Matthews Correlation Coefficient Calculator

The Matthews correlation coefficient, abbreviated MCC, is a single-score summary of binary classification performance. It combines every cell of the confusion matrix: true positives, true negatives, false positives, and false negatives. Unlike accuracy, the score remains informative when one class is much more common than the other, which makes it valuable for fraud detection, medical screening, anomaly detection, and other imbalanced problems. MCC ranges from negative one to positive one. A value of positive one indicates perfect classification, zero indicates performance with no net correlation between predictions and outcomes, and negative one indicates complete disagreement in which predictions are systematically reversed. Intermediate values should be interpreted with the costs of errors, class balance, and the operating threshold in mind rather than through a universal quality label. The numerator is true positives times true negatives minus false positives times false negatives. The denominator is the square root of four marginal totals multiplied together: predicted positives, actual positives, actual negatives, and predicted negatives. This structure makes MCC equivalent to a Pearson correlation between the observed and predicted binary labels. If any required marginal total is zero, the mathematical denominator is zero and the coefficient is undefined. The calculator also reports familiar supporting metrics. Accuracy is the proportion of all cases classified correctly. Precision is the proportion of positive predictions that are true positives. Recall, also called sensitivity, is the proportion of actual positives detected. Specificity is the proportion of actual negatives correctly rejected. These measures answer different questions, so reviewing them alongside MCC reveals whether apparently solid aggregate performance hides a weak class-specific result. Always build the confusion matrix using a clearly defined positive class and a fixed classification threshold. Reversing the positive and negative labels changes precision, recall, and specificity, although MCC itself remains consistent under simultaneous relabeling. Counts should come from data not used to fit the model, preferably a representative test set or properly constructed cross-validation predictions. MCC is especially helpful when comparing candidate classifiers across the same evaluation sample, but uncertainty still matters. A small test set can produce an unstable score, and distribution shifts can invalidate historical performance. Use this result with confidence intervals, subgroup checks, calibration analysis, and the real-world consequences of false positives and false negatives before selecting or deploying a model.