Shannon Entropy & Passwords

How much information is in a password? Shannon entropy measures its unpredictability in bits — and reveals why length beats a scramble of symbols.

Shannon Entropy & PasswordsLive

measuring information & strength

Entropy

60bits

brute-force time: 1 yr

Controls

Password / string

Shannon entropy measures information in bits — how many yes/no questions it takes to pin down a value. For a password it is length times the log₂ of the character-set size, quantifying how unpredictable it is. Each extra bit doubles the guessing effort, so length beats complexity: a long passphrase can carry more entropy than a short scramble of symbols.

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Data Inspector

Character pool62

Entropy59.5 bits

Strengthreasonable

Crack time1 yr

Governing equation

H = - i \sum p_{i} lo g_{2} p_{i} = lo g_{2} 62 = 5.95 bits/char \Rightarrow 10 \times 5.95 = 59.5 bits

Reading this result: 60 bits is reasonable for low-value logins but short of the ~60-bit bar; each added character here is worth 6.0 more bits.

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How it works

Shannon entropy quantifies information as the number of yes/no questions needed to determine a value. For a password it is the length times the log₂ of the character-set size, measuring how hard it is to guess. Each additional bit doubles the brute-force effort, so a long passphrase can be far stronger than a short, complex string. The foundation of information theory.

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