How is password entropy calculated?

Entropy in bits equals Length × log2(Character Pool Size). For example, a 12-character alphanumeric password has 12 × log2(62) ≈ 71.45 bits of entropy.

Password & Secret Entropy Calculator

Measure the information-theoretic entropy of passwords and API keys to calculate realistic offline brute-force cracking resistance.

⚡ Quick Reference Answer (AEO Summary)

Password entropy uses the Shannon formula: Entropy (Bits) = Length × log₂(Pool Size). A password exceeding 60 bits resists online attacks; 80+ bits is required for offline database protection against modern multi-GPU hashcat arrays.

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Information Entropy

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Character Pool (R)

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Password Length (L)

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Brute-Force Estimate (100B H/s)

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The Information Entropy Formula & NIST Standards

Entropy in cryptography describes the number of binary attempts an attacker must theoretically attempt to guess a secret:

E = L × log₂(R)

Where:

L = Character length of the passphrase.
R = Size of the character pool:
- Numbers only (0-9): Pool size = 10
- Lowercase letters (a-z): Pool size = 26
- Mixed case (a-z, A-Z): Pool size = 52
- Alphanumeric + symbols: Pool size = 95

NIST Special Publication 800-63B Recommendations

NIST recommends prioritizing length over character complexity. A 4-word diceware passphrase (e.g. correct horse battery staple) produces over 77 bits of entropy and is significantly easier for humans to remember while remaining mathematically infeasible for brute-force cracking.