Last updated: 2026-06-29

UUID Collision Probability

A UUID (universally unique identifier) is a 128-bit value used to label records, files, and messages without a central authority handing out numbers. Its usefulness rests on a probabilistic promise: if everyone generates random UUIDs independently, the chance that any two match is vanishingly small. This calculator quantifies that promise — given how many identifiers you generate and how many random bits each carries, it estimates the probability of a collision and the counts at which collisions become a realistic concern.

Why uniqueness is probabilistic

A random UUID is not guaranteed to be unique. It is drawn uniformly from an enormous space, and uniqueness is a statistical near-certainty rather than a logical one. A version 4 UUID has 122 random bits — the other 6 of its 128 bits encode the version and variant — which gives about $5.3 \times 10^{36}$ possible values. With a space that large, repeating a value by chance is extraordinarily unlikely, but the probability is not exactly zero.

The birthday approximation

Collisions become likely much sooner than the size of the space suggests, a fact known as the birthday problem. For a space of $2^b$ values, the probability that at least two of $n$ identifiers collide is well approximated by:

$p \approx 1 - e^{-n^2 / (2 \cdot 2^{b})}$

The 50% point — where a collision is as likely as not — is reached near the square root of the space:

$n_{50} \approx \sqrt{2 \cdot 2^{b} \cdot \ln 2}$

For 122 random bits this is about $2.7 \times 10^{18}$ identifiers, roughly 2.7 quintillion.

Worked example

Suppose you shorten identifiers to 64 random bits to save space and generate a billion of them. The collision probability is:

So at 64 bits, a billion identifiers carry about a 2.7% chance of at least one collision — small but no longer negligible. The same billion identifiers as full 122-bit version 4 UUIDs have a collision probability below $10^{-19}$.

What this means in practice

For full version 4 UUIDs at any realistic scale, collisions are not a practical concern; reaching even a one-in-a-billion chance would take on the order of $10^{14}$ identifiers. The real risks lie elsewhere: a weak or poorly seeded random number generator that produces predictable or repeated outputs, or truncating identifiers to fewer bits, which moves the birthday bound dramatically closer. If you shorten identifiers, recompute with the reduced bit count. For the same collision mathematics applied to hash functions, see the Hash Collision Probability Calculator.

These figures are approximations valid when the count is far smaller than the size of the space, which holds for every realistic use of UUIDs.