Password Generator

How This Calculator Works

A password generator creates a random string of characters from a chosen mix of letters, numbers, and symbols, strong enough that guessing it by brute force isn’t practical. Choose a length and which character types to include, and this calculator generates a password instantly — using your browser’s cryptographically secure random number source, not the weaker general-purpose randomness an ordinary “pick a random number” tool relies on.

Like this site’s Random Number Generator, the result here is deliberately not reproducible from the inputs alone — a shared link restores your settings (length and which character types you picked), not the password itself. Your generated password is never written into the URL, saved to this site’s calculation history, or sent anywhere; it only ever exists in your own browser, and running the generator again is supposed to give you something new.

The Formula

A password’s strength is measured in bits of entropy — how many yes/no guesses an attacker would need on average to find it by brute force:

$$\text{Entropy (bits)} = \vA{\text{Length}} \times \log_2(\vB{\text{Character Set Size}})$$

The character set size is the total count of every character type you selected — 26 for uppercase, 26 for lowercase, 10 for numbers, and around 25 common symbols — added together. Both a longer password and a wider mix of character types raise the entropy, but length matters more: doubling the character set size only adds 1 bit per character, while doubling the length doubles the bits outright.

Worked Example

A 12-character password using all four character types (uppercase, lowercase, numbers, and symbols):

1. Character set size: $26 + 26 + 10 + 25 = \vB{87}$ possible characters per position.
2. Entropy: $\vA{12} \times \log_2(\vB{87}) \approx 77.3 \text{ bits}$.
3. That falls in this calculator’s “Strong” band (60–79 bits) — a comfortable margin against an offline brute-force attempt with current hardware, though not quite the “Very Strong” band a longer password would reach.

Stretching the same four character types to 16 characters instead raises the entropy to about 103 bits — solidly into “Very Strong” territory, since the extra 4 characters compound the number of possible passwords far more than adding another character type would.