime. Because wind power rises roughly with speed cubed, small changes matter greatly.