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Shannon Entropy Calculator

Calculate the information entropy (uncertainty) of text strings. Analyze character distribution, bit density, and theoretical compression limits.

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About

In information theory, Shannon Entropy measures the unpredictability or "information content" of a message source. It quantifies the absolute minimum number of bits required to encode a string without losing data. A string with identical characters (e.g., "AAAAA") has an entropy of 0, while a truly random string approaches maximum entropy.

This tool is widely used by computer scientists to analyze password strength (randomness), test random number generators, or determine the compressibility of a dataset. It provides a breakdown of character frequency (p(x)) and compares the actual byte size against the theoretical ideal size.

information-theory cryptography compression entropy data-science

Formulas

Shannon Entropy H is calculated as the negative sum of the probability of each distinct character:

H(X) = − n∑i=1 p(xi) log2 p(xi)

Where p(x) is the frequency count of character x divided by the string length.

Reference Data

ScenarioEntropy (bits/symbol)Description
Constant String0"aaaaa". Complete certainty.
English Text2.3 - 4.5Natural language is redundant.
Base64 / Random5.8 - 6.0High density, used in encryption.
Binary Random1.0If symbols are only 0 and 1 with equal prob.
Max Entropy (N symbols)log2(N)Uniform distribution of all unique chars.

Frequently Asked Questions

Here, a bit represents a binary decision. An entropy of 4.5 bits means that, on average, you need 4.5 "yes/no" questions to guess the next character in the sequence.
English has high redundancy. The letter "e" is very common, "z" is rare, and "q" is almost always followed by "u". This predictability lowers the information content (entropy), which is why text files compress so well.
High entropy implies high unpredictability. A password like "Password123" has low entropy (predictable patterns). A password like "9#xK!2" has higher entropy per character, making it harder to brute-force.