Password Entropy Calculator

Estimate how hard a password is to brute-force, measured in bits of entropy.

How the Math Works

Password entropy measures the strength of a password by calculating the number of possible combinations an attacker would need to guess it. The formula entropy = length × log₂(character set size) works by first determining how many characters are available (the character set size), then calculating how many bits of information each character represents using the logarithm base 2. Multiplying this by the password length gives the total entropy in bits, where higher values indicate exponentially greater resistance to brute-force attacks.

Practical Applications

To use this calculator, first identify your password's character set - whether it contains only lowercase letters (26 characters), or includes uppercase, numbers, and symbols (up to 95 characters). Enter your password length and the calculator determines the character set size, then applies the formula to compute the entropy value. For example, a 12-character password using all common keyboard characters yields approximately 79 bits of entropy, while the same length with only lowercase letters provides only about 57 bits.

Day-to-Day Use

Understanding password entropy helps you make informed decisions about password creation and management. Generally, aim for passwords with at least 60-80 bits of entropy for important accounts, which typically means 12+ characters including a mix of uppercase, lowercase, numbers, and symbols. This knowledge also helps you evaluate password strength meters, choose between longer passwords with simpler character sets versus shorter complex ones, and understand why passphrases like 'correct horse battery staple' can be both secure and memorable.

Worked example

12 chars from all ASCII (94) → 12 × log₂(94) = 78.7 bits.

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