What is Exponential Distribution?

It describes the time between independent events in a Poisson point process (events occur continuously and independently at a constant average rate).

Relationship to Poisson?

If events follow a Poisson distribution with rate λ, the time *between* events follows an Exponential distribution with rate λ.

What is Memorylessness?

The probability that an event occurs in the next t minutes is independent of how much time has already elapsed. P(X > s+t | X > s) = P(X > t).

Exponential Distribution

Calculate probability density and cumulative probability for time-to-event models.

Rate Parameter (λ)

Events per unit time

Target Value (x)

Time or distance

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CDF F(2)

0

PDF f(2) = 0

Distribution Curve (PDF)

Mean

Variance

Formulas

PDF

CDF

Mean

Variance

Frequently Asked Questions

About the Exponential

What it calculates

This exponential solves mathematical and statistical problems using standard formulas. Calculate time between events.

When to use it

Use for homework, data analysis, exam prep, or quick verification of manual calculations.

Example

Adjust the inputs above to model your specific scenario with the Exponential.

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Exponential Distribution

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Distribution Curve (PDF)

About the Exponential

Related Calculators

Beta Distribution

Cauchy

Gamma Distribution

Log-Normal

Normal Distribution

Pareto