Random Number Generator

Discrete & Continuous Uniform Probability Distributions

A Random Number Generator (RNG) draws independent variables from a specified bounded interval [a, b] where every possible outcome possesses equal mathematical likelihood.

Statistical Mathematical Properties

• Discrete Uniform Probability Mass Function: P = (1) / (b - a + 1) = (1) / (N)

• Theoretical Expected Mean: μ = E[X] = (a + b) / (2)

• Theoretical Population Variance: σ^2 = (^2 - 1) / (12)

• Standard Deviation: σ = √((^2 - 1) / (12))

• Continuous Uniform Probability Density Function: f(x) = (1) / (b - a) for a x b

Types of Random Number Generation

• Pseudo-Random Number Generators (PRNG): Deterministic algorithms that generate long non-repeating sequences from an initial numerical seed.

• Cryptographically Secure PRNG (CSPRNG): Utilizes operating system hardware entropy (keystroke timings, thermal noise) ensuring unpredictability for encryption keys and secure tokens.

How to Use This Calculator

Enter your Minimum Value (Lower Bound) (e.g. 1), Maximum Value (Upper Bound) (e.g. 100), Quantity of Numbers to Generate (e.g. 5 in numbers), Number Type — choose from Whole Integers (e.g. 7, 42, 89), Decimals (2 Decimal Places, e.g. 14.28), Decimals (4 Decimal Places, e.g. 14.2857), Duplicate Values — choose from Unique Numbers Only (No Repeats), Allow Duplicates / Repeats, and Result Sorting — choose from As Generated (Random Order), Sort Ascending (Low to High), Sort Descending (High to Low). Results update instantly as you type — adjust any value to compare scenarios.

The Formula

Formula Reference: Random Number Generator

Input variables:

minValue — Minimum Value (Lower Bound)

maxValue — Maximum Value (Upper Bound)

quantityCount — Quantity of Numbers to Generate

numberType — Number Type

allowDuplicates — Duplicate Values

Computed outputs:

generatedNumbers — Generated Random Numbers

sampleMean — Sample Mean (Average)

sampleSum — Sum Total

theoreticalExpectedMean — Theoretical Expected Mean (μ)

generationMetadata — Probability & Pool Statistics

Mathematical relationships extracted from calculation logic:

totalRange = max - min + 1

idx = Math.floor(Math.random() * pool.length)

r = Math.random() * (max - min) + min

sum = numbers.reduce((acc, curr) => acc + curr, 0)

theoMean = safeDiv(min + max, 2)

prob = type === 'integers' ? (safeDiv(1, totalRange) * 100).toFixed(4) : 'Continuous Uniform'

Standard: NIST / ISO mathematical definitions

Worked Example

Generating 5 unique lottery numbers between 1 and 100: Produces a fair, unbiased sample (e.g. 14, 27, 53, 68, 92) with a theoretical expected mean of 50.

50.

Understanding Your Result

Evaluate your result in the context of your specific use case and relevant industry standards or reference values. A single calculated result is a starting point — test two to three scenarios to understand how sensitive the outcome is to your key input assumptions. For high-stakes decisions, verify your result against a secondary source or subject-matter expert before acting.