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Statistics

Lognormal Distribution Calculator

Evaluate cumulative probability when the natural logarithm is normally distributed.

Data stays on this deviceConvention explained below
Probability workspace
Probability workspace

Probabilities range from 0 to 1. Check whether the method gives cumulative or exact-count probability.

See the method

Set model parameters

Runs on your device

Your probability

Your result

Let’s calculate.

Use the Calculate button to see your result.

Review the method below for assumptions and conventions.

How to use this tool

  1. Enter mean of ln(x), standard deviation of ln(x), value x.
  2. Select Calculate to view the result.
  3. Check the method and assumptions below before using the result.

The method, explained

For x>0, z=[ln(x)−mu]/sigma and CDF=Φ(z); CDF=0 for x≤0.

A WORKED EXAMPLE

Using mean of ln(x) = 0, standard deviation of ln(x) = 1, value x = 1, the result is 0.5. Change these example inputs to match your task; use the method above to check each step.

Understanding your result

Parameters describe ln(X), not X itself. Uses natural logarithms; main result is P(X≤x).

What to keep in mind

Parameters describe ln(X), not X itself. Uses natural logarithms; main result is P(X≤x). A descriptive or probability calculation under the stated assumptions. Check the sample design and model before interpreting results.

Common questions

How do I use this lognormal distribution calculator?

Evaluate cumulative probability when the natural logarithm is normally distributed. Enter mean of ln(x), standard deviation of ln(x), value x. The starting example is editable; use values for the same system or project.

Which assumptions affect this result?

Parameters describe ln(X), not X itself. Uses natural logarithms; main result is P(X≤x).

Methodology maintained by ClarityKit. How these tools are built and checked.