By Freddy ·
Entropy is a measure of unpredictability, expressed in bits. Each additional bit of entropy doubles the number of possibilities an attacker has to search through before they're guaranteed to find the right one. A password with 40 bits of entropy has 2^40 (about a trillion) possible values; a password with 60 bits has 2^60, a billion times more. That exponential relationship is why small changes in password composition make an outsized difference to how brute-forceable a password actually is.
For a password generated by picking characters independently and uniformly at random from a fixed alphabet, entropy is log2(alphabet size) × length. A random lowercase-only password draws from an alphabet of 26, giving about 4.7 bits per character. Add uppercase, digits, and symbols and the alphabet grows to roughly 94 printable characters, about 6.55 bits per character. That's why expanding the character set matters less than it might seem, and length matters more: going from 26 to 94 possible characters only adds about 2 bits per character, but every extra character of length adds a full multiplier's worth of entropy regardless of alphabet.
A 12-character password using the full 94-character set has about 79 bits of entropy. A 20-character password using only lowercase letters has about 94 bits, more than the shorter, more “complex” one, despite using a smaller alphabet. This is the core insight behind the shift in password guidance over the last decade (NIST's SP 800-63B included): length is a more reliable and more usable lever than forcing arbitrary complexity rules like “must contain a symbol.”
The right target depends on what's protecting the password. A properly implemented password hashing scheme like Argon2id already makes each guess computationally expensive, so even moderate entropy (around 60 bits) becomes impractical to brute-force at scale. But defense in depth matters: you don't know in advance whether a service you trust your password to is hashing it correctly, so aiming higher costs nothing. As a practical baseline: 80+ bits of entropy (roughly 14 random alphanumeric-plus-symbol characters, or 16-18 random lowercase words) comfortably exceeds what's brute-forceable with current hardware, even against a fast, unsalted hash.
The important caveat: this math only holds for passwords generated by a genuinely uniform random process. Human-chosen passwords, even ones that “look” random, draw from a much smaller effective space, because people are predictable in ways attackers' dictionaries already account for. Use a proper random generator rather than inventing a password by hand.
The Password Generatoron this site uses the Web Crypto API's cryptographically secure random number generator, entirely in your browser, so every character is drawn from a genuinely uniform distribution.