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Exponential distribution calculator

Model waiting time between events occurring at a constant rate λ.

Selected calculation result: —

Fill in the fields above — the result is computed on this page.

x or quantile
—
Density f(x)
—
P(X ≤ x)
—
P(X ≥ x)
—
Mean 1/λ
—
Variance 1/λ²
—
Standard deviation 1/λ
—
Median ln(2)/λ
—
What these numbers mean
  • The mean and standard deviation both equal 1/λ.
  • P(X≥x) decreases exponentially as e^(−λx).

The model does not fit a changing event rate or a waiting process with memory.

How to use this page
  1. Choose density, CDF, upper tail or quantile.
  2. Enter a positive λ.
  3. Enter x or probability q.

What this page does not do: The model does not fit a changing event rate or a waiting process with memory.

Further reading

The exponential distribution models a non-negative waiting time under a constant event rate. The rate λ is the reciprocal of the mean waiting time.

Its memoryless property means that the remaining waiting time does not depend on how long you have already waited.

Frequently asked questions

How do I choose λ?

If the mean waiting time is m, then λ=1/m in the same time unit.

Is density a point probability?

No. For a continuous variable, probability at one exact point is zero.

See also

← All calculators

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