Normal Distribution Probability

Calculate cumulative probability and z-score under a normal distribution.

How this calculator works

Enter value x, mean μ, standard deviation σ. CalcStack applies the displayed formula and reports each intermediate planning value with the units shown.

Formula / method

P(X≤x) = ½[1 + erf((x−μ) ÷ (σ√2))]

Worked example

x=75, mean 60 and SD 10 gives z=1.5 and cumulative probability about 93.32%.

Assumptions and limitations

The variable is adequately modeled by a normal distribution.

Normality, outliers, discrete values and parameter uncertainty are not tested.