Exponential Distribution Calculator
PDF, CDF and survival probability from rate λ.
Enter your values
ⓘ Live results
Results
- P(X ≤ x)
- 77.687%
- P(X > x)
- 22.313%
- Density f(x)
- 0.111565
- Mean
- 2
- Median
- 1.3863
- Standard deviation
- 2
Quick answer
The exponential distribution models waiting time between random events; P(X ≤ x) = 1 − e^(−λx) with mean 1/λ.
P(X ≤ x) = 1 − e^(−λx)
How to use the Exponential Distribution Calculator
- 1Enter the rate λ — events per unit of time.
- 2Enter the value x you are testing.
- 3Read the cumulative and survival probabilities.
Worked example
Using the values the calculator loads with:
Inputs
- Rate λ0.5 per unit
- Value x3
Results
- P(X ≤ x)77.687%
- P(X > x)22.313%
- Density f(x)0.111565
- Mean2
- Median1.3863
- Standard deviation2
Frequently asked questions
What is λ in the exponential distribution?
The average number of events per unit time; if events arrive every 4 minutes, λ = 0.25 per minute.
Is the exponential distribution memoryless?
Yes — the chance of waiting another 5 minutes is the same no matter how long you already waited.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.