Hash Collision Probability Calculator

Calculate hash collision probability using birthday paradox. Find collision probability and birthday bound for hash functions.

Inputs

Hash Length

bits

Number of Hashes

Hash Function

Tab to move between fields

Results

Collision Probability

Expected Collisions

Birthday Bound

400,651,869,298,001,200,000,000,000,000,000,000,000

Time to Collision4,637,170,000,000,000,000,000,000 days

How to Use This Calculator

Enter the hash function digest size in bits.
Set the number of messages to be hashed.
Review the probability of at least one collision occurring.
Ensure the collision probability is below your application acceptable risk threshold.
For digital signatures, collision resistance requires a hash output at least twice the desired security level.

What each input means

Hash Length: Hash output length in bits
Number of Hashes: Number of hash values to compare
Hash Function: Hash function type

How this is calculated

Formula

P(collision) ≈ 1 - e^(-n²/(2×m))

Worked example, using the default values

Identify Input Parameters
Hash Length = 256, Number of Hashes = 1000000, Hash Function = 0 = 3 input(s) provided
Calculate Collision Probability
0 = 0%
Calculate Expected Collisions
Expected Collisions
0 = 0
Calculate Birthday Bound
Birthday Bound
4.006518692980012e+38 = 4.006518692980012e+38
Calculate Time to Collision
Time to Collision
4.63717e+24 = 4.63717e+24

Engine last updated July 22, 2026. Checked against 2 independently-derived tests — how we verify calculators.

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