Password entropy calculator
Password entropy measures how many guesses an attacker needs, expressed in bits. For a randomly generated password it is length multiplied by log2(pool size): a 16-character password from an 86-symbol pool carries 103 bits. Every extra bit doubles the work required to break it.
entropy = 16 x log2(95)
bits
4.4 x 10^31 possible passwords
Very strong105.1 bits of entropy
Offline attack on a fast hash: 7 trillion years
Beyond the reach of brute force. Your risk is now phishing and reuse, not guessing.
- Throttled login
- 10^21 years
- GPU, fast hash
- 7 trillion years
- GPU, PBKDF2 600k
- 10^18 years
The formula
For a secret chosen uniformly at random, entropy in bits is:
entropy = length x log2(pool size)The pool size is how many distinct symbols each position could hold: 10 for digits, 26 for lowercase, 52 for mixed case, 62 with digits added, and 86 once you include a typical symbol set. For a passphrase the same formula applies with words in place of characters, so five words from a 1,296-word list gives 5 x log2(1296) = 51.7 bits. If the concept itself is new, start with the definition of password entropy.
The reason bits are used rather than raw combination counts is that bits keep the doubling visible. Every extra bit doubles the attacker's work. Going from 50 to 60 bits is a thousandfold increase, even though the numbers look adjacent.
Entropy of common secrets
| Secret | Pool | Entropy |
|---|---|---|
| A 4-digit PIN | 10 digits | 13.3 bits |
| A 6-digit PIN | 10 digits | 19.9 bits |
| 8 lowercase letters | 26 letters | 37.6 bits |
| 8 mixed characters | 86 symbols | 51.4 bits |
| 12 mixed characters | 86 symbols | 77.1 bits |
| 16 mixed characters | 86 symbols | 102.8 bits |
| 4 random words | 1,296 words | 41.4 bits |
| 6 random words | 1,296 words | 62.0 bits |
| A 128-bit encryption key | 2 values per bit | 128.0 bits |
The assumption that breaks everything
This formula is only valid when the secret was chosen at random. That single condition is where nearly every misuse of entropy comes from.
Consider Tr0ub4dor&3. Eleven characters from an 86-symbol pool calculates to 70.7 bits, which sounds excellent. Its real strength is closer to 28 bits, because an attacker does not guess character by character — they take a dictionary word, apply the standard substitutions, capitalise the first letter, and append a symbol and a digit. That is a search space of a few hundred million, not 1021.
The practical rule: if you chose it, you cannot use this formula. Use the pattern-aware strength checker instead, which estimates the cost of the shortcut rather than the cost of brute force.
How key stretching adds free entropy
Entropy is only half of the equation. The other half is how expensive each guess is, which is set by how the site hashes your password. Running PBKDF2 at 600,000 iterations slows an attacker by a factor of 600,000 — worth about 19 extra bits, at a cost to you of a fraction of a second.
That is why a well-designed system with a 60-bit password can be safer than a badly designed one with an 80-bit password. Read why MoolKey uses 600,000 iterations.
Password entropy FAQ
- What is password entropy?
- Password entropy is the number of guesses an attacker needs on average to find your password, expressed in bits. Each bit doubles that number. A password with 40 bits of entropy takes roughly a trillion guesses; one with 80 bits takes a trillion trillion. It is the only strength measure that means anything precise.
- How do you calculate password entropy?
- For a randomly generated password, entropy in bits equals length multiplied by log2 of the pool size. A 12-character password drawn from 86 possible symbols is 12 x log2(86) = 77.2 bits. For a passphrase, it is the word count multiplied by log2 of the wordlist size.
- How many bits of entropy is enough?
- Aim for at least 60 bits on ordinary accounts and 80 or more on anything valuable. Below 45 bits, an attacker with a stolen database and a GPU wins. Above 100 bits, brute force is off the table entirely and your risk shifts to phishing, malware, and reuse.
- Does this formula work for a password I made up myself?
- No, and this is the single most misused idea in password security. The formula assumes every character was chosen uniformly at random. A password you invented follows patterns an attacker models directly, so its real entropy is a small fraction of the calculated figure.
- Why is entropy measured in bits?
- Because bits make the doubling explicit. Adding one bit doubles the attacker's work; adding ten bits multiplies it by about a thousand. Expressing strength as a raw combination count produces numbers too large to compare, while bits stay in a readable range from roughly 10 to 256.
More free tools
Every tool runs in your browser without an account. The generators, strength checker, and entropy calculator keep inputs local. The breach checker sends only a five-character hash prefix to Have I Been Pwned.
Password generator
A password generator creates a random string that no person would think of and no wordlist contains.
Passphrase generator
A passphrase is several random words joined together, such as "trout-canyon-mellow-drift".
PIN generator
A PIN generator picks digits at random instead of letting you reach for a birthday.
Strength checker
A password strength checker estimates how many guesses an attacker needs before reaching your password.
Breach check
A breach check tells you whether a password already appears in leaked data.
Make one account easier today.
Start with the password you keep reusing or the bank card that still shares a PIN. MoolKey is free, and you do not need to move everything at once.