Matthews Correlation Coefficient (MCC) Calculator

The Matthews Correlation Coefficient (MCC), also called the phi coefficient, measures the correlation between a binary classifier's predictions and the ground truth. It was introduced by B. W. Matthews in 1975 and is the metric scikit-learn exposes as matthews_corrcoef. This tool uses the same definition and returns the same numbers.

Everything starts from the four cells of a 2×2 confusion matrix: true positives (TP), true negatives (TN), false positives (FP) and false negatives (FN). The coefficient is computed in three steps:

1. Numerator: N = (TP·TN) − (FP·FN). This is positive when the correct predictions on the diagonal outweigh the errors.
2. Denominator: D = √((TP+FP)(TP+FN)(TN+FP)(TN+FN))— the square root of the product of the four row and column totals (the confusion-matrix marginals).
3. MCC = N / D, always in the range −1 to +1.

There is one important edge rule, and this tool follows the scikit-learn convention exactly: if any of the four marginals (TP+FP), (TP+FN), (TN+FP) or (TN+FN) is zero, the denominator is zero and MCC is defined as 0. A classifier that always predicts one class has no correlation with the truth, no matter how high its accuracy looks.

MCC reads −1 as total disagreement, 0 as no better than random, and +1 as perfect prediction. Because all four cells appear in the formula and the metric is symmetric under swapping the classes, it is hard to fool on skewed datasets — the property Chicco & Jurman (2020) highlight when they recommend MCC over accuracy and F1 for binary evaluation. For context the tool also derives the metrics that only use part of the matrix — accuracy (TP+TN)/n, precision TP/(TP+FP), recall TP/(TP+FN), specificity TN/(TN+FP) and F1 — so you can see exactly why MCC and accuracy can tell different stories. As a self-check it recomputes MCC through the equivalent class-proportion correlation form and shows both values.

• scikit-learn — sklearn.metrics.matthews_corrcoef (formula, range, zero-marginal convention)
• Matthews, B. W. (1975) — Comparison of the predicted and observed secondary structure of T4 phage lysozyme (original definition)
• Chicco & Jurman (2020) — The advantages of the MCC over F1 score and accuracy in binary classification evaluation, BMC Genomics 21:6

The formula and worked examples were last cross-checked against the scikit-learn matthews_corrcoef definition on 2026-07-12. All three worked examples above are reproduced exactly by the calculator.