Use this information-theory calculation when probabilities or predicted class probabilities are valid and you need a precisely defined entropy or probabilistic-loss value.

Observed label

Required integer input.

Predicted probability

Required number input.

Calculate binary cross-entropy for one observed label and predicted probability. The tool evaluates the supplied inputs together and returns the named outputs below; it does not infer omitted operating conditions or change the units shown.^[1]

Cross-entropy

The resulting cross-entropy returned as a number.

• Entropy base, averaging, class labels, clipping near zero, weighting, calibration, sample independence, and reduction convention affect the result. Low training loss does not establish generalization or causal validity.
• Use finite inputs in the displayed units and preserve more precision than the final presentation requires. Independently verify safety-critical, financial, compliance, or production decisions.

State the logarithm base and reduction, inspect calibration and class balance, and evaluate on held-out data with complementary metrics.

• Binary Entropy Calculator

  Calculate binary Shannon entropy in bits.

• Log-Loss Calculator

  Calculate mean binary log-loss across labels and predicted probabilities.

• Shannon Entropy Calculator

  Calculate Shannon entropy in bits from a discrete probability distribution.