Language Entropy Calculator
Computes the Shannon information entropy of a text based on character or symbol probabilities. Used by computational linguists and NLP researchers to quantify predictability and information density in language.
About this calculator
Shannon entropy, borrowed from information theory, measures the average uncertainty or unpredictability of symbols in a message. For a set of characters with probabilities p₁, p₂, p₃, the entropy H is: H = −(p₁ × log₂(p₁) + p₂ × log₂(p₂) + p₃ × log₂(p₃)), measured in bits. A higher entropy means the characters are more evenly distributed and the text is harder to compress or predict. A lower entropy means some characters dominate, making the text more redundant. English text typically exhibits an entropy of around 4–5 bits per character when all letters are considered. This calculator simplifies the full distribution to three probability inputs, making it ideal for classroom demonstrations or quick comparisons between small symbol sets.
How to use
Suppose you analyze a small alphabet with three characters, appearing with probabilities p₁ = 0.5, p₂ = 0.3, and p₃ = 0.2 (they must sum to 1). Enter these values into the three fields. The calculator computes: H = −(0.5 × log₂(0.5) + 0.3 × log₂(0.3) + 0.2 × log₂(0.2)) = −(0.5 × (−1) + 0.3 × (−1.737) + 0.2 × (−2.322)) = −(−0.5 − 0.521 − 0.464) = 1.485 bits. This means each character carries about 1.485 bits of information on average.
Frequently asked questions
What does a high language entropy value mean for a text?
High entropy indicates that characters or words are distributed more uniformly, making the text less predictable and harder to compress. In natural language, higher entropy often corresponds to more complex or information-dense writing. Conversely, low entropy means a few symbols dominate, as seen in highly repetitive or formulaic text. Information theorists use entropy to set theoretical limits on how efficiently a text can be encoded or transmitted.
How do probabilities need to be set when using the language entropy calculator?
All probability values entered must be non-negative and must sum to exactly 1.0, because they represent the complete probability distribution over the symbol set. For example, if three characters appear 50%, 30%, and 20% of the time, enter 0.5, 0.3, and 0.2 respectively. Entering probabilities that do not sum to 1 will produce a mathematically invalid result. If your alphabet has more than three characters, you would extend the formula with additional −pᵢ × log₂(pᵢ) terms.
Why is log base 2 used in Shannon entropy for language analysis?
Using base 2 yields entropy measured in bits, which directly corresponds to the minimum number of binary digits (0s and 1s) needed to encode each symbol on average. This makes the result directly interpretable in terms of data storage and communication efficiency. Natural logarithm (base e) would give entropy in nats, while base 10 gives hartleys — all equivalent but less intuitive for digital contexts. Base 2 has become the standard in information theory and computational linguistics.