Password entropy calculator

What entropy measures, and what it does not

Entropy, in bits, is the base-2 logarithm of the number of equally likely passwords an attacker would have to consider. Each bit doubles the number: 40 bits is a trillion-odd possibilities, 80 bits is a trillion times more. The figure describes the process that produced the password, not the password itself, and it is exact only when a program or dice picked every character or word uniformly at random. That is why this calculator asks for a length and a character set rather than for a password: it sizes passwords you are about to generate. For passwords people make up, no formula gives a trustworthy number.

The formulas

Random characters: bits = L × log₂(N), where L is the length and N the number of characters in the pool. Random words: bits = W × log₂(S), where W is the number of words and S the size of the list. Possible passwords = 2^bits. If every password is equally likely and the attacker knows the method, the expected number of guesses is half the space, 2^(bits − 1). Time to try everything = 2^bits ÷ guesses per second, and on average half of that. The guess rate is the one input that is a pure assumption, so you choose it.

Worked example: characters or words?

Twelve random characters from the 94 printable ASCII letters, digits and symbols give 78.7 bits. Six words from the 7,776-word EFF list give 77.5 bits (6 × 12.92), so the two are almost equal even though the passphrase is much longer to type. Sixteen random characters from the same 94-character pool give 104.9 bits. At an assumed one trillion guesses per second the average time to guess 77.5 bits is 3,503 years; at one billion per second it is 3.5 × 10⁶ years; at one thousand per second, 3.5 × 10¹² years. Years are Julian years of 365.25 days.

Bits per character for common pools

The 94 characters are the 26 + 26 letters, 10 digits and 32 printable ASCII punctuation symbols; the space makes 95. The “length for 80 bits” column is only a sizing aid: 80 is a round number, not a threshold recommended by any source we read.

Why the formula fails for passwords people choose

A person picking “a strong password” is not drawing characters at random from the pool, so the size of the pool says nothing about how many candidates an attacker must try, and applying L × log₂(N) to such a password can overstate its strength badly. NIST made the same point: SP 800-63B-3 (2017, updated 2020; Appendix A, since replaced) says that estimating the entropy of user-chosen passwords is difficult and that past efforts have not been particularly accurate, and treats length as a primary factor. Its successor, SP 800-63B-4 (final, July 2025), sets no entropy figure for passwords: it requires services to enforce a minimum length (15 characters for a password that is the only factor), to allow at least 64, to reject passwords on a blocklist of commonly used, expected or compromised ones, and not to impose composition rules.

Common mistakes

Typing a real password into any website to “check” it: do not. Counting the wrong pool: a generator that uses only lowercase letters and digits has 36 characters per position, even if the site accepts symbols. Treating a passphrase of words you chose as if it came from the list at random. Reusing a strong password: its entropy protects against guessing, not against the site that stores it being breached. Comparing bits across different guess rates without saying which rate you assumed. And treating this number as a verdict, since a random 12-character password and a random six-word passphrase can both be the right size for one account and wrong for another.

How do I calculate password entropy?

For a password in which every character is drawn at random from a pool of N equally likely characters, entropy in bits = length × log₂(N). Twelve characters from the 94 letters, digits and symbols on a keyboard: 12 × log₂(94) = 12 × 6.555 = 78.7 bits. That means 2^78.7 equally likely passwords, and an attacker who knows how the password was generated needs on average half of them, 2^(78.7 − 1) guesses. The formula says nothing about a password that a person made up; see the section on that below.

How many bits is a Diceware or EFF passphrase?

EFF’s long wordlist has 7,776 words (six to the fifth power, one word per roll of five dice), so each randomly picked word adds log₂(7,776) = 12.92 bits, which EFF rounds to 12.9. Six words are 77.5 bits (EFF says 77). EFF’s short lists have 1,296 words (four dice) and add 10.34 bits a word (EFF: 10.3); eight words from a short list are 82.7 bits. Diceware, created by Arnold Reinhold and first published in 1995, uses a list of the same size, 7,776 words. The bits count only if the words are picked at random, by dice or by software, not chosen because you like them.

Do capital letters, digits and symbols make a password stronger?

For a randomly generated password, a bigger pool adds log₂(N) bits per character, but a longer password adds more. Twelve random lowercase letters are 56.4 bits; the full 94-character pool lifts 12 characters to 78.7 bits; yet 15 lowercase letters alone give 70.5 bits, and 10 characters from the full pool only 65.5. Each character from a 94-symbol pool is worth 6.55 bits against 4.7 for a lowercase letter. NIST SP 800-63B-4 goes further and says services shall not impose composition rules such as requiring mixtures of character types.

What guess rate should I enter?

It is your assumption, and this page does not claim any rate is typical. The example choices are round numbers, from one thousand to one trillion guesses per second, so you can see how the answer scales: every factor of 1,000 in speed removes about 10 bits of strength. The kind of attack matters more than the number. A service that can be reached only over the network can throttle guesses: NIST SP 800-63B-4, section 3.2.2, says a verifier shall limit consecutive failed attempts on an account to no more than 100. An attacker who has stolen a database of password hashes is not limited that way and is bounded only by hardware and by how slow the hash is. Choose the rate that matches the threat you care about.

What does NIST say about passwords now?

NIST SP 800-63B-4 was published in final form in July 2025 and replaced SP 800-63B; the NIST page read on October 27, 2026 shows no later revision. Its rules are addressed to the services that check passwords. A password used as the only factor must be at least 15 characters; one used only as part of multi-factor authentication must be at least 8; services should accept at least 64 characters, printing ASCII, spaces and Unicode; they shall not impose other composition rules and shall not force periodic changes, except after evidence of compromise; and they shall compare each new password against a blocklist of commonly used, expected or compromised passwords. For passwords, NIST’s rules rest on length and blocklists rather than on an entropy figure.

Does the calculator see or save my password?

There is no password box on this page, on purpose. You enter only the length, the size of the character set (or the number of words) and a guess rate, and the arithmetic runs in your browser. Those settings are remembered in your browser so the page opens as you left it; no password, real or example, is needed or stored. If you want to know how strong your own password is, do not type it into any website: generate a new random one with a password manager or with dice and use the numbers here to size it.

Sources: EFF, “EFF’s New Wordlists for Random Passphrases” (J. Bonneau, July 2016; 7,776-word and 1,296-word lists, 12.9 and 10.3 bits per word, six-word passphrase, Diceware by Arnold Reinhold, 1995); NIST SP 800-63B-4, Digital Identity Guidelines: Authentication and Authenticator Management (final, July 2025), sections 3.1.1.2 (password verifiers) and 3.2.2 (rate limiting); NIST SP 800-63B-3 (2017, updated 2020; superseded by 800-63B-4), Appendix A “Strength of Memorized Secrets.” Related: random number generator, number base converter for the bases of encoded secrets, scientific notation calculator for the very large numbers, probability calculator and hex calculator.