# Exponential Distribution Calculator

Calculate PDF, CDF, survival probability, and interval probability for an exponential distribution

> Canonical page: https://elysiatools.com/en/tools/exponential-distribution-calculator

- **Category:** Math & Numbers

- **Keywords:** exponential distribution, waiting time, survival probability, lambda, statistics

## Overview

Calculate exponential distribution probabilities for waiting times between independent events at a constant rate.

## Inputs

- **Rate Lambda** (number)
- **Value** (number)
- **Interval Lower (Optional)** (text): e.g. 0
- **Interval Upper (Optional)** (text): e.g. 3
- **Decimal Places** (number)

## When to use

- When analyzing the time between independent events occurring at a constant average rate.
- When calculating the reliability or survival probability of a system or component over time.
- When determining the likelihood of a waiting time falling within a specific numerical interval.

## How it works

- Enter the Rate Lambda (λ), which represents the constant average rate of occurrence for your events.
- Input the target Value (x) to calculate the exact density, cumulative probability, and survival probability at that point.
- Optionally, specify an Interval Lower and Upper bound to calculate the probability of an event occurring within that specific range.
- Adjust the Decimal Places setting to control the precision of the generated JSON output.

## Use cases

- Predicting the time until the next customer arrives at a service desk.
- Estimating the lifespan or failure time of mechanical or electronic components.
- Modeling the time between incoming requests to a web server for capacity planning.

## Frequently asked questions

### What is Rate Lambda (λ)?

Rate Lambda is the rate parameter of the exponential distribution, representing the average number of events in a given time interval.

### What does the survival probability indicate?

Survival probability (calculated as 1 - CDF) represents the likelihood that an event has not yet occurred by a specific time or value.

### Can I calculate the probability between two specific times?

Yes, by entering values in the Interval Lower and Interval Upper fields, the tool will calculate the probability of the event occurring within that specific range.

### What is the difference between PDF and CDF?

The PDF (Probability Density Function) shows the relative likelihood of an exact value, while the CDF (Cumulative Distribution Function) shows the probability that a value is less than or equal to the target.

### What format are the results provided in?

The calculator outputs the results in a structured JSON format, making it easy to copy and integrate into other statistical software or scripts.

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## Samples

- [PDF Samples](https://elysiatools.com/en/samples/pdf-samples): Generated PDF samples from tools dated 2026-02-01 to 2026-02-10
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