Exponential Distribution Calculator
Calculate exponential waiting-time density, cumulative probability and survival probability.
Result for the values shown.
Calculations run in your browser.
What to enter
| Input | Meaning and units |
|---|---|
| Event rate (per time unit) | Enter event rate in per time unit; use the same basis as the other measurements. |
| Waiting time (time units) | Enter waiting time in time units; use the same basis as the other measurements. |
Understanding your result
These outputs describe the probability model and event definitions you entered. A probability is a number from 0 to 1; a probability density is not itself the probability of one exact continuous value.
Common mistakes
- Entering 25 instead of 0.25 for a probability, or assuming events are independent when the model requires that assumption.
- Confusing an exact-count probability with a cumulative probability, or replacement with sampling without replacement.
Check your calculation
- Check a zero/certain-event boundary and the stated support of the distribution against the worked example.
Calculation checks, sources and review limits
What is the probability the waiting time is at most x?
Calculate exponential waiting-time density, cumulative probability and survival probability.
Common uses
- What is the probability the waiting time is at most x
How it works
survival = exp(0 - rate * x); cdf = 1 - survival; pdf = rate * survival
Worked example
Enter Event rate: 2 per time unit; Waiting time: 0 time units. Results: Probability density: 2 per time unit; Probability waiting time is at most x: 0 ; Probability waiting time exceeds x: 1 .