What is password entropy?
Password entropy measures how unpredictable a password is, expressed in bits. Each additional bit doubles the number of guesses an attacker needs. For a randomly generated password, entropy equals the length multiplied by log2 of the pool size. A 12-character password drawn from 86 possible symbols carries 77 bits.
- Topic
- Passwords
- Also called
- entropy of a password, bits of entropy
- Reading time
- 2 min
- Reviewed
On this page
How password entropy is calculated
The formula is entropy = length x log2(pool size). Pool size is the number of distinct symbols each position could hold: 10 for digits, 26 for lowercase letters, 62 for alphanumerics, and around 86 once a typical symbol set is included.
For a passphrase the same formula applies with words in place of characters. Five words drawn at random from the 1,296-word EFF list gives 5 x log2(1296) = 51.7 bits.
How many bits are enough
Below 45 bits offers little margin against fast offline guessing. Between 60 and 80 bits is a practical target for randomly generated secrets. Above 100 bits, brute force is unlikely to be the limiting risk; phishing, malware, and password reuse usually matter more.
What people often get wrong
"My password has 70 bits of entropy because it is 11 characters long."
The formula only holds for passwords chosen at random. Tr0ub4dor&3 calculates to 70 bits but is worth closer to 28 in practice, because attackers guess a dictionary word plus standard substitutions rather than character by character.
Sources
These primary references support the terminology and current security guidance used in this definition.
