Hash Collision Probability Calculator (Birthday Bound)

Enter how many IDs you generate and how many random bits they have to see the collision risk.

By TheCalcTools Updated October 17, 2026 Formula checked and tested

Your numbers

Number of IDs or hashes

Random bits per ID

UUID v4 has 122 random bits; an 8-character base-62 code has about 47.6

Probability of at least one collision

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IDs for a 50% chance of a collision

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IDs for a one-in-a-billion chance

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This is the birthday problem: with N possible values, collisions become likely after about √N items, far sooner than N.

The chance of at least one collision among n random values is about 1 − e^(−n(n−1)/(2N)). For very small probabilities it is about n²/(2N).

P ≈ 1 − exp(−n(n − 1) ÷ (2 × 2^bits))

Using the default values shown in the calculator:

Number of IDs or hashes	1e+09
Random bits per ID	122

Result:

Probability of at least one collision	9.404e-20
IDs for a 50% chance of a collision	2710000000000000000
IDs for a one-in-a-billion chance	103000000000000

Will UUID v4 ever collide?

Practically no: you would need about 2.7 × 10¹⁸ UUIDs for a 50% chance.

How long should short codes be?

Choose enough bits that the expected number of IDs you will ever create gives a negligible probability.

This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.