Exponential Distribution
Free Exponential Distribution calculator with clear step-by-step results.
About Exponential Distribution
The exponential distribution models time between events.
Formula
Formula
PDF = λe^(−λx); CDF = 1 − e^(−λx)
Worked example
With the default values below, Exponential Distribution returns PDF at x of 0.18394. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Rate λminimum 0
- 0.5
- Time xminimum 0
- 2
Results
- PDF at x
- 0.18394
- P(X ≤ x)
- 0.63212
- Mean (1/λ)
- 2.000
Step by step
- 1Values used
- 2Formula
- 3PDF at x= 0.18394
- 4P(X ≤ x)= 0.63212
- 5Mean (1/λ)= 2.000
Assumptions and limits
- The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 5 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
How does this calculator work?
The exponential distribution models time between events.
Why does this matter?
Mean is the reciprocal of the rate.