# Uniform Distribution Calculator

Calculate PDF, CDF, survival probability, and interval probability for a continuous uniform distribution

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

- **Category:** Math & Numbers

- **Keywords:** uniform distribution, continuous distribution, probability, statistics

## Overview

Calculate probabilities for a continuous uniform distribution over a finite range [a, b].

## Inputs

- **Minimum** (number)
- **Maximum** (number)
- **Value** (number)
- **Interval Lower (Optional)** (text): e.g. 2
- **Interval Upper (Optional)** (text): e.g. 6
- **Decimal Places** (number)

## When to use

- When analyzing random variables where every outcome within a specific continuous range has an equal chance of occurring.
- When calculating the probability of an event falling between two distinct values in a continuous dataset.
- When verifying statistical homework or building probability models for simulations and risk assessments.

## How it works

- Enter the minimum and maximum boundaries of your uniform distribution.
- Input a specific target value to calculate its cumulative probability (CDF) and probability density (PDF).
- Optionally, provide an upper and lower interval bound to calculate the probability of an event occurring within that specific range.
- Set your preferred decimal precision and generate the statistical results instantly.

## Use cases

- Estimating wait times for a bus or train that arrives at strictly regular intervals.
- Modeling random number generation in computer simulations and gaming mechanics.
- Calculating the probability of manufacturing defects when errors are equally likely to occur at any point along a production line.

## Frequently asked questions

### What is a continuous uniform distribution?

It is a probability distribution where all values within a specified continuous range [a, b] are equally likely to occur, resulting in a flat, rectangular probability density.

### What does the PDF represent in this calculator?

The Probability Density Function (PDF) represents the constant probability density for any value within the defined minimum and maximum bounds. It is calculated as 1 divided by the difference between the maximum and minimum.

### How is the CDF calculated?

The Cumulative Distribution Function (CDF) calculates the probability that a random variable is less than or equal to your specified target value.

### Can I calculate the probability between two numbers?

Yes, by entering values into the optional Interval Lower and Interval Upper fields, the tool will calculate the exact probability of an outcome falling within that specific range.

### What happens if my target value is outside the minimum and maximum bounds?

If the value is below the minimum, the CDF is 0. If it is above the maximum, the CDF is 1. The PDF outside the bounds is always 0.

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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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