Exponential Distribution Calculator
Enter the rate (or the mean time between events) and a value of x.
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Exponential Distribution Calculator by TheCalcTools
How the Exponential Distribution Calculator works
The exponential distribution models the time until an event when events happen at a constant average rate: P(X ≤ x) = 1 − e^(−λx). Its mean is 1/λ and its median ln 2 ÷ λ.
It is memoryless: having waited already does not change the chance of waiting longer. It is used for arrivals in queues and lifetimes of components with a constant failure rate.
The formula
Worked example
Using the default values shown in the calculator:
| Parameter given as | Mean time between events |
|---|---|
| Mean (μ) | 10 |
| Rate (λ) | 0.1 |
| Value x | 5 |
| Percentile to find | 90 % |
- With a mean of 10, the chance of an event within 5: 0.393469.
- Median 6.9315; 90% of waits are under 23.0259.
Result:
| P(X ≤ x) | 0.393469 |
|---|---|
| P(X > x) | 0.606531 |
| Mean | 10.0000 |
| Median | 6.9315 |
| Value at the percentile | 23.0259 |
Frequently asked questions
How does it relate to the Poisson distribution?
If events follow a Poisson process with rate λ, the gaps between them are exponential with the same λ.
Sources and further reading
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This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.