Uniform Distribution Calculator

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

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

Example Results

1 examples

Evaluate a uniform range from 0 to 10

Find density, cumulative probability, and interval probability for a continuous uniform distribution.

{
  "result": {
    "pdf": 0.1,
    "cdf": 0.4,
    "intervalProbability": 0.4
  }
}
View input parameters
{ "minimum": 0, "maximum": 10, "value": 4, "intervalLower": "2", "intervalUpper": "6", "decimalPlaces": 4 }

Key Facts

Category
Math, Date & Finance
Input Types
number, text
Output Type
json
Sample Coverage
4
API Ready
Yes

Overview

The Uniform Distribution Calculator is a statistical utility designed to compute the Probability Density Function (PDF), Cumulative Distribution Function (CDF), and interval probabilities for a continuous uniform distribution. By defining the minimum and maximum bounds of your dataset, you can instantly determine the likelihood of specific outcomes or ranges occurring within a perfectly flat probability model.

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.

Examples

1. Calculating Wait Time Probabilities

Operations Analyst
Background
A subway train arrives exactly every 15 minutes. A passenger arrives at the station at a random time.
Problem
Determine the probability that the passenger will wait 5 minutes or less.
How to Use
Set the minimum to 0 and maximum to 15. Enter 5 as the target value.
Example Config
Minimum: 0, Maximum: 15, Value: 5
Outcome
The calculator returns a CDF of 0.3333, meaning there is a 33.33% chance the wait time will be 5 minutes or less.

2. Quality Control Tolerances

Manufacturing Engineer
Background
A machine cuts pipes to lengths uniformly distributed between 100 cm and 105 cm.
Problem
Find the probability that a randomly selected pipe falls within the acceptable tolerance range of 101 cm to 103 cm.
How to Use
Input 100 as the minimum and 105 as the maximum. Set the Interval Lower to 101 and Interval Upper to 103.
Example Config
Minimum: 100, Maximum: 105, Interval Lower: 101, Interval Upper: 103
Outcome
The tool calculates an interval probability of 0.4000, indicating a 40% chance the pipe meets the specific tolerance.

Try with Samples

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FAQ

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.

API Documentation

Request Endpoint

POST /en/api/tools/uniform-distribution-calculator

Request Parameters

Parameter Name Type Required Description
minimum number Yes -
maximum number Yes -
value number Yes -
intervalLower text No -
intervalUpper text No -
decimalPlaces number No -

Response Format

{
  "key": {...},
  "metadata": {
    "key": "value"
  },
  "error": "Error message (optional)",
  "message": "Notification message (optional)"
}
JSON Data: JSON Data

AI MCP Documentation

Add this tool to your MCP server configuration: 

{
  "mcpServers": {
    "elysiatools-uniform-distribution-calculator": {
      "name": "uniform-distribution-calculator",
      "description": "Calculate PDF, CDF, survival probability, and interval probability for a continuous uniform distribution",
      "baseUrl": "https://elysiatools.com/mcp/sse?toolId=uniform-distribution-calculator",
      "command": "",
      "args": [],
      "env": {},
      "isActive": true,
      "type": "sse"
    }
  }
}

You can chain multiple tools, e.g.: `https://elysiatools.com/mcp/sse?toolId=png-to-webp,jpg-to-webp,gif-to-webp`, max 20 tools.

If you encounter any issues, please contact us at [email protected]