Password Strength and Entropy Explained

Entropy measures how unpredictable a password is, in bits. It is not a measure of how complicated a password looks to a human — it is a measure of how many attempts a brute-force attacker would need on average to guess it, assuming every character was chosen uniformly at random from a known set of possibilities.

The formula is simple: entropy = length × log₂(charset size). Each bit of entropy doubles the number of possible passwords, so entropy grows linearly with length but only logarithmically with how many different characters are allowed — length matters more than character variety.

Charset size drives less than you'd think

Going from lowercase-only to the full printable set roughly adds two more bits per character — going from 8 characters to 16 characters adds 8 more characters' worth of bits entirely. Length wins.

What entropy looks like in practice

* Illustrative only. "Guesses per second" varies by orders of magnitude depending on the hashing algorithm, not whether the password is salted: a modern GPU can try billions of guesses per second against a fast hash like raw MD5 or SHA-256, but only a few hundred per second against a properly configured bcrypt or Argon2 hash. Salting stops one precomputed table from cracking every account at once — it has no effect on how fast a single already-captured hash can be attacked. Entropy tells you the size of the search space — it says nothing about how fast an attacker can search it.

How many bits is enough?

These are the same cutoffs this site's password generator uses for its live strength meter, so the label it shows you maps directly back to the entropy math above.

Where the math breaks down: humans aren't random

The entropy formula assumes every character is chosen independently and uniformly at random. A password a person invents rarely is. P@ssw0rd123! is 12 characters across the full character set and scores well on paper, but it follows an extremely common substitution pattern (@ for a, 0 for o) that password-cracking dictionaries specifically test for. Its real-world resistance is far below its theoretical entropy.

This is why modern guidance (including NIST SP 800-63B) has shifted away from mandating character-class complexity rules and toward encouraging length — random passphrases or, better, passwords generated by a tool that actually samples uniformly at random rather than a human trying to "look random."

What actually protects an account

• Length over complexity — a longer password with a smaller charset often beats a shorter one with every character class forced in.
• Uniqueness per site — entropy is irrelevant if the same password is reused and one of the sites using it is breached. Credential-stuffing attacks replay leaked username/password pairs against other sites, not brute-force guessing.
• A password manager — the practical way to have both a genuinely random password and a different one per site, without memorizing any of them.
• Two-factor authentication — makes a leaked or guessed password alone insufficient, independent of how strong it was.

A tool like this site's password generator uses the browser's cryptographically secure random number generator to sample uniformly at random from the selected character set, so the entropy math actually applies — unlike a password a person invents under the illusion of randomness.