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Password Strength Explained: Entropy, Length and Passphrases

Security · Updated October 2, 2026 · 4 min read

Password advice is full of rules — one uppercase letter, one symbol, change it every 90 days — that do surprisingly little. What actually protects an account is that its password is random, long, and used nowhere else. This guide explains why, with numbers.

Strength is the number of possibilities

For a randomly generated password, strength is the number of passwords the generator could have produced. It is measured in bits of entropy: length × log2(size of the character set). Each extra bit doubles the number of guesses an attacker needs.

Password                         Entropy
8 random letters + digits (62)   48 bits
12 random, all symbols (88)      78 bits
16 random letters + digits       95 bits
20 random, all symbols (88)     129 bits
4 random words (7,776-word list)  52 bits
6 random words                    78 bits

These figures apply only to random choices. A password a person invents — a word, a name, a date with a symbol on the end — has far less entropy than its length suggests, because attackers try those patterns first.

How long would cracking take?

Online guessing against a login page is slow and usually rate-limited. The real threat is offline cracking: when a site is breached and its password hashes leak, attackers can test guesses on their own hardware. Against a fast, unsalted hash, a rig making a trillion guesses per second would need on average about half of the following to find a random password:

  • 8 random letters and digits (48 bits): under 4 minutes to try every possibility.
  • 4 random words (52 bits): about an hour.
  • 12 random characters from all four sets (78 bits): roughly 6,800 years.
  • 16 random letters and digits (95 bits): over a billion years.

Well-run services store passwords with slow, salted algorithms such as bcrypt, scrypt or Argon2, which cut that guessing rate by many orders of magnitude. You cannot know how a site stores your password, so choose one that survives the worst case.

Why length beats complexity

Each extra random character multiplies the possibilities by the size of the character set; switching from letters-and-digits to all four character sets only raises that multiplier from 62 to about 88. So 16 random letters and digits (95 bits) beat 12 characters with symbols (78 bits), and are easier to type on a phone. Complexity rules help most when a site caps the length.

Current guidance from NIST (SP 800-63B) reflects this: favour length, allow long passphrases and all printable characters, check new passwords against lists of breached passwords, and do not force periodic changes without evidence of compromise.

A practical setup

  1. Use a password manager and let it generate a unique random password of 16 characters or more for every account.
  2. Protect the manager with a long passphrase of five or six randomly chosen words — the one password you memorise.
  3. Turn on two-factor authentication, preferably an authenticator app, a security key or a passkey rather than SMS, for email, banking and your password manager first.
  4. Change a password when a service reports a breach or you suspect a compromise, not on a fixed calendar.
  5. Never reuse passwords. Reuse — not weak passwords — is how most accounts are taken over after a different site is breached.

Passkeys

Passkeys replace passwords with a key pair stored on your device or in your password manager. There is nothing to guess and nothing reusable to leak, and they cannot be phished onto a fake site because they are bound to the real one. Where a service offers passkeys, they are the strongest option; keep a strong password and recovery codes as a fallback.

Hashing is not encryption

Sites should never be able to show you your password, because they should store only a hash of it. General-purpose hashes like SHA-256 — available in the hash generator here for checking file integrity — are deliberately fast, which makes them the wrong tool for password storage; password-hashing algorithms are deliberately slow and salted. If a site ever emails you your existing password in plain text, assume it is stored insecurely and use a unique password there.

If a service you use is breached

  1. Change the password for that service, and anywhere else you used the same or a similar password.
  2. Turn on two-factor authentication if you have not already.
  3. Watch for phishing emails that mention the breach — attackers use the news as cover.
  4. Check whether your email address appears in known breaches using a reputable breach-notification service.
  5. If payment details were involved, watch your statements and consider asking your bank for a new card.

Security questions are effectively extra passwords that are easier to guess. Answer them with random values stored in your password manager rather than your real mother’s maiden name or first pet.

Are password managers safe?

Reputable password managers encrypt your vault on your own device with a key derived from your master password, so the provider stores only encrypted data and cannot read your passwords. The risk is concentrated in the master password and the devices you unlock the vault on — which is why it should be a long, unique passphrase protected by two-factor authentication, and why device security updates matter. Even accounting for that risk, a manager with unique random passwords is far safer than reusing a handful of memorable ones.

Two-factor methods compared

  • SMS codes: better than nothing, but vulnerable to SIM-swap attacks and phishing.
  • Authenticator apps (TOTP): codes generated on your phone; much stronger than SMS, though a convincing phishing site can still relay a code in real time.
  • Security keys and passkeys: resistant to phishing because they check the website’s real address. The strongest option for important accounts.
  • Backup codes: store them in your password manager or print them, so losing a phone does not lock you out.

Tools used in this guide