Input
64 bits, N = 1,000,000,000
Collision probability
About 2.7%
Design Tools
Hash Collision Calculator — Birthday Paradox Estimate
Estimate the probability of at least one collision for a given hash bit length and sample size using the birthday-paradox approximation. Useful for short IDs and truncated checksums. Calculation stays in the browser.
HashCollisionMath
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Hash Collision Calculator
Calculate the exact statistical probability of a hash collision (Birthday Paradox) occurring given the space size and number of generated tokens. Useful when deciding if an 8-char short ID is strictly enough.
Bits
Total Possible Combos (Space) 2^32
Probability of at least 1 Collision
68.8% P ≈ 1 - e^(-N^2 / 2H)
Use cases
- Check whether a short-link or invite-code space is large enough
- Estimate risk when truncating hashes for checksums
- Compare collision rates across bit lengths at a fixed N
How to use
- Choose or enter the hash bit length
- Enter expected sample size N
- Read and copy the collision probability
Example input and output
FAQ
Is the result exact?
No. It uses the approximation 1 - e^(-N² / 2H) for order-of-magnitude judgment, not a formal counting proof.
How should I choose bits?
Match the ID space size—for example 32, 64, or 128—or use presets aligned with CRC16, short MD5, UUID, or SHA-256 scale.
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