basic

Log-Normal Distribution Mean and Variance Calculator

E[X] = e^(μ+σ²/2); Var[X] = (e^σ²−1)·e^(2μ+σ²).

Calculates the log-normal mean E[X] = exp(μ+σ²/2), median exp(μ), mode exp(μ−σ²), and variance (e^(σ²)−1)·e^(2μ+σ²) from the log-scale parameters μ and σ.

Nadia Almasri By Nadia Almasri
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

E[X] = e^(μ+σ²/2); Med = e^μ; Mode = e^(μ−σ²)

In depth

Calculates the log-normal mean E[X] = exp(μ+σ²/2), median exp(μ), mode exp(μ−σ²), and variance (e^(σ²)−1)·e^(2μ+σ²) from the log-scale parameters μ and σ.