Quick guide
How to use this calculator
- Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
- Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
- Read the result together with its assumptions and interpretation. Statistical output summarizes uncertainty under a model; it does not repair biased data or establish causation.
Calculation method
How the triangular distribution calculator works
The triangular density rises linearly from a to mode c and falls linearly from c to b, where a≤c≤b and a<b.
A triangular model is a bounded judgment model when only endpoints and a defensible most-likely value are available.
Worked example
Triangular Distribution example
Minimum 0, mode 5, and maximum 10 give mean 5 and cumulative probability 0.5 at x=5.
The triangular density rises linearly from a to mode c and falls linearly from c to b, where a≤c≤b and a<b.
Supported inputs
Precision and limits
Model and design
The three points are subjective model inputs rather than fitted evidence; endpoint modes are allowed but the minimum must be below the maximum.
Numerical scope
Inputs use double-precision numerical methods with guarded domains. Datasets accept up to 10,000 finite plain-decimal values. Extremely large parameters or probabilities deep in a numerical tail may require specialist statistical software.
Interpretation
A triangular model is a bounded judgment model when only endpoints and a defensible most-likely value are available.
Decision boundary
The calculator does not validate how data were collected, diagnose dependence or bias, choose a scientifically meaningful effect, or replace review by a qualified statistician for consequential research, medical, regulatory, safety, or policy decisions.
Privacy
Entered values and calculated results stay in this browser and are not sent to an analytics service.
Continue calculating