Statistics Calculators

Shannon Entropy Calculator

Calculate the Shannon entropy of a probability distribution, in bits — a measure of uncertainty or information content.

Shannon entropy —

Maximum possible entropy —

Efficiency (entropy ÷ max entropy) —

About the Shannon Entropy Calculator

Shannon entropy quantifies the average amount of uncertainty or "surprise" in a set of possible outcomes. It's highest when every outcome is equally likely and lowest (zero) when one outcome is certain.

Formula: H = −∑ pⁱ × log₂(pⁱ), measured in bits

Enter a probability or relative weight for each possible outcome — they'll be normalized to sum to 1 automatically. Shannon entropy underlies data compression limits, decision-tree splitting criteria, and measures of diversity or randomness in information theory.