Password Entropy Calculator
Enter your password length and check the character types you use. The calculator returns the entropy in bits, a strength rating, the total number of possible combinations, and how long a brute-force attack would take at three realistic attack speeds. Results update as you type.
Formula
Worked example
A 12-character password using lowercase, uppercase, and digits draws from a pool of 62 characters. E = 12 x log2(62) = 12 x 5.954 = 71.4 bits. The total combinations are 62^12 = roughly 3.2 x 10^21. Against an offline fast attack at 10 billion guesses per second, the expected crack time is about 5 million years.
What is password entropy?
Password entropy is a measurement of how unpredictable a password is, expressed in bits. It comes from information theory, where Claude Shannon showed that the minimum number of binary digits needed to represent a message from a set of R equally likely symbols is log2(R) bits per symbol. For passwords, each character is a "symbol" chosen from a pool of R possible characters, and if a password is L characters long, its entropy is E = L x log2(R) bits. Doubling the pool size adds one bit of entropy per character. Adding one character to the length adds log2(R) bits, which is why length is the biggest lever you have.
How the character pool affects strength
The pool size R is determined by which character types you use. Lowercase letters alone give R = 26 (about 4.7 bits per character). Adding uppercase doubles the pool to 52 (about 5.7 bits per character). Adding digits brings it to 62 (about 5.95 bits per character). Adding all 32 symbols available on a standard US keyboard pushes it to 94 (about 6.55 bits per character). The jump from 62 to 94 adds less than one bit per character, so at a fixed length, expanding the pool gives diminishing returns compared to simply making the password longer. A 16-character lowercase-only password (75 bits) is stronger than an 8-character all-types password (52 bits).
Understanding crack time estimates
The crack time estimates assume an attacker tries all possible passwords in a brute-force search. On average they will find the password after trying half the total combinations, so the expected time is (pool^length / 2) / guesses-per-second. Online attacks are limited by the server to around 1,000 guesses per second. An offline attack, where the attacker has a copy of hashed passwords, runs at hardware speed - roughly 10 billion guesses per second on a single modern GPU. A large distributed cluster can reach 100 trillion guesses per second. Real-world attackers also use wordlists, common patterns, and credential stuffing, which can crack predictable passwords far faster than the brute-force estimate. Entropy measures theoretical best-case resistance, not resistance to dictionary attacks.
How to build a high-entropy password
The fastest path to high entropy is length. A passphrase of four to five random common words is easy to remember and can reach 50-70 bits with a tiny pool (26 lowercase plus spaces). If you must use a shorter password, enable all four character types to maximise the pool. Avoid predictable substitutions such as "3" for "e" or "!" at the end, because attackers know these patterns and include them in their wordlists. The best practice is to use a password manager to generate and store a random 16-plus-character password for every account, with all character types enabled, so you never have to remember or reuse it. Enable two-factor authentication wherever available as a second line of defence if a password is compromised.
Entropy strength bands
| Entropy (bits) | Strength | Account type | Example: pool-94 password length |
|---|---|---|---|
| Below 28 | Very Weak | No account | < 5 characters |
| 28-35 | Weak | Throwaway accounts only | 5-6 characters |
| 36-59 | Fair | Low-value accounts | 7-10 characters |
| 60-79 | Strong | Standard accounts | 11-13 characters |
| 80-99 | Very Strong | Financial / email accounts | 14-17 characters |
| 100+ | Excellent | Critical / master passwords | 18+ characters |
Industry-wide guidance on minimum entropy levels for different account types. Bits are calculated as length x log2(pool size).
Frequently asked questions
How many bits of entropy does a password need?
It depends on the threat. For accounts protected only by an online login (which is rate-limited by the server), 40-50 bits is generally sufficient. For accounts where an attacker could get an offline copy of the hashed password, you want at least 60 bits to resist a fast GPU attack, and 80 bits or more for financial or email accounts. Critical or master passwords benefit from 100 bits or more. A 16-character password using all four character types (pool 94) reaches about 105 bits.
Is a long passphrase better than a short complex password?
Usually, yes. Length is the dominant factor in entropy. A 20-character passphrase using only lowercase letters has about 94 bits of entropy, which is stronger than a 10-character password using all four types (about 66 bits). Passphrases are also much easier to remember. The caveat is that the words must be chosen at random, not a phrase you invented, because short memorable phrases are in attacker wordlists.
Does this calculator check whether my actual password is weak?
No. This calculator uses the theoretical entropy formula based on what character types and length you tell it. It does not analyse the specific characters you chose, so it cannot detect dictionary words, patterns, keyboard walks, or repeated characters. A password like "Aaaaaaaa1!" is 10 characters using all four types, but it is trivially cracked by any wordlist attack. For real-world strength testing, complement entropy analysis with a dedicated password strength tool such as zxcvbn, which penalises common patterns.
What is the difference between entropy bits and password strength?
Entropy bits are a mathematical quantity that measures the size of the search space an attacker must explore if using pure brute force. Password strength is a broader concept that also accounts for how predictable the password is. A password can have high theoretical entropy (many bits) but low real-world strength if it contains dictionary words, common substitutions, or follows known patterns. Use entropy as a lower bound on complexity and a separate pattern-analysis tool for a fuller picture.
Why do the crack-time estimates vary so much between scenarios?
Because online and offline attack rates differ by many orders of magnitude. Online attacks are throttled to roughly 1,000 guesses per second by login servers and account lockouts. An offline attack, which happens after a site suffers a data breach and the attacker downloads the password hashes, runs at full GPU speed, about 10 billion guesses per second for a well-optimised attack. A distributed cluster of many GPUs can reach 100 trillion guesses per second. A password that would take centuries online might fall in hours offline, which is why you should assume every account could be breached and set entropy accordingly.
Should I use all four character types in every password?
Not necessarily. Some sites reject certain symbols, and using all types in a short password (say, 8 characters) still produces only moderate entropy. A better strategy is to maximise length first, then add character types. If a site forces a maximum length of 12 and allows symbols, use all four types. If you are generating a passphrase of 20 or more characters, pure lowercase is already very strong. Always use whatever gives the highest entropy within the site's constraints.