Passphrase Entropy Calculation
How to calculate passphrase entropy in bits — word count, word list size, and attack resistance.
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Passphrase Entropy Calculation Passphrase entropy in bits = word count × log₂(word list size). For the EFF Large List (7,776 words), each word contributes 12.92 bits — a 6-word passphrase gives 77.5 bits of entropy. --- What about The Formula? Where is the total number of distinct words in the list, and each word is selected uniformly at random from that list. | Word List | Size | Bits Per Word | 5 Words | 6 Words | 7 Words | |-----------|------|---------------|---------|---------|---------| | EFF Large List | 7,776 | 12.92 | 64.6 | 77.5 | 90.4 | | EFF Short List 1 | 1,296 | 10.34 | 51.7 | 62.0 | 72.4 | | Original Reinhold Diceware | 7,776 | 12.92 | 64.6 | 77.5 | 90.4 | | Random English words (100k) | 100,000 | 16.61 | 83.0 | 99.7 | 116.3 | | Randomly chosen letters (a-z) | 26 | 4.70 | —…
Frequently Asked Questions
How is passphrase entropy calculated?
Passphrase entropy is calculated as: entropy = word_count × log2(word_list_size). Each word drawn uniformly at random from a list of N words contributes log2(N) bits of entropy. For the EFF Large List (7,776 words), each word contributes log2(7776) ≈ 12.92 bits. A 6-word passphrase has 77.5 bits of entropy.
How many bits of entropy do I need?
NIST SP 800-63B recommends at least 112 bits for high-value accounts using memorised secrets when offline attacks are possible. For typical online accounts with rate limiting and account lockout, 60–80 bits is sufficient. For master passwords (password managers, encryption keys) where offline attacks are possible, aim for 100+ bits.
What is the NIST recommendation for password entropy?
NIST SP 800-63B (Digital Identity Guidelines) no longer recommends specific character composition rules or forced rotation policies. Instead it focuses on length, breached password checking, and rate limiting. For memorised secrets, it requires at least 8 characters and recommends 15+ for high-security contexts. Entropy requirements depend on the attack model (online vs offline).
How does passphrase length affect entropy?
Entropy scales linearly with word count. Each additional word from the EFF Large List adds 12.92 bits. Going from 5 words (64.6 bits) to 6 words (77.5 bits) adds 12.92 bits — roughly 8,000× more guessing work. The relationship is multiplicative in guessing difficulty: each bit doubles the number of guesses required.
What is a guessing attack on a passphrase?
An offline guessing attack occurs when an attacker obtains a stolen password hash and guesses candidates against it locally, without rate limiting. At 10 billion guesses/second (modern GPU hashcat speed against bcrypt), a 50-bit passphrase takes about 3 years; 60 bits takes 3,000 years; 80 bits takes 3 billion years. Online attacks are rate-limited and far slower.
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