Hash Collision Probability Calculator

ANA›Life Services Authority›National Calculator Authority›Hash Collision Probability Calculator

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Hash Collision Probability Calculator

Estimate the probability of at least one hash collision (birthday problem) given the number of possible hash values and the number of items hashed.

Hash Size (bits)

Common values: 32, 64, 128, 160, 256, 512

Number of Items (n)

How many distinct items are hashed

Preset Hash Functions

-- Select Preset -- CRC-32 (32 bits) FNV-64 / SipHash (64 bits) MD5 / MurmurHash3 (128 bits) SHA-1 (160 bits) SHA-256 (256 bits) SHA-512 (512 bits)

Calculate Fill in the fields and click Calculate.

function hasApplyPreset() { const preset = document.getElementById('has-preset').value; if (preset) { document.getElementById('has-bits').value = preset; } }

function hasCalc() { const bitsRaw = document.getElementById('has-bits').value.trim(); const itemsRaw = document.getElementById('has-items').value.trim(); const resultDiv = document.getElementById('has-result');

// --- Input Validation --- if (bitsRaw === '' || itemsRaw === '') { resultDiv.innerHTML = 'Please fill in all fields.'; return; }

const bits = parseFloat(bitsRaw); const n = parseFloat(itemsRaw);

if (!Number.isInteger(bits) || bits 512) { resultDiv.innerHTML = 'Hash size must be an integer between 1 and 512 bits.'; return; } if (!Number.isFinite(n) || n Number of items must be a positive integer.'; return; }

// --- Core Calculation --- // Number of possible hash values: H = 2^bits // Exact birthday probability: P(collision) = 1 - prod_{k=0}^{n-1} (1 - k/H) // Approximation (valid when n 0 (n very large relative to H), collision is essentially 1.

let collisionProb; let approxNote = '';

const logNumer = Math.log(n) + Math.log(n - 1) - Math.log(2); // log(n(n-1)/2) const logExponent = logNumer - logH; // log(n(n-1)/(2H))

if (logExponent > 700) { // exponent >> 1, collision probability ≈ 1 collisionProb = 1.0; } else { const exponent = Math.exp(logExponent); // n*(n-1)/(2H) const pNoCollision = Math.exp(-exponent); collisionProb = 1 - pNoCollision; approxNote = ' (birthday approximation)'; }

// --- Expected number of collisions --- // E[collisions] ≈ n(n-1) / (2H) [expected number of colliding pairs] let expectedCollisions; if (logExponent > 700) { expectedCollisions = Infinity; } else { expectedCollisions = Math.exp(logExponent); }

// --- Items needed for 50% collision probability --- // n_50 ≈ sqrt(2 * H * ln(2)) = sqrt(2 * ln(2)) * 2^(bits/2) // log(n_50) = 0.5 * log(2*ln(2)) + bits/2 * log(2) const logN50 = 0.5 * Math.log(2 * Math.LN2) + (bits / 2) * Math.LN2; const n50 = Math.exp(logN50);

// --- Format helpers --- function fmtProb(p) { if (p >= 0.9999999) return '≈ 100% (certain)'; if (p = 1e15) return x.toExponential(4); if (x >= 1000) return Math.round(x).toLocaleString(); return x.toPrecision(6); }

function fmtBig(x) { if (!isFinite(x)) return '∞'; if (x > 1e100) { const exp = Math.log10(x); return '10^' + exp.toFixed(1); } if (x > 1e15) return x.toExponential(3); return Math.round(x).toLocaleString(); }

// Risk level let riskLabel, riskColor; if (collisionProb Hash Space (H = 2${bits})${H_display} Items Hashed (n)${n.toLocaleString()} Collision Probability${approxNote} ${fmtProb(collisionProb)} Risk Level${riskLabel} Expected Colliding Pairs${fmtSci(expectedCollisions)} Items for 50% Collision Risk≈ ${fmtBig(n50)} `; }

#### Formula

Birthday Problem (Exact):

P(collision) = 1 − ∏k=0n−1 (1 − k / H)

where H = 2b is the number of possible hash values for a b-bit hash.

Approximation (accurate when n ≪ H):

P(collision) ≈ 1 − e−n(n−1) / (2H)

Items needed for 50% collision probability:

n50% ≈ √(2H · ln 2) ≈ 1.1774 · √H

Expected number of colliding pairs:

E[collisions] ≈ n(n−1) / (2H)

#### Assumptions & References

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References

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