Is this normal distribution calculator free?

Yes. It is 100% free to use with no sign-up, subscriptions, or hidden limits.

What do μ (mean) and σ (standard deviation) do?

μ shifts the curve left/right (center), and σ controls the spread (how wide or narrow the bell curve is).

PDF gives the density at x (the bell curve height). CDF gives the probability that X ≤ x (area under the curve).

Enter a probability p (for example 0.95) in the Quantile/Inverse CDF section to compute the x value where CDF(x)=p.

Yes. Calculations run locally in your browser (no uploads). After the first load, it can work offline in many cases.

Set mean, deviation, and the query points to compute PDF, CDF, and ranges.

Auto update Standard normal

Mean μ Std dev σ x p (0-1) Central area c Lower bound a Upper bound b Precision Shaded area

Quick ranges

Confidence

Instant outputs with tail probabilities and range areas.

PDF CDF Right tail (1 − CDF) Two-tailed p z-score Quantile Central lower Central upper Sample P(a≤X≤b) Outside P(X≤a or ≥b)