It's tempting to judge a password's strength by eye, does it have symbols, numbers, mixed case, and it looks strong. But real password strength is a mathematical quantity called entropy, measured in bits, and it depends on the size of the character pool a password draws from and its length, not on whether it happens to look scrambled to a human observer.
What entropy actually measures
Entropy answers one question: how many guesses would an attacker who knows the password's format need to try, on average, before finding it? If a password uses a pool of N possible characters per position and is L characters long, the total number of possible combinations is N^L, and entropy in bits is log2(N^L), or L × log2(N). A 8-character password using only lowercase letters (a pool of 26) has about 8 × log2(26) ≈ 37.6 bits of entropy. Adding uppercase, digits, and symbols expands the pool to around 95 characters, so the same 8-character length jumps to about 8 × log2(95) ≈ 52.6 bits, a real but modest improvement.
Length matters more than pool size once you compare it directly: extending that same 95-character-pool password from 8 to 16 characters roughly doubles the bits of entropy to about 105 bits, a far bigger jump in guessing difficulty than switching from lowercase-only to a full symbol set at a fixed short length. That's the mathematical reason a long passphrase of random lowercase words routinely out-scores a short password stuffed with symbols.
Why 'P@ssw0rd!' scores badly despite looking complex
Entropy calculated from character-pool size assumes each character is chosen independently and unpredictably. Real password crackers don't brute-force character by character, they use dictionaries of common words, known substitution patterns (@ for a, 0 for o, ! at the end), and lists of billions of previously breached passwords. "P@ssw0rd!" technically draws from a large character pool, but because it's a well-known word with well-known substitutions, it falls in the first few thousand guesses of any competent cracking tool, its theoretical entropy massively overstates its real-world resistance.
A password strength tool worth trusting checks both: the raw theoretical entropy from length and character variety, and pattern-based red flags like dictionary words, keyboard walks (qwerty, asdf), and repeated characters. The Password Strength Checker evaluates both dimensions and estimates realistic crack time rather than just reporting a character-pool number that can be misleading on its own.
Generating passwords with real entropy
The most reliable way to get a genuinely high-entropy password is to generate one randomly rather than inventing one by hand, since human-created passwords consistently cluster around predictable patterns even when people are actively trying to be random. The Password Generator produces cryptographically random passwords at a chosen length and character set, and the Passphrase Generator builds long, memorable multi-word passphrases using genuinely random word selection, which is often easier to type and remember than a random symbol string at equivalent entropy.