How to use the exponential distribution calculator
Find the probability a waiting time is below a value, plus the mean and median of an exponential distribution. Enter rate λ (events per unit time), time value in the fields above; the probability x ≤ value, mean waiting time, median waiting time are computed instantly and plotted on the chart so you can see how the answer changes.
Common searches this calculator answers include “exponential distribution probability”, “waiting time probability”, “mean time between events”, “calculate exponential distribution”, “find probability x ≤ value”.
Formula
Variables
- lam — Rate λ (events per unit time)
- xv — Time value
Worked example
With rate λ (events per unit time) = 0.5, time value = 2, the calculator gives probability x ≤ value ≈ 63.21206 %; mean waiting time ≈ 2 units; median waiting time ≈ 1.386294 units.
Frequently asked questions
What is the exponential distribution calculator used for?
Find the probability a waiting time is below a value, plus the mean and median of an exponential distribution. It helps with questions such as “exponential distribution probability”, “waiting time probability”, “mean time between events”.
What is the formula for the exponential distribution calculation?
Probability X ≤ value (%) = 100 × (1-exp(-lam × xv)). Mean waiting time (units) = 1 / lam. Median waiting time (units) = ln(2) / lam. Here lam is rate λ (events per unit time), xv is time value.
What inputs do I need for the exponential distribution calculator?
You need rate λ (events per unit time), time value. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use the exponential distribution calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the exponential distribution result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.