Lognormal Distribution Calculator

Lognormal Distribution Calculator

Calculate lognormal probabilities, density, and summary statistics from the distribution parameters.

Last updated: June 2026 | By Patchworkr Team

Lognormal Solver
Probability
0.755891
P(X ≤ x)
PDF
0.156874
CDF
0.755891
Mean
1.648721
Median
1
Mode
0.367879
Std Dev
2.161197

What Is a Lognormal Distribution?

A lognormal distribution describes a positive random variable whose logarithm is normally distributed. It is common in finance, reliability analysis, and growth processes where values multiply rather than add.

How to Use the Lognormal Calculator

  1. Enter mu and sigma for the underlying normal distribution of ln(X).
  2. Enter a positive x value.
  3. Choose the probability mode.
  4. Read the probability and summary statistics in the result panel.
F(x) = Φ((ln(x) - mu) / sigma)

Worked Example

With mu = 0, sigma = 1, and x = 2, the calculator returns the cumulative probability and related statistics.

P(X ≤ 2)

Frequently Asked Questions

Why must x be positive?

The lognormal distribution only exists for positive values because it is defined through ln(X).

What does sigma represent?

Sigma is the standard deviation of ln(X), not the standard deviation of X itself.

Can I ask for a between probability?

Yes. Choose the between mode and provide both x and x2 with x2 greater than x.

Does the calculator accept decimals?

Yes. Any finite real mu, sigma, and x values are accepted as long as the domain restrictions are met.

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