Password Entropy Calculator
Password entropy in bits from length and character set, with the size of the search space and the time to crack at a guess rate you set.
Password Entropy Calculator: with the default inputs, entropy is 71.45.
10¹¹/s is a realistic GPU rig against a fast hash (MD5, SHA-1, NTLM). Use 10⁴ for bcrypt at cost 12, or 10 for a rate-limited login form.
Bits. Each extra bit doubles the work an attacker has to do.
- Character set size
- 62
- Possible passwords
- 3.23 × 10^21
- Time to crack (average)
- 511 years, 2 months
- Time to crack (exhaustive search)
- 1022 years, 4 months
- Verdict
- Strong — impractical to brute-force offline with today's hardware
- Bits per character
- 5.954
- Equivalent random word count (EFF list)
- 5.5
- Length needed for 80 bits
- 14
Assumptions
- The password is generated uniformly at random from the selected character set — the only case where this arithmetic is honest.
- The attacker knows the length and the character set, which is the standard conservative assumption.
- Average crack time is half the exhaustive search; a lucky attacker is faster.
- The guess rate is constant; real hardware gets faster every year.
- Symbols default to the 32 punctuation characters on a US keyboard.
| Length | Entropy (bits) | Possible passwords | Average crack time |
|---|---|---|---|
| 6 | 35.7 | 5.68 × 10^10 | under a second |
| 8 | 47.6 | 2.18 × 10^14 | 18.2 minutes |
| 10 | 59.5 | 8.39 × 10^17 | 48.6 days |
| 12 | 71.5 | 3.23 × 10^21 | 511 years |
| 14 | 83.4 | 1.24 × 10^25 | 1.96 × 10^6 years |
| 16 | 95.3 | 4.77 × 10^28 | 7.55 × 10^9 years |
| 20 | 119.1 | 7.04 × 10^35 | 1.12 × 10^17 years |
| 24 | 142.9 | 1.04 × 10^43 | 1.65 × 10^24 years |
At 100,000,000,000 guesses per second. Each extra character multiplies the work by 62× — which is why length beats complexity every time.
How this is worked out
The formula
Character set size N = 26 (lower) + 26 (upper) + 10 (digits) + symbols Entropy (bits) = length × log₂(N) Search space = N^length = 2^entropy Average time to crack = search space ÷ 2 ÷ guesses per second Example: 62 characters, length 12 → 12 × log₂(62) = 71.45 bits
Open How it’s calculated above to see this worked through with your own numbers.
What you enter
- Password length
- A number.from 1 to 128 · whole numbers only · defaults to 12
- Lowercase letters (a–z)
- Turn this on or off.defaults to on
- Uppercase letters (A–Z)
- Turn this on or off.defaults to on
- Digits (0–9)
- Turn this on or off.defaults to on
- Symbols (!@#$…)
- Turn this on or off.defaults to off
- Attacker's guess rate
- 10¹¹/s is a realistic GPU rig against a fast hash (MD5, SHA-1, NTLM). Use 10⁴ for bcrypt at cost 12, or 10 for a rate-limited login form.1 or more · defaults to 100000000000
- How many symbols are allowed(under More options)
- 32 is the punctuation on a US keyboard. Some sites allow far fewer, which shrinks the search space.from 1 to 64 · whole numbers only · defaults to 32
What you get back
- Entropymain answer
- Bits. Each extra bit doubles the work an attacker has to do.
- Character set size
- Possible passwords
- Time to crack (average)
- Time to crack (exhaustive search)
- Verdict
- Bits per character
- Equivalent random word count (EFF list)
- Length needed for 80 bits
What this assumes
- The password is generated uniformly at random from the selected character set — the only case where this arithmetic is honest.
- The attacker knows the length and the character set, which is the standard conservative assumption.
- Average crack time is half the exhaustive search; a lucky attacker is faster.
- The guess rate is constant; real hardware gets faster every year.
