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For K-12 Students · Shannon Entropy

Shannon Entropy for a certificate

Built for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework. Simulate a certificate live below — adjust the inputs and watch it respond, right in your browser.

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.

▶ Run in Python

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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More with Shannon Entropy

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Frequently asked questions

Is this good for k-12 students?: Yes — this version of "Shannon Entropy for a certificate" is framed for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.