Password strength meters that show a colored bar or a "Weak / Medium / Strong" label are guessing. Some count character types; some check length; some look for dictionary words. None of them agree. The only mathematically rigorous measure of password strength is entropy — and once you understand it, you'll be able to evaluate any password accurately.
Entropy: a measure of unpredictability
Entropy, in the context of passwords, measures how unpredictable a password is — specifically, how many guesses an attacker would need to try before finding it by brute force. It's expressed in bits.
One bit of entropy means there are two equally likely possibilities (like a coin flip). Two bits means four possibilities. Each additional bit doubles the number of possibilities. At 60 bits of entropy, there are 260 ≈ 1.15 quadrillion possible passwords. At 128 bits, there are more possible passwords than atoms in the observable universe.
The formula
Password entropy is calculated as:
Where pool_size is the number of possible characters that could appear in each position, and length is the number of characters in the password.
For a password using only lowercase letters (a–z), pool size = 26. For one using lowercase + uppercase + digits + symbols, pool size ≈ 94. For each character position, you get log₂(94) ≈ 6.55 bits of entropy. A 16-character password with that character set has approximately 16 × 6.55 = 104.8 bits of entropy.
Practical entropy benchmarks
| Entropy | Crack time (10B guesses/sec) | Assessment |
|---|---|---|
| < 28 bits | Instantly | Very Weak — never use |
| 28–35 bits | Seconds to minutes | Weak — avoid |
| 36–59 bits | Hours to years | Fair — low-value accounts only |
| 60–79 bits | Thousands of years | Strong — good for most accounts |
| 80–99 bits | Billions of years | Very Strong — excellent |
| 100+ bits | Beyond any attack | Excellent — use for critical accounts |
Why entropy depends on character pool, not just length
Consider two 10-character passwords: iloveyou12 (predictable, dictionary-based) vs kX#9mQvR2! (random, all character types). They're the same length, but their effective entropy is radically different.
The word-based password is not drawn from a pool of 9410 possibilities — it comes from a much smaller pool of dictionary-based patterns. An attacker using a rule-based dictionary attack will crack it in milliseconds. The random password's entropy is genuinely 10 × 6.55 ≈ 65.5 bits, requiring years of brute-force effort.
This is why "clever" passwords — substituting @ for a, 3 for e, adding 123 at the end — don't actually improve entropy in practice. Crackers apply these rules automatically. Only genuine randomness produces the theoretical entropy the formula promises.
Entropy vs password length: which matters more?
Both matter, but length has slightly more leverage because it multiplies entropy linearly (each character adds the same number of bits). Adding one character to a 94-character pool password adds ~6.55 bits. Switching from lowercase-only (26) to all types (94) adds log₂(94/26) ≈ 1.85 bits per character — meaningful, but less than adding a character.
The practical takeaway: prioritize length first, then maximize the character pool. A 20-character lowercase-only random password has 20 × 4.7 = 94 bits of entropy — stronger than a 12-character password with all character types at 78.6 bits.
How our tools use entropy
Our Password Strength Checker calculates entropy in real time based on the actual character types present in your password and shows you the estimated crack time. Our generator defaults to 16 characters for over 104 bits of entropy — well above the recommended threshold for strong passwords.