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
| Password | Pool | Length | Entropy | Offline crack time (10¹⁰ guesses/s) |
|---|---|---|---|---|
| 123456 | — | 6 | ~0 (in every dictionary) | instant |
| P@ssw0rd! | pattern | 9 | ~30 bits effective | minutes |
| 8 random mixed | 94 | 8 | 52 bits | ~14 years |
| 12 random mixed | 94 | 12 | 79 bits | ~10¹⁰ years |
| 5-word passphrase | 7,776 (diceware) | 5 words | 65 bits | ~10⁵ years |
| 16-char random | 94 | 16 | 105 bits | beyond 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
- Unique per site — credential stuffing (trying leaked email/password pairs everywhere) is the #1 real-world account takeover method; uniqueness kills it.
- Random, not clever — "Tr0ub4dor&3" follows a human pattern crackers model; "correct horse battery staple" style random words beat it.
- 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
- "Complexity requirements make it strong" — P@ssw0rd1 satisfies every rule and tops breach dictionaries; length and uniqueness matter, symbol theater doesn't.
- Forced 90-day rotation — NIST withdrew the advice: forced changes breed +1 increments ("Summer2024"→"Summer2025"). Change on evidence of compromise only.
- 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'").
- Browser-saved = password manager — better than reuse, but dedicated managers add breach alerts, secure sharing, and phishing-resistant autofill domain checks.
- 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.