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Password Entropy: The Math Behind Why 'Password123' Is Weak

DEV Community·Snappy Tools·about 1 month ago
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When a password manager or security tool tells you a password is "weak" or "strong", it's usually measuring entropy. Here's what entropy means, how to calculate it, and why it matters more than complexity requirements. What is password entropy? Entropy, in this context, measures the unpredictability of a password — specifically, how much information an attacker would need to guess it. It's measured in bits. The formula: entropy = log₂(pool_size) × password_length Enter fullscreen mode Exit fullscreen mode Where pool_size is the number of possible characters. For an 8-character password using only lowercase letters (26 characters): entropy = log₂(26) × 8 = 4.7 × 8 ≈ 37.6 bits Enter fullscreen mode Exit fullscreen mode For an 8-character password using lowercase + uppercase + digits + symbols (95 characters): entropy = log₂(95) × 8 = 6.57 × 8 ≈ 52.5 bits Enter fullscreen mode Exit fullscreen mode Higher entropy = more guesses needed to crack = stronger password.…

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