Exponential Distribution Calculator
Calculate exponential distribution using your data.
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What this tool does
Calculate exponential distribution using your data. The exponential distribution models waiting time between Poisson events and is memoryless: elapsed waiting does not change the distribution of the remaining wait.
How to use the Exponential Distribution Calculator
- Enter or select rate (λ, events per unit time).
- Enter or select time (x).
- Read the calculated result; change any measurement to compare alternatives.
Formula
CDF P(X ≤ x) = 1 − e^(−λx); survival P(X > x) = e^(−λx); mean = 1/λ; median = ln(2)/λ
- lam
- Rate (λ, events per unit time)
- x
- Time (x)
The exponential distribution models waiting time between Poisson events and is memoryless: elapsed waiting does not change the distribution of the remaining wait.
Worked example
For exponential distribution calculator, the following measurements illustrate the exact method: Rate (λ, events per unit time): 0.5; Time (x): 2.
Inputs
- Rate (λ, events per unit time)0.5
- Time (x)2
Result
- P(X ≤ x) — event by time x (%)63.21
- P(X > x) — still waiting (%)36.79
- Mean waiting time2
- Median waiting time1.39
Results explained
- P(X ≤ x) — event by time x (%)
- P(X ≤ x) — event by time x (%) from the formula above. The exponential distribution models waiting time between Poisson events and is memoryless: elapsed waiting does not change the distribution of the remaining wait.
- P(X > x) — still waiting (%)
- P(X > x) — still waiting (%) from the formula above. The exponential distribution models waiting time between Poisson events and is memoryless: elapsed waiting does not change the distribution of the remaining wait.
- Mean waiting time
- Mean waiting time from the formula above. The exponential distribution models waiting time between Poisson events and is memoryless: elapsed waiting does not change the distribution of the remaining wait.
- Median waiting time
- Median waiting time from the formula above. The exponential distribution models waiting time between Poisson events and is memoryless: elapsed waiting does not change the distribution of the remaining wait.
Frequently asked questions
CDF P(X ≤ x) = 1 − e^(−λx); survival P(X > x) = e^(−λx); mean = 1/λ; median = ln(2)/λ
The exponential distribution models waiting time between Poisson events and is memoryless: elapsed waiting does not change the distribution of the remaining wait.
Enter numbers only, in the units and format each label describes. Remove missing values rather than substituting zero, unless zero is a real observation.
No. Results describe the numbers you entered. Statistical inference also depends on sampling design, independence, model fit and interpretation; a p-value is not the probability that a hypothesis is true.
No. Every calculation, including the distribution algorithms, runs entirely in your browser.