Exponential Distribution Calculator

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Choose whether to enter the rate lambda directly or the mean (average waiting time). Both describe the same distribution.
The average number of events per unit of time (or distance). Must be greater than 0.
Point mode computes PDF and CDF at a single x. Interval mode finds P(x1 < X < x2). Inverse mode solves for x given a cumulative probability.
The value at which to evaluate the distribution. Must be >= 0.
PDF - f(x)
0.303265

Probability density at x. The height of the exponential curve at this point.

Rate parameter (lambda)0.5
CDF - P(X <= x)0.393469
Survival - P(X > x)0.606531
Mean (mu)2
Median1.3863
Variance (sigma squared)4
Standard deviation (sigma)2
0.39346965.3% below · x

Exponential distribution with lambda = 0.5000 (mean = 2.0000)

  • With lambda = 0.5000, events occur on average every 2.0000 units of time. The median waiting time is 1.3863, shorter than the mean because the exponential distribution is right-skewed.
  • At x = 1, there is a 39.35% chance the event has already occurred and a 60.65% chance it has not yet happened.
  • The exponential distribution has the memoryless property: knowing that an event has not yet occurred gives no information about how much longer you will wait.

Next stepIf events cluster in groups rather than arriving one at a time, consider the Poisson distribution for counts or the Gamma distribution for the sum of multiple exponential waiting times.

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