Passphrase Strength Calculator
A passphrase is a sequence of randomly chosen words that provides high cryptographic entropy while remaining human-memorable. This calculator uses the standard diceware formula: entropy (bits) = number of words multiplied by log2 of the wordlist size. The EFF large diceware wordlist has 7,776 words (each word chosen by five dice rolls), giving about 12.92 bits per word. NIST SP 800-63B recommends at least 112 bits for sensitive authentication. A 9-word diceware passphrase delivers approximately 116 bits, well above that threshold and easy to memorize compared to a random 20-character password.
Passphrase entropy formula
Entropy (bits) = words × log2(wordlist size)
Each word chosen randomly from a wordlist of size W contributes log2(W) bits of entropy, because there are W equally probable choices. For the EFF large diceware list (W = 7,776), each word adds log2(7,776) = 12.925 bits. Six words give 77.55 bits; nine words give 116.33 bits.
Understanding passphrase strength ratings
- Below 60 bits: weak, vulnerable to offline attack with modern hardware.
- 60 to 80 bits: moderate, adequate for low-sensitivity online services with rate limiting.
- 80 to 112 bits: strong, meets NIST SP 800-63B Level 2 requirements.
- 112 to 128 bits: very strong, suitable for sensitive accounts and long-lived credentials.
- 128 bits and above: excellent, exceeds NIST minimum for high-value targets.
Passphrase strength calculator: frequently asked questions
How is passphrase entropy calculated?
Entropy in bits equals the number of words multiplied by log2 of the wordlist size. For a 6-word diceware passphrase from a 7,776-word list (5 dice rolls per word), entropy is 6 x log2(7776) = 6 x 12.92 = 77.5 bits.
How many bits of entropy does NIST recommend?
NIST SP 800-63B recommends at least 112 bits of security strength for general-purpose authentication. For high-value accounts, 128 bits or more is advised. A 10-word diceware passphrase delivers about 129 bits.
What is the EFF large wordlist size?
The EFF large diceware wordlist contains 7,776 words (6^5), one per five-dice roll. The EFF short list contains 1,296 words. Choosing the larger list gives more entropy per word.
Does adding special characters significantly increase entropy?
Character substitutions add modest entropy. Increasing the number of words is far more effective. Adding one word from a 7,776-word list adds ~12.9 bits, while a single special character from 32 symbols adds only ~5 bits.
What is the difference between a password and a passphrase?
A password is typically a short string of mixed characters. A passphrase is a sequence of random words. Passphrases can achieve high entropy while remaining memorable, as shown by research cited in NIST SP 800-63B.
Official sources
- NIST SP 800-63B Digital Identity Guidelines: pages.nist.gov/800-63-3/sp800-63b.html.
- EFF Diceware Wordlists: eff.org.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.