Lognormal distribution calculator
Parameters μ and σ describe ln(X), not X itself.
Selected quantiles
| p | Quantile |
|---|---|
| Fill in the fields above — the result is computed on this page. | |
How do I use this page?
- Choose density, cumulative probability or quantile.
- Enter μ, positive σ and x or p.
- Read the result, distribution summaries and quantiles.
What this page does not do: The model cannot represent zero or negative values. Before fitting data, inspect ln(X), observation independence and the sampling process.
Further reading
Theory — what is the lognormal distribution?
A variable X follows a lognormal distribution when ln(X) is normally distributed with mean μ and standard deviation σ. The distribution only takes positive values and is right-skewed, so its mean, median and mode differ from one another. The calculator lets you enter μ and σ and returns probabilities and quantiles for X itself, not for its logarithm. Note that μ is not the mean of X — the actual mean of X equals exp(μ + σ²/2), so reading μ directly as an average would be a mistake.
Frequently asked questions
Is μ the mean of X?
How do I estimate parameters from data?
See also
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Compare two proportions in an A/B test. Calculate conversion rates, difference, uplift, z score, p value and c
A/B test planning — sample size, MDE and duration
Plan a two-proportion experiment, estimate detectable effect and traffic duration.
ACF and PACF autocorrelation calculator
Calculate ACF and PACF across time-series lags. Review the chart, reference bounds and coefficient table.