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Log-Normal Distribution μ & σ Calculator

If ln(X) ~ N(μ, σ²) — median, mean, and variance of X.

Calculates the PDF, CDF, mean, median, mode, and variance of a log-normal distribution from its log-scale parameters μ and σ.

Dr. Helena Ortiz By Dr. Helena Ortiz
Published Last reviewed 1 min read

Inputs

Results

Enter values and click Calculate to see results.
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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

Median = e^μ; Mean = e^(μ+σ²/2); Var = (e^σ²−1)×e^(2μ+σ²)

In depth

Calculates the PDF, CDF, mean, median, mode, and variance of a log-normal distribution from its log-scale parameters μ and σ.