Core answer: Password strength scales with LENGTH × randomness: entropy ≈ length × log₂(character pool). A 16-char lowercase password (26¹⁶) ≈ 75 bits — centuries to brute-force; an 8-char "complex" P@ssw0rd pattern ≈ 30 bits — hours. Use a unique random password per site via a password manager; add 2FA on email, banking, and your password manager itself.

The entropy math

PasswordPoolLengthEntropyOffline crack time (10¹⁰ guesses/s)
1234566~0 (in every dictionary)instant
P@ssw0rd!pattern9~30 bits effectiveminutes
8 random mixed94852 bits~14 years
12 random mixed941279 bits~10¹⁰ years
5-word passphrase7,776 (diceware)5 words65 bits~10⁵ years
16-char random9416105 bitsbeyond heat death

Online attacks (rate-limited) vs offline (database leak, 10¹⁰+ guesses/s with GPUs) differ by a factor of a billion — that's why site breaches, not login pages, are the real threat model.

The three rules that actually protect you

  1. Unique per site — credential stuffing (trying leaked email/password pairs everywhere) is the #1 real-world account takeover method; uniqueness kills it.
  2. Random, not clever — "Tr0ub4dor&3" follows a human pattern crackers model; "correct horse battery staple" style random words beat it.
  3. 2FA on the crown jewels — email resets everything else; banking moves money. Hardware keys > authenticator apps > SMS (SIM-swap vulnerable).

Worked examples

Example 1 — The breach cascade. You reuse "Sunshine2020!" on a forum and your bank. The forum leaks in 2024; bots try the pair on 500 banking sites within hours. One unique password per site reduces this to a forum problem, not a life problem.

Example 2 — Passphrase construction. Roll dice for 5 random words: "glacier trumpet velvet canoe orbit" ≈ 65 bits, typeable in 6 seconds, memorable in a day.

Example 3 — Master password. Your manager's master password needs the most strength you'll ever memorize: 6+ random words (77+ bits), written on paper in a drawer for the first month.

Common mistakes and myths

  1. "Complexity requirements make it strong" — P@ssw0rd1 satisfies every rule and tops breach dictionaries; length and uniqueness matter, symbol theater doesn't.
  2. Forced 90-day rotation — NIST withdrew the advice: forced changes breed +1 increments ("Summer2024"→"Summer2025"). Change on evidence of compromise only.
  3. Security questions as secrets — your mother's maiden name is on genealogy sites; answer with random words stored in your manager ("What street? → 'purple-anvil-73'").
  4. Browser-saved = password manager — better than reuse, but dedicated managers add breach alerts, secure sharing, and phishing-resistant autofill domain checks.
  5. Writing passwords down is always bad — a paper list in a locked drawer beats Password123 reused everywhere; threat models differ for home users vs open offices.