Normal Distribution Calculator
Find the probability density and cumulative probability for a normal value.
Results update as you type.
About this calculator
The normal (Gaussian) distribution is the classic bell curve. Given a value x, a mean μ and a standard deviation σ, this calculator returns the probability density at x, the cumulative probability P(X ≤ x) (the area to the left), the right-tail probability P(X ≥ x) and the equivalent z-score. The cumulative values use an accurate error-function approximation of the standard-normal integral.
Frequently asked questions
What is the difference between the pdf and the cdf?
The probability density (pdf) is the height of the bell curve at x; it is not a probability by itself. The cumulative distribution (cdf) is the area under the curve up to x, which gives the probability of a value at or below x.
Why is the probability of an exact value zero?
For a continuous distribution like the normal, any single exact point has zero probability — only ranges have non-zero probability. That is why we report the density at x and the cumulative area rather than P(X = x).
Results are estimates for general guidance only, not financial, medical or tax advice.