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Password Strength Explained: Entropy, Crack Time and What Actually Works

Last updated: September 2026 · Independently QA-tested formulas

Quick answer: Password strength is entropy: bits = log2(pool size) × length. Bigger pool and more characters multiply. The password generator builds high-entropy passwords and shows the math, while the entropy calculator and crack-time tool break down any password's realistic resistance.

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 entropy formula (the only one you need)

bits = log2(alphabet size) × length

The alphabet is the set of characters a cracker must try. Common pools:

PoolSizeBits per character
Digits only (0–9)103.32
Lowercase a–z264.70
+ uppercase525.70
+ digits (62)625.95
Full keyboard (94)946.55
3,000 common words3,00011.55

Worked examples

Why length beats symbol swaps

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.

Crack time — with the honest caveat

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.

Practical rules

Assumptions and limitations

Related calculators

Frequently asked questions

Is 'P@ssw0rd!' a strong password?

No — dictionary word + cosmetic substitutions. Cracking tools try those variants early. A 4-word passphrase beats it at a fraction of the memorization cost.

How long should a password be in 2026?

14+ random characters or a 4-word passphrase for everyday accounts; 16+ or 5 words for banking and email.

Does complexity still matter?

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.

Why shouldn't I reuse passwords?

One breach plus credential stuffing equals many compromised accounts. A password manager makes uniqueness free.

Are passphrase words really random enough?

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.