Generate unbiased random numbers for lottery picks, dice rolling, classroom sampling, and research datasets. Includes seed-based reproducibility, distribution histogram, chi-square uniformity scoring, and CSV export — all free.
Generate numbers in any custom range. Supports seed for reproducibility.
Same seed + same settings = identical sequence every time. Uses Mulberry32 PRNG. Document the seed value in research methodology sections for peer-review reproducibility.
Free calculators for age, date differences, working hours, day counting, time durations, and more
Math.random() — implemented as xorshift128+ in Chrome/V8 and Firefox/SpiderMonkey. Specification: ECMA-262 §21.3.2.27. Passes BigCrush statistical test suite.Games, educational simulations, statistical sampling, reproducible research (with seed), lottery number picking, raffle draws, and classroom activities. Applicable per IETF RFC 4086 for non-cryptographic randomness.
Cryptographic key generation, security tokens, password hashing salts, regulated gambling systems, or any application where mathematical unpredictability is a security requirement. For cryptographic use, call crypto.getRandomValues() directly (CSPRNG, built into all modern browsers).
Integer mapping uses Math.floor(random() × (max − min + 1)) + min — the standard modulo-free approach that avoids modulo bias for arbitrary integer ranges.
Privacy & data safety: All generation runs locally in your browser. No numbers, inputs, seed values, or settings are transmitted to any server. Nothing is stored, logged, or tracked.
The term "random number generator" covers three fundamentally different technologies. Choosing the wrong type is a common mistake — it either wastes resources (TRNG for a game) or creates security vulnerabilities (PRNG for encryption). Here is how they differ:
| Type | Mechanism | Predictable? | Best For |
|---|---|---|---|
| PRNG | Deterministic algorithm (xorshift128+, Mulberry32, Mersenne Twister). Seeded from system clock or user input. | Yes, if seed is known | Games, simulations, statistical sampling, lottery picks, classroom activities, reproducible research |
| CSPRNG | Cryptographically secure algorithm (ChaCha20, AES-CTR, Fortuna). Collects entropy from OS-level hardware events. | No | Password generation, encryption keys, session tokens, OAuth nonces, API secrets |
| TRNG | Physical entropy: atmospheric noise (RANDOM.ORG), thermal noise, radioactive decay, quantum phenomena. | No | Government lotteries, hardware security modules (HSMs), high-stakes scientific research requiring true entropy |
This tool uses: Math.random() (xorshift128+ in V8) for unseeded generation, and Mulberry32 for seeded/reproducible generation. Both are high-quality PRNGs appropriate for all non-cryptographic use cases. Reference: IETF RFC 4086 — Randomness Requirements for Security.
Use Dice mode for D&D, Pathfinder, Warhammer, board games, or any tabletop RPG. Roll D4 through D100. Roll multiple dice simultaneously and see the total and average per die. The expected value of a D6 is 3.5; rolling 4D6 has an expected total of 14. This is displayed automatically so you can compare actual rolls against statistical expectation.
Use Lottery mode for fair winner selection in giveaways, raffles, and sweepstakes. Numbers are drawn without replacement, exactly like real lottery mechanics. US Powerball jackpot odds: 1 in 292,201,338. Mega Millions: 1 in 302,575,350. No combination is more likely than another — every set has equal odds. For transparent public draws, share your seed value before generating so participants can verify the outcome independently.
Use Research mode with seed-based generation for reproducible random sampling. Generate datasets up to 1,000 numbers with CSV export including algorithm metadata for academic citation. Compatible with R (read.csv()), Python pandas (pd.read_csv()), SPSS, and Excel. Document your seed value in the methodology section to satisfy peer-review reproducibility requirements.
Use Standard mode to pick student roll numbers, assign random quiz questions, form random groups, or demonstrate probability concepts. The distribution histogram makes the law of large numbers visible — generate 10 numbers and the distribution is uneven; generate 1,000 and the histogram converges to uniform. This is a powerful live demonstration of a foundational probability theorem.
Uses Math.random() as defined in the ECMAScript specification (ECMA-262). In V8-powered browsers (Chrome, Edge, Node.js) this is implemented as xorshift128+, which passes the BigCrush test suite — the most stringent standard statistical randomness test available. Firefox/SpiderMonkey also uses a variant of xorshift128+. The exact implementation varies by JavaScript engine; all major engines use high-quality PRNGs.
Uses the Mulberry32 algorithm developed by Tommy Ettinger. Formula: t = (seed += 0x6D2B79F5); t = Math.imul(t ^ t>>>15, 1|t); t ^= t + Math.imul(t ^ t>>>7, 61|t). Mulberry32 passes all standard Diehard randomness tests and produces statistically uniform output across the full 32-bit integer range. The same seed always produces the same sequence — by design, for reproducibility.
Numbers are mapped from the [0, 1) float to integer range [min, max] using Math.floor(random() × (max − min + 1)) + min. This is the standard modulo-free approach that avoids modulo bias for arbitrary integer ranges.
The uniformity score uses a chi-square goodness-of-fit test against the expected uniform distribution. Bins = min(10, floor(n / 10)). The chi-square statistic is normalized against the degrees of freedom to produce a 0–100 score. This methodology is equivalent to the statistical validation approach described in RFC 4086 §3.
Cryptographic key generation, security tokens, password hashing salts, encryption initialization vectors, gambling systems regulated by gaming authorities, or any context where mathematical unpredictability is a security requirement. For those use cases, use the browser's crypto.getRandomValues() API (CSPRNG, available in all modern browsers).
There is no 'most random' number. In a statistically uniform distribution, each number from 1 to 10 has exactly a 10% probability of being selected. Research in cognitive psychology shows humans avoid selecting 1 and 10 (extremes) and over-select 7, making human 'random' guessing systematically biased. A computer PRNG has no such bias — every number has equal probability.
A PRNG using Math.random() is theoretically predictable if the full internal state (128-bit in xorshift128+) is known — which is not normally accessible from a browser. For all practical non-security purposes, PRNG outputs cannot be predicted. For security applications requiring true unpredictability, use crypto.getRandomValues() (CSPRNG), which is computationally infeasible to predict even with knowledge of all previous outputs.
Use Dice mode and select D6 (6-sided). Each face (1–6) appears with equal probability of 1/6 ≈ 16.67%, simulating a fair die. For multiple dice, the total follows an approximately normal (bell-curve) distribution — this is the central limit theorem in action, demonstrable using the histogram feature.
Assign each participant a unique number (1, 2, 3...). Enter 1 as minimum and the participant count as maximum. Generate one number. The process is entirely unbiased. For transparent public giveaways, enable seed mode and announce the seed value before generating — participants can then verify the outcome independently by replicating the generation with the same seed.
The law of large numbers states that as sample size increases, the observed frequency of each outcome converges toward its theoretical probability. Generate 10 numbers between 1 and 100 and the distribution looks clustered; generate 1,000 and the histogram becomes nearly uniform. This convergence is visible in real time using the distribution histogram — a practical demonstration of a foundational theorem in probability theory.