Shannon Entropy Calculator

Shannon entropy measures the average amount of information produced by a stochastic source of data. The mathematical formula for Shannon entropy H(X) over a discrete random variable X with possible outcomes and associated probabilities P(x) is expressed as: H(X) = - sum(P(x) * log2(P(x))) across all states. If a probability is zero, the term evaluates to zero since log2(0) is undefined, preventing mathematical errors. The final output is measured in bits, where higher values indicate greater system unpredictability and lower values represent higher certainty.

Imagine evaluating a simple discrete random variable with two possible outcomes: Outcome A has a probability of 0.75, and Outcome B has a probability of 0.25. First, calculate the individual contribution of Outcome A: -0.75 * log2(0.75). Since log2(0.75) is approximately -0.415, the contribution equals 0.311 bits. Next, calculate Outcome B: -0.25 * log2(0.25). Because log2(0.25) is -2.0, this contribution equals 0.500 bits. Summing these values gives a total Shannon entropy of 0.311 + 0.500 = 0.811 bits, indicating moderate uncertainty in the system.

Always ensure that your input probabilities sum up to exactly 1 (or 100 percent) for a mathematically valid probability distribution. When analyzing continuous data, remember that you must bin or discretize your values before calculating Shannon entropy. Pay close attention to near-zero probabilities, as rounding errors can occasionally distort logarithmic calculations in complex datasets.