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Log-normal distribution calculator

The log-normal distribution calculator returns probabilities and quantiles for a positive variable whose logarithm is normal.

What is Log-normal distribution calculator?

A log-normal arises when effects multiply rather than add, which is why concentrations, titres, incubation periods and incomes are so often log-normal rather than normal.

The parameters describe log(X), not X — a common source of error. The median of X is exp(meanlog), while its mean is larger, at exp(meanlog + sdlog²/2).

When should I use Log-normal distribution calculator?

Working with assay concentrations or antibody titres.
Finding a reference limit on a skewed, positive-valued analyte.
Converting between the log scale and the original units.

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.