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Statistics

Triangular Distribution Calculator

Calculate cumulative probability for a bounded triangular model with a specified mode.

Data stays on this deviceConvention explained below
Probability workspace
Probability workspace

Probabilities range from 0 to 1. Check whether the method gives cumulative or exact-count probability.

See the method

Set model parameters

Runs on your device

Your probability

Your result

Let’s calculate.

Use the Calculate button to see your result.

Review the method below for assumptions and conventions.

How to use this tool

  1. Enter minimum, maximum, most likely value, value x.
  2. Select Calculate to view the result.
  3. Check the method and assumptions below before using the result.

The method, explained

CDF is (x−a)²/[(b−a)(mode−a)] below the mode and 1−(b−x)²/[(b−a)(b−mode)] above it, with endpoint limits.

A WORKED EXAMPLE

Using minimum = 0, maximum = 10, most likely value = 4, value x = 1, the result is 0.025. Change these example inputs to match your task; use the method above to check each step.

Understanding your result

Main result is P(X≤x). A triangular model uses a bounded range and mode; it does not establish that real observations follow this distribution.

What to keep in mind

Main result is P(X≤x). A triangular model uses a bounded range and mode; it does not establish that real observations follow this distribution. A descriptive or probability calculation under the stated assumptions. Check the sample design and model before interpreting results.

Common questions

How do I use this triangular distribution calculator?

Calculate cumulative probability for a bounded triangular model with a specified mode. Enter minimum, maximum, most likely value, value x. The starting example is editable; use values for the same system or project.

Which assumptions affect this result?

Main result is P(X≤x). A triangular model uses a bounded range and mode; it does not establish that real observations follow this distribution.

Methodology maintained by ClarityKit. How these tools are built and checked.