Password Entropy Explained
The single number most password strength meters are built on — what it measures, how to calculate it by hand, and where it falls short.
What Entropy Measures
Entropy measures how unpredictable a password is, expressed in bits. Each bit doubles the number of possible values an attacker would need to try. It answers one specific question: if this password were generated by picking each character independently and uniformly at random from a defined pool, how many possible passwords could have resulted?
The Formula
Where "pool size" is the number of distinct characters available at each position. A password using only lowercase letters has a pool of 26; adding uppercase, digits and symbols brings it to roughly 94.
Worked Example
A 16-character password using all four character types (uppercase, lowercase, digits, symbols — pool of 94):
This means there are roughly 2¹⁰⁵ possible passwords matching that description — an astronomically large number, larger than the number of atoms in the observable universe multiplied many times over.
Pool Size by Character Type
| Character set | Pool size | Bits per character |
|---|---|---|
| Lowercase only (a-z) | 26 | 4.70 |
| Lowercase + uppercase (a-zA-Z) | 52 | 5.70 |
| Alphanumeric (a-zA-Z0-9) | 62 | 5.95 |
| All types (a-zA-Z0-9 + symbols) | ~94 | 6.55 |
| Digits only (0-9) | 10 | 3.32 |
Entropy Thresholds
| Entropy | Rating | Guidance |
|---|---|---|
| < 28 bits | Very Weak | Crackable in seconds to minutes — change immediately |
| 28-39 bits | Weak | Inadequate for any real account |
| 40-59 bits | Fair | Marginal — acceptable only for the lowest-risk, throwaway accounts |
| 60-79 bits | Strong | Adequate for most everyday accounts |
| 80+ bits | Very Strong | Recommended for high-value or sensitive accounts |
Why Entropy Isn't the Whole Story
Password123! has a pool of 94 characters and a length of 12, giving a theoretical entropy of ~79 bits — "Strong" by the numbers. In reality, it's one of the most commonly used passwords in every breach database, crackable in milliseconds by any tool that checks common passwords first. The formula doesn't know that; it only knows length and pool size.
This is exactly why every generator on this site uses crypto.getRandomValues() for actual random selection — entropy calculations are only meaningful when the password truly was generated with uniform randomness, which a human typing at a keyboard cannot reliably replicate.
Calculating Entropy for a Passphrase
The same formula applies, but the "pool" is the wordlist size and the "length" is the word count:
A 5-word passphrase from a 7,776-word list: 5 × log₂(7776) = 5 × 12.9 ≈ 65 bits. See Password vs Passphrase for a full comparison.
Frequently Asked Questions
60+ bits is strong for everyday accounts; 80+ bits is recommended for high-value accounts. Below 40 bits should be treated as weak regardless of appearance.
No. Entropy is a theoretical measure based purely on length and pool size assuming true randomness. A password can have high theoretical entropy and still appear in breach databases.
Entropy assumes uniform random selection. A human-chosen password's real unpredictability is usually far lower than its theoretical entropy, because human choices cluster around familiar words and patterns that cracking tools specifically target.
Calculate the entropy of a real password
See the exact bits and pool size for any password, in your browser.
Use the Entropy Calculator →