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Weibull Wind Speed Distribution Probability Density Calculator

The two-parameter Weibull probability density function is the standard meteorological model for quantifying wind turbine annual energy yield (AEP).

Calculated Result
10.031 % / (m/s)

Probability Density f(v)

Cumulative Probability F(v)

58.3%

Exceedance Probability (1 - F)

41.7%

Calculation Breakdown

  1. Evaluate 2-parameter Weibull PDF f(v) = (k/c)·(v/c)^(k-1)·exp(-(v/c)^k)f(8) = (2.2 / 8.5) * (8 / 8.5)^(2.2 - 1) * exp(-(8 / 8.5)^2.2) = 0.10031

Weibull Probability Density Curve

Interactive visualization based on your current inputs

Density (%)
0.02.85.68.4114 m/s6 m/s8 m/s10 m/s14 m/sSpeed (m/s)Density (%/(m/s))

What Is the Weibull Wind Speed Distribution Probability Density Calculator?

The two-parameter Weibull probability density function is the standard meteorological model for quantifying wind turbine annual energy yield (AEP).

How Does the Weibull Wind Speed Distribution Probability Density Calculator Work?

The calculation evaluates user-provided measurements using recognized domain equations, converts between measurement units, and adjusts for real-world efficiency factors.

Weibull Wind Speed Distribution Probability Density Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

f(v) = \frac{k}{c} \left(\frac{v}{c}\right)^{k - 1} \exp\left[-\left(\frac{v}{c}\right)^k\right], \quad F(v) = 1 - \exp\left[-\left(\frac{v}{c}\right)^k\right]

The scale parameter c reflects average windiness, while shape factor k describes wind speed variability (k = 2 is Rayleigh distribution).

How to Use the Weibull Wind Speed Distribution Probability Density Calculator

  1. Enter your primary measurements in the input fields above.
  2. Select your preferred units (e.g. metric or imperial) if applicable.
  3. Review or adjust operational assumptions such as field efficiency.
  4. Click Calculate to instantly generate the full results breakdown and visual chart.
  5. Use the Reset button at any time to clear the form and test a new scenario.

Step-by-Step Example Calculation

Offshore Wind Farm Resource

Input Values:

windSpeedMps:8
scaleParameterC:8.5
shapeParameterK:2.2

Understanding Your Result

Your calculated result represents the realistic operational capacity or baseline output under the specified conditions. Comparing theoretical and effective outputs reveals the direct impact of turns, overlap, and practical downtime.

Factors That Affect the Result

Field terrain, operator experience, equipment maintenance, overlap margin, and weather conditions can significantly influence real-world output.

When Should You Use This Calculator?

Use this calculator whenever you need quick, verified estimates for job planning, budgeting, equipment sizing, or project timelines.

Assumptions & Limitations

  • Evaluation provides both point probability density and cumulative distribution F(v).

Frequently Asked Questions

Calculation Accuracy & Reference Note

This calculator implements verified, deterministic mathematical equations based on published standards. Results should be treated as professional engineering estimates; always verify critical operations with local equipment manuals and site inspections.

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