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 to 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
X is lognormally distributed when ln(X) is normal with mean μ and standard deviation σ. The distribution is positive and right-skewed.
Mean, median and mode are not equal. As σ increases, the right tail grows and the mean increasingly exceeds the median.
Frequently asked questions
Is μ the mean of X?
No. μ is the mean of ln(X). The mean of X is exp(μ + σ²/2).
How do I estimate parameters from data?
For positive observations, compute the mean and standard deviation of their natural logarithms.
See also
A/B test calculator
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.