Triangular Distribution Calculator
Evaluate a continuous triangular CDF, density and moments from lower, modal and upper values.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Use the two quadratic CDF branches meeting at the entered interior mode, clipping outside the support.
CDF=(x−a)²/((b−a)(c−a)) below mode; 1−(b−x)²/((b−a)(b−c)) above mode
Worked example
Minimum 0, mode 4 and maximum 10 give CDF 0.4 and density 0.2 at x=4, with mean 14/3.
Assumptions and input details
Requires minimum < mode < maximum. This is a triangular distribution, not a PERT beta model. End-mode degenerate triangles are outside this tool’s scope.
References: NIST: probability distributions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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