What the lognormal distribution models
A random variable is lognormally distributed if the natural logarithm of that variable follows a normal distribution. This shape naturally arises for quantities that are the product of many small independent factors and cannot go below zero, such as stock prices, incomes, or particle sizes.
How this calculator works
Enter μ and σ, the mean and standard deviation of ln(X) (not of X itself), and a value x. The calculator computes the probability density f(x) and the cumulative probability P(X ≤ x) using the standard lognormal formulas, along with the mean and variance of X itself, which differ from μ and σ because of the exponential transformation.
Because the lognormal distribution is right-skewed, its mean is always higher than its median. This tool is intended for general statistics education and data analysis.