Matthews Correlation Coefficient (MCC) Calculator
Calculate the Matthews Correlation Coefficient, a balanced measure of binary classification quality even on imbalanced data.
Inputs
Matthews Correlation Coefficient
0.8262
Numerator
67,800
Denominator
82,059.7343
Step by step
Numerator: (TP × TN) − (FP × FN)
(80 × 850) − (20 × 10)
= 67800
Denominator: √[(TP+FP)(TP+FN)(TN+FP)(TN+FN)]
√[(80+20)(80+10)(850+20)(850+10)]
= 82059.7343
MCC: numerator / denominator
67800 ÷ 82059.7343
= 0.8262
How it works
The Matthews Correlation Coefficient (MCC) is a single-number summary of binary classification quality that uses all four confusion matrix values: MCC = (TP×TN − FP×FN) / √[(TP+FP)(TP+FN)(TN+FP)(TN+FN)]. It ranges from -1 (total disagreement) through 0 (no better than random) to +1 (perfect prediction). Unlike accuracy or F1, MCC accounts for true negatives directly and remains informative even on severely imbalanced datasets, which is why it's often recommended as the preferred single-metric summary for binary classifiers.
Formula
MCC = (TP * TN - FP * FN) / sqrt((TP + FP)(TP + FN)(TN + FP)(TN + FN))
- TP
- True positives
- TN
- True negatives
- FP
- False positives
- FN
- False negatives
Frequently Asked Questions
Why is MCC considered better than accuracy for imbalanced data?
MCC incorporates all four confusion matrix cells (TP, TN, FP, FN) in a balanced way, so a model that only performs well on the majority class will not score highly, unlike accuracy which can be dominated by the majority class.
What does an MCC of 0 mean?
An MCC of 0 indicates the classifier's predictions are no better than random guessing given the class distribution — it carries no useful correlation between predictions and actual labels.
Can MCC be undefined?
Yes — if the denominator is zero (which happens when the model predicts only one class, or the confusion matrix has an entire row or column of zeros), MCC is undefined; this calculator returns 0 in that case as a safe fallback.