Password Entropy Calculator
Calculate the precise mathematical entropy of a password in bits using the Shannon formula
H = L × log₂(N). See a complete breakdown of the character pool,
the full formula with your values substituted in, and how many guesses are required
to crack it at various attack speeds.
H = L × log₂(N) gives the theoretical maximum entropy in bits.
Common pool sizes: lowercase only = 26, lowercase + uppercase = 52, + digits = 62, + symbols = 94.
Entropy measures the unpredictability of a password in bits. Each additional bit doubles the number of guesses required to crack it by brute force.
The formula H = L × log₂(N) calculates theoretical maximum entropy, where L is the length and N is the pool of possible characters. A password of length 12 using all 94 printable ASCII characters has 12 × log₂(94) = 78.7 bits.
This is theoretical entropy — the real effective entropy may be lower if the password follows a predictable pattern (dictionary word, date, keyboard walk). The Password Strength Checker accounts for patterns; this tool shows the mathematical maximum.
| Entropy Range | Strength | Recommendation |
|---|---|---|
| < 28 bits | Very Weak | Cracked in seconds by any modern attack |
| 28 – 35 bits | Weak | Vulnerable to offline attacks within hours |
| 36 – 59 bits | Fair | Acceptable for low-value accounts only |
| 60 – 79 bits | Strong | Good for most personal accounts |
| 80 – 99 bits | Very Strong | Resistant to all practical attacks |
| 100+ bits | Excellent | Unbreakable for any foreseeable attack |
Frequently Asked Questions
What is password entropy?
Entropy measures unpredictability in bits: H = L × log₂(N), where L is the length and N is the character pool size. Higher entropy means exponentially more guesses required.
Does this calculator send my password anywhere?
No. All calculation is done locally in JavaScript. Your password is never transmitted.
How many bits of entropy do I need?
For online accounts: 60+ bits. For offline-cracked systems: 80+ bits. 100+ bits is effectively uncrackable.
Why is effective entropy lower than theoretical?
Theoretical entropy assumes pure randomness. Patterns, dictionary words, and predictable substitutions reduce actual entropy significantly.