What is Password Entropy?
Password entropy is a mathematical measurement of password unpredictability, expressed in bits. Each additional bit of entropy doubles the number of guesses an attacker must attempt to brute-force the password.
The Shannon Entropy Formula
For a uniformly random password generated from a fixed character pool R of length L:
Mathematical Equation
E = L ร \log_2(R)
Where:
Character Pool Sizes ($R$)
Why Length Beats Complexity
Compare these two passwords:
1
Short & Complex (8 chars, full pool $R=94$):
Mathematical Equation
E = 8 ร \log_2(94) = 8 ร 6.55 = 52.4 bits
2
Long & Simple (16 chars, lowercase only $R=26$):
Mathematical Equation
E = 16 ร \log_2(26) = 16 ร 4.70 = 75.2 bits
The 16-character lowercase passphrase is over 8 million times harder to crack (2^{75.2 - 52.4} โ 2^{22.8}) than the complex 8-character password.
