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Weibull Distribution Calculator — result sheet
Calculate Weibull density, cumulative probability, reliability, and mean from shape, scale, and evaluation value.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: PDF=(k/λ)(x/λ)^(k−1)exp(−(x/λ)^k); CDF=1−exp(−(x/λ)^k); reliability=exp(−(x/λ)^k); mean=λΓ(1+1/k).
The two-parameter Weibull model is flexible because its shape parameter changes the failure-rate pattern while scale sets the time scale.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Shape parameter — minimum 1.0E-6; maximum 100
- Scale parameter — minimum 1.0E-6; maximum 1000000000000
- Evaluation value — minimum 0; maximum 1000000000000
Worked example
| Input | Value |
|---|---|
| Shape parameter | 2 |
| Scale parameter | 10 |
| Evaluation value | 8 |
CDF ≈ 0.473; reliability ≈ 0.527; mean ≈ 8.862.
Assumptions and limits
- The shape and scale are positive and the evaluation value is nonnegative.
- The location parameter is fixed at zero.
- Parameter fitting, censoring, competing risks, and reliability decisions are not inferred.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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