Password Combination Calculator

Why Count Password Combinations?

Every extra character and character type multiplies the number of possible passwords an attacker must guess. Counting combinations helps you estimate brute-force resistance before choosing a policy. Related tools: Password Strength Analyzer and Strong Password Generator.

Permutations With Repetition

Passwords allow repeated characters, so the base count is $n^k$, where $n$ is the size of the allowed character set and $k$ is password length. If you require at least one uppercase letter, one digit, or one symbol, invalid passwords are removed using the inclusion-exclusion principle.

$$\text{Valid passwords} = n^k - \sum |A_i| + \sum |A_i \cap A_j| - \cdots$$

Example

With lowercase, uppercase, and digits only ($n = 62$) and length 8, there are $62^8 \approx 2.18 \times 10^{14}$ unrestricted passwords. Requiring at least one uppercase and one digit removes passwords built from only lowercase, only uppercase, or only digits.