Lognormal Distribution Calculator

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The mean of the natural logarithm of X. Controls the scale of the distribution. Also called the log-mean or location parameter.
The standard deviation of the natural logarithm of X. Must be positive. Also called the log-standard-deviation or shape parameter.
Choose whether to evaluate the distribution at a specific x, find the x for a given probability, or just view summary statistics.
The positive value at which to evaluate the PDF and CDF. Must be greater than zero.
Mean (expected value)
1.648721

exp(mu + sigma^2 / 2)

Median1
Mode0.367879
Variance4.670774
Standard deviation2.161197
Skewness6.184877
PDF at x0.39894228
P(X <= x)0.5
P(X > x)0.5
25th percentile (Q1)0.509416
75th percentile (Q3)1.963031
95th percentile5.180252
99th percentile10.240474
0.569.1% below · x

Lognormal(mu=0, sigma=1): mean 1.6487, median 1.0000

  • The mean is 1.6487, the median is 1.0000, and the mode is 0.3679.
  • Because the mean exceeds the median, the distribution is right-skewed: a long tail extends toward large values, and the typical (median) value is below the average.
  • Skewness is 6.1849. Higher sigma values produce heavier right tails and greater skewness.
  • At x = 1: 50.00% of the distribution lies at or below this value, and 50.00% lies above it.

Next stepIf you collected real data, you can back out mu and sigma from the sample by computing the mean and standard deviation of the log-transformed values.

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