Confusion Matrix Calculator — Accuracy, Precision, Recall, F1 & MCC

A binary confusion matrix has four cells. True Positives (TP) and True Negatives (TN) are correct predictions; False Positives (FP) are Type I errors (a negative flagged as positive) and False Negatives (FN)are Type II errors (a positive that slipped through). Their sum is the sample size N. Every metric below is a closed-form function of these four integers, using the definitions in the scikit-learn model-evaluation documentation and the Wikipedia confusion-matrix table.

• Accuracy = (TP + TN) / N
• Precision (PPV) = TP / (TP + FP)
• Recall / Sensitivity (TPR) = TP / (TP + FN)
• Specificity (TNR) = TN / (TN + FP)
• F1 = 2·TP / (2·TP + FP + FN)
• Fβ = (1 + β²)·TP / ((1 + β²)·TP + β²·FN + FP)
• Balanced accuracy = (Recall + Specificity) / 2
• MCC = (TP·TN − FP·FN) / √((TP+FP)(TP+FN)(TN+FP)(TN+FN))
• κ = (pₒ − pₑ) / (1 − pₑ), pₒ = Accuracy

The three summary scores earn their place by resisting the accuracy paradox. On a dataset that is 98% negative, a model that predicts "negative" for everything scores 0.98 accuracy while catching no positives at all. F1 collapses because recall is zero; balanced accuracy drops to 0.50 because it averages the two class-wise rates; MCC and Cohen's kappa fall near zero because both correct for the majority-class baseline — kappa by subtracting the chance agreement pₑ computed from the row and column totals, MCC by using all four cells as a correlation. When accuracy looks high but MCC is low, this tool shows a note so you weigh the right metric.

Two safeguards keep the numbers trustworthy. First, any metric whose denominator is zero is reported as undefinedrather than a silent 0 or NaN — precision needs TP + FP > 0, MCC needs every matrix margin non-zero. Second, F1 is computed two independent ways — from the raw counts and as the precision×recall harmonic mean — and the two are reconciled, which is what the "Matches scikit-learn" badge attests. Nothing you type is uploaded; the whole calculation happens in your browser.

• scikit-learn — Metrics and scoring: quantifying the quality of predictions
• Wikipedia — Confusion matrix (derived-rate table)
• Chicco & Jurman (2020) — Advantages of MCC over F1 and accuracy, BMC Genomics 21:6
• Cohen (1960) — A coefficient of agreement for nominal scales

These are mathematical definitions, not rates that change over time. The formulas on this page were last cross-checked against the scikit-learn documentation on 2026-07-08.