How Secure is Your Password? Calculating Shannon Entropy in the Browser

We've all seen password strength meters on sign-up forms. Most of them rely on simplistic, static rules: "Must contain at least 8 characters, one number, and one special character." But from a mathematical standpoint, these rules are a poor proxy for actual password security. A password like Tr0ub4dor&3 conforms to these rules but is far easier to compromise than a randomly generated four-word passphrase like correct-horse-battery-staple . To truly measure password security, we have to look at information theory and compute its Shannon Entropy . Here is how password entropy works, the math behind it, and how you can calculate it directly in the browser with 100% client-side privacy. What is Password Entropy? In cryptography, entropy is a measure of the unpredictability or randomness of a password. It is expressed in bits . An entropy of $N$ bits means there are $2^N$ possible combinations that an attacker would have to guess in a worst-case brute-force search. < 28 bits: Very weak (easily guessed in milliseconds). 28 to 35 bits: Weak (cracked in minutes or hours). 36 to 59 bits: Reasonable protection (days to months). 60 to 127 bits: Very strong (takes years to decades to crack). 128+ bits: Extremely secure (mathematically unfeasible to crack). The Mathematical Formula To calculate the entropy ($E$) of a password, we use the following equation: $$E = L \times \log_2(R)$$ Where: $L$ is the length of the password (number of characters). $R$ is the size of the pool of unique characters from which the password is drawn. $\log_2(R)$ is the binary logarithm of the pool size, representing the amount of information carried by each character. Determining Pool Size ($R$) To find $R$, we analyze which character sets are present in the password string: Lowercase letters ( a-z ): 26 characters Uppercase letters ( A-Z ): 26 characters Numbers ( 0-9 ): 10 characters Common special characters/punctuation: 33 characters (e.g., !@#$%^&*()-_=+[]{}|;:',.<>/? etc.) If a password uses ch