What is Shannon entropy?

Shannon entropy (H) measures the average unpredictability of a symbol source. It is defined as H = -sum(p_i * log2(p_i)) where p_i is the probability of each symbol. The unit is bits per symbol.

What is the maximum possible entropy?

For a source with N distinct symbols, the maximum entropy is log2(N) bits, achieved when all symbols are equally probable. For byte data (256 possible values), the theoretical maximum is 8 bits/byte.

What does a low entropy value mean?

Low entropy means the data is highly predictable or repetitive. For example, the string "aaaaaaa" has entropy 0, because every character is the same and carries no new information.

Can I use this to test password strength?

Entropy is one indicator of unpredictability. A password with high Shannon entropy has diverse character usage, making it harder to guess. However, true password security also depends on length and the search space of the generation method.

What is self-information?

Self-information (surprisal) of a symbol is -log2(p) bits. Rare symbols carry more information than common ones. Shannon entropy is simply the expected (average) self-information across all symbols.

Does capitalization matter?

Yes. The calculator is case-sensitive by default, treating "A" and "a" as distinct symbols. Toggle the case-insensitive option to merge them.

Shannon Entropy Calculator

Name: Shannon Entropy Calculator
Availability: InStock
Author: Nham Vu

Paste any text string to instantly compute its Shannon entropy in bits, with a full symbol frequency and self-information table.

Input

Case-insensitive (treat A = a) Ignore whitespace characters

Entropy Result

Enter text or probabilities on the left to compute entropy.

Symbol Frequency Table

Results appear here.

Symbol	Count	Probability	Self-info (bits)	Contribution

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Summary

Paste any text string to instantly compute its Shannon entropy in bits, with a full symbol frequency and self-information table.

How it works

Enter a text string in the input field, or switch to manual probability mode.
The tool counts each unique character and calculates its frequency.
Each symbol's probability p is used to compute self-information: -log2(p) bits.
Shannon entropy H is the probability-weighted average: H = -sum(p * log2(p)).
Results update in real time as you type, showing the full frequency table.

Use cases

Estimate the compressibility of a string before applying compression.
Verify the randomness quality of generated passwords or tokens.
Analyze character distribution in dataset fields or log entries.
Learn information theory by experimenting with different inputs.
Check if a ciphertext has near-maximum entropy (8 bits/byte for good encryption).
Compare entropy across different natural languages or encodings.

Frequently Asked Questions

Last updated: 2026-07-01 · Reviewed by Nham Vu