Triangular Distribution Calculator (Best, Most Likely, Worst Case)

What this tool does

When all you know is a best case, a most likely case and a worst case — a task duration, a cost, a demand — the triangular distribution is the simplest honest model. Its mean is just (a + b + c) ÷ 3, and when the worst case is far from the most likely value the mean and median both sit above it, which is why expecting the 'most likely' figure is usually optimistic. The calculator also gives the value you can stay under with a chosen confidence, e.g. the 80th percentile used to set a safe deadline or budget. It is cruder than a three-point PERT estimate, which weights the most likely value more heavily.

Formula

mean = (a + b + c) ÷ 3 · variance = (a² + b² + c² − ab − ac − bc) ÷ 18 · F(x) = (x − a)² ÷ ((b − a)(c − a)) up to the mode c, then 1 − (b − x)² ÷ ((b − a)(b − c))

Variables

Worked example

Limitations

• The calculation runs at full precision and only the display is rounded. If you copy an intermediate value and retype it, small differences can appear.
• The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.