Password entropy calculator
Work out how many bits of entropy a random password has from its length and character pool, and see the formula calculated step by step.
Strong. 2^71.5 ≈ 10^NaN possibilities.
Entropy by length and pool
Read across to see how a bigger pool helps; read down to see how length helps far more.
| Length | Digits (10) | Lower (26) | Alnum (62) | ASCII (94) |
|---|---|---|---|---|
| 8 | 27 | 38 | 48 | 52 |
| 10 | 33 | 47 | 60 | 66 |
| 12 | 40 | 56 | 71 | 79 |
| 16 | 53 | 75 | 95 | 105 |
| 20 | 66 | 94 | 119 | 131 |
| 24 | 80 | 113 | 143 | 157 |
| 32 | 106 | 150 | 191 | 210 |
Values in bits. 80+ bits resists any realistic offline attack.
What the number means
Entropy is the base-2 logarithm of the number of equally likely passwords a generator could have produced. It’s a property of the method, not the string: “kX9#” from a random generator and “kX9#” typed by a cat on a keyboard look identical, but only one came from a known, uniform process.
Each extra bit doubles the attacker’s work. Going from 60 to 70 bits multiplies it by 1,024. On average an attacker searches half the space before hitting the right one, so average guesses = 2E−1.
When the formula lies
People don’t pick characters uniformly. “Password1!” has 10 characters from a 94-character pool, which the formula scores at 65.5 bits, yet it’s near the top of every cracking list. For passwords a human chose, use the password strength checker, which models real attacker guesses.
To get a password where the formula does hold, use the password generator or the passphrase generator (12.9 bits per word).
Questions people ask
What is password entropy?
Entropy measures how unpredictable a password is, in bits. Each bit doubles the number of guesses an attacker needs. A password with 60 bits of entropy has 2^60, about 1.15 × 10^18, equally likely possibilities.
What is the password entropy formula?
For a password whose characters are chosen uniformly at random: E = L × log2(R), where L is the length and R is the size of the character pool. For words chosen at random from a list, R is the list size and L is the number of words.
How many bits of entropy is a good password?
As a rule of thumb: under 40 bits is weak, 60 bits resists most online and slow-hash attacks, 80 bits resists well-funded offline attacks, and 100+ bits is beyond any foreseeable brute force. A random 16-character password from all 94 printable characters has about 105 bits.
Why does a checker give my password less entropy than this calculator?
The formula assumes every character was chosen at random. If you chose the password yourself, it probably contains words, names or patterns that attackers try first, so its real entropy is much lower. Use the password strength checker for human-chosen passwords.