Last updated: September 2026 · Independently QA-tested formulas
Most password advice is folklore — swap a for @, add a number, change it every 90 days. The actual math is simpler and more useful: strength is a bit count, and a few honest calculations show where real strength comes from.
The alphabet is the set of characters a cracker must try. Common pools:
| Pool | Size | Bits per character |
|---|---|---|
| Digits only (0–9) | 10 | 3.32 |
| Lowercase a–z | 26 | 4.70 |
| + uppercase | 52 | 5.70 |
| + digits (62) | 62 | 5.95 |
| Full keyboard (94) | 94 | 6.55 |
| 3,000 common words | 3,000 | 11.55 |
Cracking tools try human patterns first: dictionary words, then leet-speak variants (a→@, s→$, o→0), then append years. P@ssw0rd! survives none of those filters. Meanwhile every extra random character multiplies the search space by the full pool size. A cracker facing 75 bits of lowercase does 223 ≈ 8 million times more work than one facing 52 bits of keyboard chaos.
Offline attack speed depends on the hash: against fast hashes (unsalted MD5/SHA-1, still common in old leaks) consumer GPUs test billions of guesses per second; against properly salted slow hashes (bcrypt, Argon2) the same hardware manages thousands. That spread is why good sites store passwords slowly — the slow storage is a defense. Crack-time estimates are therefore a range, not a guarantee; treat any single number as one scenario.
No — dictionary word + cosmetic substitutions. Cracking tools try those variants early. A 4-word passphrase beats it at a fraction of the memorization cost.
14+ random characters or a 4-word passphrase for everyday accounts; 16+ or 5 words for banking and email.
Less than length and uniqueness. NIST SP 800-63B emphasizes length, screening against breached passwords and rate-limiting over symbol rules that create predictable patterns.
One breach plus credential stuffing equals many compromised accounts. A password manager makes uniqueness free.
Only if chosen from a fixed wordlist with a random process (like diceware or a generator). Picking words you like collapses the entropy dramatically.
Estimates are illustrative math, not security guarantees. Follow your provider's current guidance for account recovery and 2FA.