Password Entropy Calculator

Entropy here is the base-2 logarithm of the number of equally likely candidates an attacker must search, so a password drawn uniformly at random from an alphabet of N symbols at length L carries L times log2(N) bits. The per-character yield is 4.70 bits for lowercase only, 5.95 bits once uppercase and digits are added, and 6.57 bits across the 95 printable ASCII characters. Length is the stronger lever because it multiplies rather than adds: moving from 8 to 16 characters on the full ASCII set doubles entropy from about 53 to about 105 bits, whereas adding symbols to an 8-character password gains only around 15 bits. Expected search time is half the keyspace divided by the guess rate, which is the arithmetic behind the crack-time figure on this page. Working thresholds are roughly 40 bits for throwaway accounts, 60 to 80 bits for accounts worth defending, and 128 bits for cryptographic keys. Two caveats matter more than the formula. First, the guess rate is a property of the defender's hashing choice, not the password: a commodity GPU can test billions of MD5 or SHA-256 candidates per second but only tens of thousands of bcrypt candidates at cost factor 12, and online attacks against a rate-limited login are limited to a few attempts per second. A change of hash can move the estimate by ten orders of magnitude while the entropy number stays fixed. Second, this formula only describes randomly generated strings. Human-chosen passwords carry far less entropy than their character composition implies because they follow predictable patterns such as capitalizing the first letter, appending a digit and a symbol, and substituting the at sign for the letter a. A string like P@ssw0rd scores respectably here and falls in milliseconds to any dictionary-plus-rules attack.

The measure itself comes from Claude Shannon's 1948 paper A Mathematical Theory of Communication, which defined information entropy in bits and, in follow-up work published in 1951, estimated the entropy of ordinary English text at roughly one bit per character, an early demonstration that a string's length overstates its unpredictability. Applying that framework to authentication began with Unix. Robert Morris and Ken Thompson documented the crypt password scheme and per-user salting in their 1979 paper Password Security: A Case History, which measured how quickly real user-chosen passwords fell to guessing and set the template for empirical password research. Formal guidance followed decades later and then reversed itself. NIST Special Publication 800-63, published in 2004 with an entropy-estimation appendix authored by Bill Burr, gave the world the composition rules requiring mixed character classes and periodic rotation. Burr publicly said in 2017 that he regretted those recommendations, and the 2017 revision SP 800-63B dropped both composition mandates and scheduled expiry in favor of longer passphrases, screening against known breached password lists, and multi-factor authentication. Practical countermeasures developed in parallel: Arnold Reinhold published the Diceware word list in 1995, providing 7776 words and therefore 12.9 bits per word for physically generated passphrases; Niels Provos and David Mazieres introduced the deliberately slow bcrypt at USENIX in 1999; and the Password Hashing Competition run from 2013 to 2015 selected Argon2, which adds memory hardness to resist GPU and ASIC attacks.