Hash Collision Probability Calculator – Birthday Problem
Calculate the probability of a hash collision using the birthday paradox.
About This Calculator
Calculate the probability of a hash collision using the birthday paradox. Use the calculator above for instant results.
Worked Examples
- Probability: 1.16% of at least 1 collision
- 32-bit hash for 10K items: low but non-trivial risk
Answer: 1.16% collision probability
- Probability: ≈0% — astronomically unlikely
Answer: Effectively zero
- With 100 items in 256 buckets: ~86% collision probability!
Answer: 86% — need bigger hash
Who Uses This Calculator?
Understand birthday paradox in hashing.
Evaluate hash function security.
Choose hash size for data structures.
Birthday paradox probability demo.
Common Mistakes to Avoid
❌ Birthday paradox is counterintuitive
Only 23 people in a room gives 50% chance two share a birthday (365 'buckets'). Same math applies to hash collisions.
❌ Cryptographic vs non-cryptographic
SHA-256 (256-bit) is practically collision-free for any real dataset. MD5 (128-bit) was broken for cryptographic use but still OK for checksums.
Frequently Asked Questions
Birthday paradox formula?
P ≈ 1 - e^(-n²/2k) where n = items and k = possible hash values.
When does collision probability hit 50%?
At approximately √(2 × k × 0.693) items. For 32-bit: √(2 × 4B × 0.693) ≈ 77,000 items.
Collision resistance in crypto?
SHA-256: 2^128 operations to find collision (birthday attack on 256-bit = 2^128). Practically impossible with any realistic computing power.