Security advice often mentions "entropy" as though it explains everything. But what does it actually mean, and why does it matter for your passwords? Here's the plain-English version.
Entropy is unpredictability
In information theory, entropy measures how unpredictable something is. High entropy = hard to guess. Low entropy = easy to guess. When applied to passwords, entropy (measured in bits) tells us roughly how many guesses an attacker would need to crack it by brute force.
Each additional bit of entropy doubles the number of guesses required. So a password with 40 bits of entropy needs about a trillion guesses. A password with 41 bits? Two trillion. The math scales fast.
How entropy is calculated
The formula is straightforward: Entropy = length × log₂(charset size)
- Lowercase only (26 chars): ~4.7 bits per character
- Lower + upper (52 chars): ~5.7 bits per character
- Lower + upper + digits (62 chars): ~5.95 bits per character
- All printable characters (94 chars): ~6.55 bits per character
This means a random 16-character password using all character types has roughly 104 bits of entropy. That's effectively uncrackable with any foreseeable hardware.
The critical word: "random"
The formula above assumes every character is chosen randomly from the full character set. Human-chosen passwords radically depart from this. P@ssw0rd might theoretically have 52+ bits of entropy by the formula, but its actual "guessing entropy" — accounting for the fact that it follows a known dictionary-word pattern — is closer to 1–2 bits. Attackers try it in the first thousand guesses.
⚠️ Theoretical vs. practical entropy: Always think about practical entropy — how many guesses does an attacker actually need, given that they use dictionaries and rules? This is what zxcvbn measures, and it's far more meaningful than the formula alone.
What entropy level should you aim for?
Current guidance from NIST and cryptographers:
- Below 40 bits — crackable quickly even with modest hardware. Avoid.
- 40–60 bits — acceptable for low-value accounts, offline attacks are a concern
- 60–80 bits — good for most accounts, resists offline fast-hash attacks for years
- 80+ bits — excellent, resists even future hardware for the foreseeable future
A random 12-character password (all character types) gives ~79 bits. A random 16-character password gives ~105 bits. Either is a good target for important accounts.
✅ Bottom line: Length beats complexity. Adding two random characters to a password adds more security than switching from lowercase to mixed-case. Our generator defaults to 16 characters — start there.