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Length beats cleverness: how long a password should be, and the arithmetic that proves it

Entropy in plain words, a table of length against character set, passphrases against passwords, and what to do when a site you use is breached.

6 min readUpdated October 27, 2026

Skip the readingPassword Generator: Make random passwords and passphrases and see how many bits of entropy they have.

The quick answer

You need a new password and want one that is strong without being clever. Make a random one with the password generator and put it straight into a password manager.

  1. Pick Password (a string of characters) or Passphrase (random words, easier to type and read out).
  2. Set the length. The generator starts at 20 characters, or 6 words for a passphrase.
  3. Press Copy and save it in your password manager before you close the page, because the page does not remember it.
  4. Use a different one for every account. If a site rejects some symbols, edit the symbol list, or turn symbols off and add a few characters.
Password GeneratorMake a random password or passphrase and see its strength in bits.Open it

The generator's own guidance: 16 random characters is plenty for ordinary accounts, 20 or more suits email, banking and your password manager, and 8 or more words suits a secret you must type from memory.

Entropy in plain words

Entropy counts how many different results a generator could have produced, written in bits. One bit is two possibilities, and every extra bit doubles the number, so 10 bits is 1,024. For a password of n characters picked at random from a pool of p characters, the entropy is n × log2(p) bits. A lowercase letter adds 4.70 bits, a digit 3.32 and a character from all 94 printable ASCII characters 6.55.

LengthDigits (10)Lowercase (26)Letters and digits (62)All 94 characters
826.6 bits37.6 bits47.6 bits52.4 bits
1239.9 bits56.4 bits71.5 bits78.7 bits
1653.2 bits75.2 bits95.3 bits104.9 bits
2066.4 bits94.0 bits119.1 bits131.1 bits

Twelve random lowercase letters (56.4 bits) beat eight characters from the full set (52.4 bits). Sixteen lowercase letters (75.2 bits) come within 3.5 bits of twelve characters from everything (78.7 bits). Going from lowercase to all 94 characters adds 1.85 bits per character, while one more lowercase letter adds 4.70, so one extra letter is worth about two and a half characters of added variety.

ClipLime's default symbol list has 23 symbols, so its full pool is 26 + 26 + 10 + 23 = 85 characters, and the default 20 characters come to about 128 bits. These figures are exact for a secret from a random generator and say nothing about one you invented.

What the bits mean, as an illustration

Here is one illustration, not a prediction. It assumes an attacker who has stolen a list of fast hashes, knows how the secret was made and tries 100 billion guesses a second, the assumption the generator page uses. The time is the average, half of the search space. A site that limits login attempts, or stores passwords with a slow hash, is far harder to attack.

Random secretBitsAverage time in this illustration
8 characters, all 9452.4about 8 hours
12 lowercase letters56.4about 5.5 days
6 words60.0about 67 days
16 lowercase letters75.2about 7,000 years
12 characters, all 9478.7about 75,000 years
8 words80.0about 190,000 years

The ordering is the point: length moves a secret up the table faster than a wider character set does.

Passphrases: words instead of symbols

A passphrase is several random words joined together. The generator draws each word from a list of 1,024, and 1,024 is 2 to the power of 10, so every word adds exactly 10 bits.

WordsBitsSame strength as this many random characters from all 94
4406.1
5507.6
6609.2
88012.2
1010015.3

Bit for bit, a passphrase is as strong as a random password. The difference is the cost: 10 bits take one word of about five letters, but only about one and a half characters in a full symbol password. Choose words when you must type the secret on a phone or read it aloud.

The strength comes entirely from the words being picked at random. A phrase you invent, such as a lyric or a sentence about your pet, is far weaker than its length suggests, and swapping letters for look-alike symbols adds almost nothing because attackers try those swaps first. Capitalizing each word adds no strength, and a random number from 0 to 99 on the end adds about 6.6 bits. Six words suits an account behind a slow hash. For a password manager's master password, use 8 or more.

Why reuse is the real danger

Once you use it twice, a 128 bit password is only as safe as the least careful site that holds it. When one site is breached, attackers try the leaked address and password on other services, so length cannot rescue a reused password. The first rule is one password per account. The second is two-factor sign-in wherever it is offered, so that a stolen password is not enough on its own. A strong password does not help if it is typed into a fake page, and a fake page can sometimes relay a one-time code, which passkeys and security keys resist.

A password manager makes one password per account practical by remembering them for you, at the cost of trusting one product and one master secret, so choose with care, protect it with a long passphrase and two-factor sign-in, and keep a recovery plan.

What a generator in the browser does, and does not do

  • It makes every character with crypto.getRandomValues, the random source your browser uses for encryption keys, and never Math.random, which is not designed to be unpredictable.
  • It picks fairly. Using the remainder of a random number would make some characters slightly likelier, so values that would cause that are redrawn. Asking for at least one character of each kind makes it start over until a password qualifies, which costs about a tenth of a bit at 20 characters.
  • It stores and sends nothing, not even your settings. Copy the password before you leave.
  • It cannot know where you will type the password, how that site stores it, or whether the page asking for it is a fake.

To check, open the Network tab in your developer tools and press Generate new: no request is made. For more assurance, load the page, switch off your connection and generate, which the page says works the same offline.

Secrets, identifiers and tokens

A UUID is an identifier, not a secret. A version 4 UUID carries 122 random bits (128 minus 6 fixed ones), but the standard does not promise it is unguessable and a version 7 shows when it was made, so make IDs with the UUID generator and secrets with the password generator. A password stored as Base64 in a config file is still a plain password, as Base64 encoding and decoding explained shows with the Base64 decoder.

The signing secret for an HS256 token should be at least 256 bits. At 6.55 bits per character that is 40 random characters, and decoding a JWT token explains why. Sites should store a slow, salted hash of your password. Fast hashes such as the ones in the hash generator let an attacker try billions of guesses a second against a leaked list, and verifying a download with a hash covers what they are good for instead.

If a site you use was breached

  1. Change the password on that site now, to a new random one.
  2. Change it everywhere else you used it, starting with your email and anything that handles money. Email can reset your other accounts.
  3. Turn on two-factor sign-in for the accounts that offer it.
  4. Check the recovery address, phone number and any mail forwarding on your email account. Someone with access may have changed them.
  5. Be careful with messages that mention the breach. Type the site's address yourself instead of following a link.
Password GeneratorMake a new random password for each account you need to change.Open it

Try it yourself

Questions people ask

How long should my password be?

For ordinary accounts, 16 random characters is plenty. Use 20 or more for email, banking and your password manager. If you must type it from memory, use a passphrase of 8 or more random words. Make them with the password generator.

Is a passphrase better than a password?

Bit for bit they are equal, so the question is which you can use. A passphrase is easier to type and say, but only if the words are chosen at random. A phrase you made up is much weaker than it looks.

What does 80 bits of entropy mean?

It means the generator could have produced about 2 to the power of 80 different results, roughly 10 to the power of 24. An attacker guessing blindly would need on the order of that many tries, and each extra bit doubles it.

Is it safe to generate a password in a web page?

It can be, when the page makes the password in your browser and sends nothing, which you can confirm in the Network tab. You still trust the page's code, so for the highest assurance load it, disconnect and then generate. Either way, save the result in a password manager before you close the page.

Why does a site reject my generated password?

Some sites refuse certain symbols or cap the length. Edit the symbol list or turn symbols off, then add a few characters to make up for it. If you run the site yourself, allow long passwords and every symbol, and store them with a slow, salted hash.

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