Random Number Generator

True randomness versus pseudorandomness

A pseudorandom generator is a deterministic algorithm. Given the same starting seed it produces the same sequence forever. That is a feature for simulations and reproducible tests, and a fatal flaw for anything secret.

A cryptographically secure generator is seeded from physical entropy the operating system collects — interrupt timings, hardware noise, on-chip instructions such as RDRAND — and is designed so that observing past output tells you nothing about future output.

This tool uses crypto.getRandomValues(), which is the browser’s interface to that CSPRNG. Math.random() is not, and its output has been reverse-engineered from a handful of observed values in every major engine.

Modulo bias, and why this tool avoids it

The obvious way to get a number in a range is random() % range. It is also subtly wrong.

Suppose your source produces values 0–255 and you want 1–10. There are 256 possible inputs and 10 outputs, and 256 is not divisible by 10. Values 0–5 each occur 26 times across the range while 6–9 occur 25 times, so the low outcomes are about 4% more likely.

The fix is rejection sampling: discard any source value that falls in the uneven tail and draw again.

function randInt(lo, hi) {
  const range = hi - lo + 1;
  const limit = Math.floor(2**32 / range) * range;
  let r;
  do {
    r = crypto.getRandomValues(new Uint32Array(1))[0];
  } while (r >= limit);   // reject the biased tail
  return lo + (r % range);
}

The loop almost never runs twice, and the result is exactly uniform. This is the algorithm behind every number on this page.

Shuffling correctly

The list shuffle uses the Fisher-Yates algorithm, walking backwards through the array and swapping each element with a randomly chosen earlier one. Every one of the n! orderings is equally likely.

The common broken alternative is array.sort(() => Math.random() - 0.5). It looks elegant and produces a badly non-uniform distribution, because sort algorithms assume a consistent comparator and an inconsistent one leaves elements near their original positions. Microsoft used this exact approach in a 2008 browser ballot screen and Internet Explorer appeared in the first position far more often than chance allows.

// Correct: Fisher-Yates
for (let i = a.length - 1; i > 0; i--) {
  const j = randInt(0, i);
  [a[i], a[j]] = [a[j], a[i]];
}

What each mode is for

• Integers with no repeats — raffle draws, sampling rows from a dataset, assigning unique slots. Implemented as a full shuffle then a slice, so it is uniform even when you draw most of the range.
• Decimals — Monte Carlo inputs, jitter values, synthetic test data.
• Dice and coins — tabletop games and teaching probability. The summary line reports the actual heads/tails split so you can watch the law of large numbers at work.
• Hex bytes — nonces, initialisation vectors and API key material. For passwords use the dedicated password generator, which reports entropy.
• Pick and teams — fair selection from a list, and splitting a group into balanced teams by dealing round-robin from a shuffled list.

Frequently Asked Questions