Matthews Correlation Coefficient (MCC) Calculator

About the Matthews Correlation Coefficient (MCC) Calculator

The Matthews Correlation Coefficient (MCC) is a balanced way to score binary classifiers, especially when the classes are imbalanced and accuracy alone can be misleading.

This calculator takes a confusion matrix and reports MCC alongside the other metrics people commonly compare against it: accuracy, balanced accuracy, precision, recall, specificity, F1, Cohen's kappa, and related rates. That makes it easier to see why two models with similar accuracy can still have very different practical quality.

MCC ranges from −1 to +1, where +1 is perfect agreement, 0 is no useful discrimination, and −1 means the predictions are effectively inverted.

When This Page Helps

MCC is useful because it stays informative when the class balance is skewed and when a model can game accuracy by overpredicting the majority class. Comparing it directly against accuracy, F1, and balanced accuracy helps show whether the classifier is genuinely useful or only superficially impressive.

How to Use the Inputs

1. Enter TP (true positives), FP (false positives), FN (false negatives), and TN (true negatives).
2. Or select a preset scenario to explore different classifier behaviors.
3. Review the MCC value and its interpretation.
4. Check the visual confusion matrix to verify your inputs.
5. Compare MCC with accuracy, F1, and balanced accuracy.
6. Examine the complete metrics table for a 360° view of classifier performance.
7. Use the MCC interpretation guide to assess production-readiness.

Example Calculation

Tips & Best Practices

• Try "All Positive Pred" preset — accuracy looks reasonable but MCC reveals zero discrimination.
• Compare MCC with F1: they agree for balanced classes but diverge for imbalanced ones.
• MCC = √(Informedness × Markedness) gives a geometric interpretation.
• If MCC is negative, literally flipping all predictions improves the classifier.
• For medical screening (high FN cost), focus on recall alongside MCC.
• Use the "Imbalanced (95-5)" preset to understand why accuracy alone fails.

MCC vs. Accuracy: The Imbalanced Data Problem

Consider a disease affecting 1% of patients. A classifier that always predicts "healthy" achieves 99% accuracy — impressive-looking but useless. Its MCC is exactly 0, correctly indicating no discriminative ability. This example explains why MCC has become the recommended primary metric in machine learning competitions and medical AI.

Mathematical Properties of MCC

MCC is the Pearson correlation between actual and predicted binary labels (encoded 0/1). This means all properties of Pearson correlation apply: MCC = +1 implies perfect prediction, −1 implies perfect inverse prediction, and 0 implies independence. The formula (TP·TN − FP·FN)/√((TP+FP)(TP+FN)(TN+FP)(TN+FN)) is equivalent to Pearson r on binary variables.

When Other Metrics Complement MCC

MCC gives one number but hides the precision-recall tradeoff. If FP and FN have very different costs — false positive in cancer screening vs. false negative — you need precision and recall separately. ROC-AUC shows performance across all thresholds. Use MCC as the primary evaluation metric, then drill into precision, recall, and domain-specific costs for deployment decisions.

Frequently Asked Questions

• Why is MCC better than accuracy for imbalanced data?

  If 95% of samples are negative, predicting "always negative" gives 95% accuracy but MCC = 0 (no useful discrimination). MCC requires good performance on both classes, making it impossible to game with trivial strategies.

• What's the relationship between MCC and other metrics?

  MCC = √(Informedness × Markedness) when both are positive. It's also the geometric mean of the regression coefficients of the problem and its dual. MCC incorporates all four confusion matrix cells equally.

• Can MCC be used for multi-class classification?

  Yes. MCC generalizes to multi-class problems using the full confusion matrix rather than only the four binary cells. The formula is more involved, but the same idea holds: it measures agreement between predicted and true labels while accounting for class imbalance.

• When is MCC = 0 exactly?

  MCC = 0 when TP·TN = FP·FN. This occurs for random guessing, "always positive" (TN=FN=0), or "always negative" (TP=FP=0) strategies. Any strategy that ignores the true labels gives MCC = 0.

• How does MCC compare to Cohen's kappa?

  Both measure binary agreement beyond chance, but MCC is symmetric and treats both classes equally. Kappa can be biased by prevalence and marginal distributions. MCC is generally preferred in machine learning; kappa in inter-rater reliability studies.

• What MCC threshold indicates a useful classifier?

  No universal threshold exists, but MCC > 0.3 suggests the classifier adds value beyond random, MCC > 0.5 indicates moderate utility, and MCC > 0.7 is considered strong. The required threshold depends on the cost of false positives vs. false negatives in your domain.