Shannon entropy calculator
Paste text, a key, token, password, log sample, or data string and measure Shannon entropy per symbol. Switch between characters, UTF-8 bytes, words, and lines; report bits, nats, dits, or trits; compare per-line or per-paragraph entropy; and inspect the symbol-frequency table locally in your browser.
About this tool
Shannon entropy measures how unpredictable a sequence is from its observed symbol frequencies. If every symbol appears equally often, entropy is high; if one symbol dominates, entropy is low. This calculator reports that value as entropy per symbol plus the derived totals people usually need for quick checks: total information, maximum possible entropy for the observed alphabet, efficiency, redundancy, perplexity, and a ranked frequency table.
It is an order-0 frequency calculation. It does not understand grammar, keyboard walks, leaked passwords, Markov models, or how an attacker guesses secrets. Use it as a compact information-theory measurement, not as a password-strength guarantee.
Worked example — password
With the default character basis, password has eight characters and seven distinct character values because s appears twice. The report shows:
Entropy: 2.7500 bits per character
Total information: 22.0000 bits across 8 characters
Distinct characters: 7
Maximum entropy for this alphabet: log2(7) = 2.8074 bits per character
Efficiency: 97.9539% (redundancy 2.0461%)
Perplexity: 6.7272 equally likely characters
That number is the entropy of the observed string. It does not mean the word password is safe; dictionary knowledge makes it easy to guess.
Symbol basis
- Characters counts Unicode scalar values. This is the usual choice for text keys and passwords.
- Bytes counts UTF-8 bytes and produces the familiar 0–8 bits per byte range for binary-like text.
- Words counts whitespace-separated tokens, useful for prose or passphrases.
- Lines treats each whole line as one symbol, useful for repeated log events or list values.
Scope and units
The default scope scores the whole input once. Use Each line or Each paragraph to find which records are repetitive versus varied; the combined report is still printed after the per-part summary.
Bits are base-2 units (shannons). Nats use base e, dits use base 10, and trits use base 3. Perplexity stays the effective number of equally likely symbols, regardless of the unit selected.
Limits and edge cases
- Input is capped at 1 MiB and 20,000 lines/paragraphs for split scopes.
- Precision is 0–10 decimal places; frequency rows are capped at 64.
- Whitespace filtering removes whitespace characters for character/byte mode and blank lines for line mode. Word mode already splits on whitespace.
- A single repeated symbol has 0 entropy but 100% efficiency by convention because the one-symbol distribution is trivially uniform.
- Binary files are better handled by byte-oriented tooling; this page measures pasted text.
FAQ
Is this the same as password strength?
No. Shannon entropy here is computed only from the symbols in the pasted string. It does not know that password, qwerty, dates, or dictionary words are common guesses. A random-looking 12-character token and a memorized word can have similar frequency entropy but very different attack resistance. Treat this as a measurement of symbol distribution, not a security score.
When should I choose bytes instead of characters?
Choose bytes when you want the conventional 0–8 bits/byte view or when UTF-8 encoding itself matters. Non-ASCII characters occupy multiple bytes, so byte entropy can differ from character entropy. For human text, characters or words are usually easier to interpret.
What does maximum entropy mean?
Maximum entropy is the value the input would have if every distinct symbol you observed appeared equally often. For seven distinct characters in bits, it is log2(7). Efficiency is the measured entropy divided by that maximum. High efficiency means the observed counts are close to uniform; it does not prove the data was generated randomly.
Why do two differently ordered strings get the same entropy?
This calculator uses an order-0 model: it counts how often symbols appear and ignores their order. abababab and aabbaabb therefore have the same entropy because both contain four a and four b. If you need sequence predictability, you need a model that considers n-grams or transitions.
What is perplexity?
Perplexity is base^entropy: the effective number of equally likely symbols. An entropy of 2 bits per character has perplexity 4, meaning the distribution behaves like four equally likely characters even if the real alphabet is larger.
Developer & Automation Access
Run it from the terminal
Same engine as this page, headless — via the gizza CLI:
gizza tool entropy-calculator "password"New to the CLI? Get gizza →
Open it by URL
Pre-fill and auto-run this tool with query parameters — the names match the API/CLI:
https://gizza.ai/tools/entropy-calculator/?text=password&basis=characters&unit=bits&scope=whole&ignore_case=true&ignore_whitespace=true&precision=4&show_frequencies=true&top_symbols=12Machine-readable descriptor: tool.json — title + parameters JSON Schema for agents.