entropy calculator - Aaron Graves, PhDude Replica

Shannon Entropy Calculator

Compute entropy from probabilities, counts, or raw text.

Input mode

Enter probabilities

Use commas, spaces, or new lines between values.

Log base

Automatically normalize probabilities if they do not sum to 1

What is entropy?

In information theory, entropy measures uncertainty. If outcomes are evenly spread, entropy is high. If one outcome is very likely and others are rare, entropy is low. This idea helps you quantify how “surprising” a source of information is.

H = -Σ p_i log_b(p_i)

Here, p_i is the probability of outcome i, and b is the log base. Base 2 gives entropy in bits, base e gives nats, and base 10 gives hartleys.

How to use this entropy calculator

Probabilities mode: Enter values like 0.5, 0.25, 0.25.
Counts mode: Enter frequencies like 50, 30, 20; the tool converts them to probabilities.
Text mode: Paste a text sample; entropy is based on character frequencies.
Choose a log base to control output units.
Click Calculate Entropy to see entropy, max entropy, perplexity, and per-symbol contributions.

How to interpret the output

Entropy (H)

This is the average information per event. Higher values mean more unpredictability.

Maximum entropy

For n distinct outcomes, the maximum is log_b(n), reached when all outcomes are equally likely.

Evenness and redundancy

Evenness compares actual entropy to the theoretical maximum. Redundancy is the complement, showing how much structure or predictability exists in the distribution.

Perplexity

Perplexity is b^H. It can be read as the “effective number of equally likely choices.”

Common mistakes to avoid

Supplying probabilities that are negative or all zero.
Forgetting that probabilities should sum to 1 (unless auto-normalization is enabled).
Using too little text in text mode, which can produce unstable estimates.
Comparing entropy values from different bases without converting units.

Where entropy is useful

Data science: feature selection and impurity measures.
Compression: lower entropy often means better compression potential.
Cryptography: randomness and key quality checks.
NLP: language-model evaluation and uncertainty estimation.
Ecology: diversity metrics based on species distribution.

Final note

Entropy is a simple but powerful lens for understanding randomness, structure, and information content. Use this calculator to quickly test distributions, compare datasets, and build intuition for uncertainty.