Cumulative P(X ≤ x)75.5891%Probability X is below 2.0
Expected Mean (μᵣ)1.65Expected Value
Median (eᶿ)1.0050th Percentile
Mode
0.37
Std Dev (σᵣ)
2.16
Prob Density f(x)
0.1569
Strictly positive values only. Standard for finance & nature.
About this calculator
Overview
A variable follows a log-normal distribution if its natural logarithm is normally distributed. It is strictly positive and typically right-skewed, making it the standard for modeling variables that cannot be negative, such as stock prices, biological growth, or income distributions.
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Pro Tips
The value of x must be strictly positive (x > 0).
The shape parameter σ (standard deviation of the log) must also be positive.
The median of the distribution is exactly exp(μ).
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Fun Facts
"Wealth and income often follow this distribution because growth is multiplicative (the rich get richer effect)."
"In finance, the Black-Scholes option pricing model assumes stock prices follow a log-normal distribution."
"Many environmental quantities, like the size of oil fields or rainfall amounts, are naturally log-normal."
