Random Number Generator
Generate results with the Random Number Generator — set your parameters and get cryptographically-random output instantly.
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Math.random() returns a float in [0,1). Multiply by the range size and add the minimum to get a uniformly distributed integer in [min, max].
Last reviewed: December 2025
Worked Examples
Example 1: Single random number 1-100
Example 2: 5 lottery numbers 1-49
Background & Theory
The Random Number Generator is grounded in the established principles and formulas described below. Mathematics rests on a hierarchy of number systems, each extending the previous. The natural numbers (1, 2, 3, ...) support counting and ordering. The integers add negative values and zero, enabling subtraction without restriction. The rational numbers, expressible as p/q where p and q are integers and q is nonzero, close the system under division. The real numbers fill the gaps left by irrationals such as the square root of 2 or pi, forming a complete ordered field. The complex numbers, written as a + bi where i is the square root of negative one, complete the algebraic closure of the reals and allow every polynomial to have a root. Prime factorization states that every integer greater than one is uniquely expressible as a product of primes, a result known as the Fundamental Theorem of Arithmetic. Computing the greatest common divisor (GCD) of two integers relies most efficiently on the Euclidean algorithm: repeatedly replace the larger number with the remainder when it is divided by the smaller, until the remainder is zero. The last nonzero remainder is the GCD. The least common multiple (LCM) follows from the identity LCM(a, b) = |a * b| / GCD(a, b). Modular arithmetic defines equivalence classes of integers that share the same remainder under division by a modulus n. Fermat's Little Theorem and Euler's Theorem arise from this structure and underpin modern cryptography. Logarithms are the inverses of exponential functions. If b raised to the power x equals y, then the logarithm base b of y equals x. The natural logarithm uses base e, approximately 2.71828. Combinatorics counts arrangements and selections. The number of ordered arrangements (permutations) of r objects from n distinct objects is nPr = n! / (n - r)!. The number of unordered selections (combinations) is nCr = n! / (r! * (n - r)!). Pascal's triangle arranges these binomial coefficients so that each entry equals the sum of the two entries directly above it. The Fibonacci sequence, defined by F(1) = 1, F(2) = 1, and F(n) = F(n-1) + F(n-2), appears throughout nature and connects deeply to the golden ratio via Binet's formula.
History
The Random Number Generator builds on a long history of ideas and practice, traced below. Mathematics as a systematic discipline traces to ancient Mesopotamia. Babylonian clay tablets dating to around 1800 BCE demonstrate knowledge of quadratic equations, Pythagorean triples, and base-60 arithmetic, suggesting a practical mathematical tradition far preceding Greek formalism. Euclid of Alexandria compiled the Elements around 300 BCE, establishing the axiomatic method that would define rigorous mathematics for over two thousand years. His work organized plane geometry, number theory, and proportion into logically chained propositions derived from a small set of postulates. The algorithm bearing his name for computing GCDs appears in Book VII and remains in use today. In the 9th century, the Persian scholar Muhammad ibn Musa Al-Khwarizmi wrote Al-Kitab al-mukhtasar fi hisab al-jabr wal-muqabala, the treatise whose title gave algebra its name. He systematized the solution of linear and quadratic equations and described procedures that operated on unknowns as objects, a conceptual leap away from purely numerical calculation. Rene Descartes introduced coordinate geometry in 1637 by uniting algebra and Euclidean geometry, allowing curves to be studied through equations. This synthesis set the stage for calculus. Isaac Newton and Gottfried Wilhelm Leibniz independently developed calculus during the 1660s and 1670s, triggering a priority dispute that lasted decades and divided British and Continental mathematicians. Carl Friedrich Gauss proved the Fundamental Theorem of Algebra in 1799, showing that every nonconstant polynomial has at least one complex root. His Disquisitiones Arithmeticae of 1801 established modern number theory. David Hilbert's formalist program at the turn of the 20th century sought to place all of mathematics on an explicit axiomatic foundation, a project that Kurt Godel's incompleteness theorems of 1931 showed to be fundamentally limited. Alan Turing's work in the 1930s on computability introduced the theoretical model of the stored-program computer and linked mathematical logic directly to the limits of algorithmic calculation. His proof that no algorithm can decide in general whether an arbitrary program will halt or run forever placed fundamental boundaries on what mathematics can mechanically determine, and it opened the discipline now known as theoretical computer science.
Frequently Asked Questions
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy
Random Number Generator Formula
floor(Math.random() × (max - min + 1)) + min
Math.random() returns a float in [0,1). Multiply by the range size and add the minimum to get a uniformly distributed integer in [min, max].
Random Number Generator — Worked Examples
Example 1: Single random number 1-100
Problem:Min: 1, Max: 100, Count: 1
Solution:floor(Math.random() × 100) + 1
Result:e.g. 73
Example 2: 5 lottery numbers 1-49
Problem:Min: 1, Max: 49, Count: 5
Solution:5 independent draws each uniformly distributed in [1,49]
Result:e.g. 7, 23, 31, 42, 48
Random Number Generator — Frequently Asked Questions
Is Math.random() truly random?
No. Math.random() is a pseudo-random number generator (PRNG) — it uses a deterministic algorithm seeded internally by the browser. The output appears random and passes statistical tests, but it is not cryptographically secure. For passwords, tokens, or security-sensitive values, use crypto.getRandomValues() instead. For games, simulations, and lotteries, Math.random() is perfectly adequate.
What is the difference between random and pseudo-random?
True random numbers derive from physical phenomena — radioactive decay, thermal noise, atmospheric static — and are fundamentally unpredictable. Pseudo-random numbers are produced by algorithms: given the same starting seed, the sequence repeats identically. Modern PRNGs like xorshift128+ (used in V8 for Math.random()) produce sequences that are statistically indistinguishable from true random for most practical purposes.
How to pick random lottery numbers?
Set Min to 1 and Max to the highest number in your lottery (e.g., 49 for most 6/49 lotteries), then set Count to how many numbers you need (e.g., 6). Each generated number is independently chosen from the full range. Note: since the lottery draw is also random, using a random generator gives you the same statistical odds as any other selection method.
What is a fair random number generator?
A fair RNG produces each number in the range with equal probability — a uniform distribution. This generator uses the formula: floor(Math.random() × (max - min + 1)) + min, which gives every integer in [min, max] an equal 1/(max-min+1) chance. Fairness can be verified by generating a large sample and confirming each value appears roughly equally often.