Password Entropy: What "Strong" Actually Means in Bits
The red-yellow-green bar under a password field is a guess, usually a rough heuristic about length and character variety with no consistent standard behind it. The actual measure of how hard a password is to guess is entropy, expressed in bits, and it comes from an exact formula rather than a vibe.
The formula
Entropy in bits = length × log2(charset size). Charset size is how many distinct characters could appear in each position: 26 for lowercase-only, 62 for upper+lower+digits, roughly 94 if you allow the full printable-symbol set on a keyboard. log2 of that number tells you how many "yes/no" bits of information one random character from that set represents.
A 12-character password drawn randomly from a 62-character set: log2(62) ≈ 5.95 bits per character, times 12 characters = about 71.5 bits. Stretch the same password to 16 characters and it's 5.95 × 16 ≈ 95.3 bits. Four extra characters added roughly 24 bits, not a proportionally small bump. That's because of what a bit actually means here.
Why each bit doubles the work, not adds to it
Entropy is a count of doublings. A password with n bits of entropy has 2^n equally likely possibilities to search through in the worst case. Going from 71 bits to 72 bits doesn't make a password 1% harder to crack, it makes the search space exactly twice as large, because 2^72 is double 2^71. That compounding is why length matters so much more than it intuitively seems to: each additional random character doesn't add a fixed amount of security, it multiplies the remaining work by the charset size.
What the numbers mean in practice
Bit counts only mean something next to real-world cracking speed, so as rough, current-hardware benchmarks:
- Below 40 bits — crackable in seconds to minutes against an offline hash dump on consumer hardware. Fine for nothing.
- ~60 bits — a reasonable floor for a low-value account you don't reuse elsewhere, where a breach is an inconvenience, not a disaster.
- 80+ bits — the range to aim for on anything that guards money, identity, or your password manager itself. Well beyond what's practical to brute-force even at scale.
- 100+ bits — effectively uncrackable by exhaustive search with any hardware that exists today or is likely to exist soon. Beyond this point, entropy stops being the weak link.
Entropy doesn't protect a reused or leaked password
All of this math assumes an attacker has to brute-force the password, trying combinations blind. That's not how most real password compromises happen. Credential-stuffing attacks take a password already exposed in a previous breach and simply try it, verbatim, against other sites, no guessing involved. A dictionary attack tries known common passwords and variations of them first, and a 100-bit-theoretical password that happens to be a slightly modified word from a breach list gets tried in the first few thousand attempts, not the last 2^100th. Entropy measures resistance to a blind brute-force search. It says nothing about a password that's already sitting in a leaked-credentials database.
Getting a high-entropy password without doing the math yourself
Password Generator lets you set length and character set directly and generates a genuinely random string from them, so the entropy is exactly what the formula above predicts, not an estimate. Want to run this exact formula against a password you already have, instead of generating a new one? Use Password Entropy Checker.
Related guides
For how that randomness is actually produced under the hood, see how Kit-Bin's password generator gets its randomness. For whether a random string is even the right choice for a given password, see passphrase vs random password.