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Normal distribution calculator

The normal distribution calculator returns tail probabilities and critical values for a Normal(μ, σ) variable — the z-table, computed exactly rather than looked up.

What is Normal distribution calculator?

The normal distribution is the limiting shape of a sum of many small independent effects, which is why it stands behind the z-test, the large-sample confidence interval and the residual assumptions of regression.

Standard tables print P(Z ≤ z) for the standard normal to two or three decimals. This computes it for any mean and SD, in both directions, with full double precision — so there is no interpolating between table rows.

When should I use Normal distribution calculator?

Converting a z-score into a p-value, or a confidence level into a z multiplier.
Checking how extreme an observation is under an assumed mean and SD.
Reading off the 1.96 that sits behind every 95% interval.

What data does it need?

Distribution parameters, plus a value x, a tail probability p, or both.

What does it report?

For x: the density or exact probability and each tail. For p: the lower, upper and two-tailed critical values.

What does it assume?

None — this evaluates a distribution rather than testing data against one.