The Science of Password Entropy: Why Length Trumps Complexity

For years, users have been told to create passwords that look like P@ssw0rd!12. We were taught that "complexity"—the mixing of symbols, numbers, and cases—was the only way to stay safe. However, modern cybersecurity science has proven that this advice is not only frustrating for users but mathematically inferior to a more important metric: Length.

This guide explores the concept of Password Entropy, the mathematical measurement of how unpredictable a password is, and why a long string of simple words is significantly harder to crack than a short string of complex characters.

In the context of passwords, Entropy is measured in "bits." Each bit of entropy doubles the amount of work an attacker must do to guess your password.

If a password has 1 bit of entropy, there are 2 possibilities (0 or 1).

If it has 10 bits, there are 1,024 possibilities.

If it has 80 bits, there are approximately 1.2 septillion (1,200,000,000,000,000,000,000,000) possibilities.

To be considered "strong" against modern GPU-based brute-force attacks in 2026, a password should aim for at least 70 to 80 bits of entropy.