- Symbols default to the 32 punctuation characters on a US keyboard.
About this calculator
Password entropy measures how many guesses an attacker has to make, expressed in bits so the numbers stay manageable. Every extra bit doubles the work. The arithmetic is simple: entropy = length × log₂(alphabet size), so a 12-character password drawn from the 62 letters and digits is 12 × 5.954 = 71.45 bits, meaning 2^71.45 ≈ 3.2 × 10²¹ possibilities.
The assumption that makes this number a lie
That figure is correct only if the password was generated uniformly at random by a machine. Entropy is a property of the process that generated the password, not of the string itself. "Tr0ub4dor&3" and a random 11-character string have identical length and character classes, and wildly different real strength — because password crackers do not brute-force in alphabetical order. They start with leaked password lists, then dictionary words, then rules: capitalise the first letter, append a year, swap a→@, e→3, o→0, add an exclamation mark. Those transformations are cheap and they are exactly what humans do.
A human-chosen password of 12 characters is empirically worth somewhere around 20 to 30 bits, not 71. The gap is the whole reason password managers and generated passwords exist. If you did not roll dice or press a "generate" button, treat everything below as an optimistic upper bound.
Reading the crack time
The guess rate is an input because it varies by six orders of magnitude depending on what the attacker is attacking:
- Online, rate-limited login: maybe 10–100 guesses per second before lockout. Almost any password survives.
- Offline, fast hash (MD5, SHA-1, NTLM, unsalted SHA-256): 10¹⁰–10¹² per second on a modern multi-GPU rig. This is the default here, and it is the case that matters, because it is what a database breach hands the attacker.
- Offline, slow hash (bcrypt at cost 12, scrypt, Argon2id): 10³–10⁵ per second. Deliberately slow hashing buys about 20 bits of effective strength — which is why it matters more than your password policy does.
The headline time is the average: an attacker searching a uniform space finds the answer after half of it, so the expected time is the exhaustive time halved.
Length beats complexity
Adding a character multiplies the search space by the alphabet size; adding the whole symbol set multiplies it by about 1.5. Going from 8 to 12 lowercase-plus-digit characters gains 20 bits. Adding every symbol on the keyboard to an 8-character password gains 5. This is why current guidance — NIST SP 800-63B — dropped composition rules ("must contain an uppercase letter and a symbol") entirely: they push users toward predictable patterns while barely moving the maths.
Passphrases work for the same reason. Five words picked randomly from the EFF's 7,776-word list is 64.6 bits, six words is 77.5, and both are far easier to type than the equivalent random string.
What entropy does not cover
Reuse, phishing, malware, a shoulder surfer, a bad password-reset flow, and a site storing your password in plaintext. None of them care how long your password is. Multi-factor authentication and unique passwords per site defeat attacks that no amount of entropy touches.
Frequently asked questions
▸How many bits of entropy does a 12-character password have?
With lowercase, uppercase and digits (62 characters) it is 12 × log₂(62) = 71.45 bits. Add symbols for a 94-character set and it rises to 78.7 bits.
▸Is entropy a reliable measure of password strength?
Only for randomly generated passwords. Entropy describes the generator, not the string — a human-chosen password of the same length and character classes is typically worth 20–30 bits because crackers try human patterns first.
▸How much entropy is enough?
Against an offline attack on a fast hash, 60 bits is the practical floor and 80+ is comfortable. Against a properly rate-limited login, far less is fine. The hashing algorithm the site uses matters as much as your password does.
▸Are passphrases better than complex passwords?
For the same entropy they are far easier to type and remember. Five random words from the EFF 7,776-word list give 64.6 bits; six give 77.5. The words must be chosen randomly, not written as a sentence.
▸Do symbols help?
Less than length does. Adding all 32 symbols multiplies the search space by about 1.5 per character, while adding four more characters multiplies it by 62⁴ — about 15 million.
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