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Hash Collision Birthday Calculator

Estimate collision probability and birthday-bound sample thresholds for an ideal hash output of a chosen bit length.

Estimate collision probability and birthday-bound sample thresholds for an ideal hash output of a chosen bit length.

How it works

The calculator uses the birthday approximation for an ideal uniformly distributed n-bit hash. With k samples, λ = k(k−1)/(2×2^n) and collision probability is approximately 1−e^(−λ).

The formula

λ = k(k−1) / (2 × 2^n); P ≈ 1 − e^(−λ)

n is hash-output bits, k is the number of samples, λ is expected colliding-pair intensity. Collision security is shown as n/2 bits for an ideal hash.

Worked example

For a 256-bit ideal hash, the 50% birthday threshold is about 4.0×10^38 samples, illustrating why collision strength is roughly 128 bits rather than 256.

For educational and technical analysis only. Not financial advice, wallet software, transaction signing, or a security audit. Protocol and wallet behavior can differ. Never enter a seed phrase, private key, xprv or wallet password into He-Sab or any website.

Frequently asked questions

What does this calculator calculate?

Estimate collision probability and birthday-bound sample thresholds for an ideal hash output of a chosen bit length.

Should I enter a seed phrase, private key, xprv or wallet password?

No. These calculators do not need secret wallet material. Never paste a seed phrase, private key, xprv or wallet password into He-Sab or any website.

Is the result authoritative for moving real funds?

No. It is an educational technical estimate. Confirm results with current Bitcoin or Lightning software, specifications and a safe test environment before using real funds.

Last content reviewSeptember 10, 2026
Editorial reviewHe-Sab Editorial Review

Sources and references

These sources are used to verify terminology, formulas, and information related to this calculator.