Machine Learning Confusion Matrix & Classification Metrics Calculator

Statistical & Machine Learning Evaluation: The 2x2 Confusion Matrix

A confusion matrix tabulates the performance of a supervised binary classification algorithm against known ground-truth labels:

• The Four Fundamental Quadrants:

• True Positives (TP): Actual positive events correctly predicted as positive.

• True Negatives (TN): Actual negative events correctly predicted as negative.

• False Positives (FP - Type I Error): Negative events incorrectly predicted as positive (false alarm).

• False Negatives (FN - Type II Error): Positive events incorrectly predicted as negative (missed detection).

• The Accuracy Paradox: In imbalanced datasets (e.g. 99% non-fraud, 1% fraud), a trivial model predicting 'no fraud' always achieves 99% accuracy while having 0% sensitivity. F1-Score, Balanced Accuracy, and MCC must be used instead of accuracy on skewed classes.

• Precision vs. Recall Trade-Off: High Precision is crucial when False Positives are expensive (spam filters), while high Recall is paramount when False Negatives are dangerous (cancer screening, disease detection).

• Matthews Correlation Coefficient (MCC): Widely considered by statisticians as the single most informative metric because it produces high scores only if the model performs well across all four quadrants.

How to Use This Calculator

Enter your True Positives (TP) (e.g. 85 (Correctly identified positive cases)), False Positives (FP - Type I Error) (e.g. 15 (Negative cases incorrectly called positive)), False Negatives (FN - Type II Error) (e.g. 10 (Positive cases missed / called negative)), and True Negatives (TN) (e.g. 190 (Correctly identified negative cases)). Results update instantly as you type — adjust any value to compare scenarios.

The Formula

Machine Learning Confusion Matrix Classification equations:

Accuracy = (TP + TN) / (TP + TN + FP + FN)

Sensitivity (Recall, TPR) = (TP) / (TP + FN), Specificity (TNR) = (TN) / (TN + FP)

Precision (PPV) = (TP) / (TP + FP), Negative Predictive Value (NPV) = (TN) / (TN + FN)

F1-Score = 2 × (Precision × Recall) / (Precision + Recall) = (2TP) / (2TP + FP + FN)

Matthews Correlation Coefficient (MCC) = ((TP × TN) - (FP × FN)) / (√((TP + FP)(TP + FN)(TN + FP)(TN + FN)))

Balanced Accuracy = (Sensitivity + Specificity) / (2), Youden's J = Sensitivity + Specificity - 1

Worked Example

For example, evaluating a medical diagnostic test or ML binary classifier with and : Overall Accuracy is . Sensitivity (Recall) is . Specificity is . Precision (PPV) is . The F1-Score is and MCC is 0.

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Understanding Your Result

Evaluate your result in the context of your specific use case and relevant industry standards or reference values. A single calculated result is a starting point — test two to three scenarios to understand how sensitive the outcome is to your key input assumptions. For high-stakes decisions, verify your result against a secondary source or subject-matter expert before acting.