Matthews Correlation Coefficient (MCC), F1-Score, Cohen’s Kappa & Youden’s J Calculator

Evaluate imbalanced binary classifiers via MCC, F1, Precision, Recall, Specificity, and Youden’s J.

Matthews Correlation Coefficient (MCC)
0.841 MCC (−1 to +1)
F1-Score (Harmonic Precision-Recall) 0.872 F1
Balanced Accuracy ((Sens + Spec)/2) 92.885 %
Youden’s J Statistic (Sens + Spec − 1) 0.858 J
Inputs
⚡ Scenarios:
TP
True Positives (TP).
FP
False Positives (FP / Type I Error).
FN
False Negatives (FN / Type II Error).
TN
True Negatives (TN).
Results & Graph
Matthews Correlation Coefficient (MCC)
0.841 MCC (−1 to +1)
F1-Score (Harmonic Precision-Recall)
0.872 F1
Balanced Accuracy ((Sens + Spec)/2)
92.885 %
Youden’s J Statistic (Sens + Spec − 1)
0.858 J

Matthews Correlation Coefficient (MCC)

Graph 1 • MCC, F1 & Confusion Matrix • Domain Architecture & Live Telemetry Maps True Positives Tp, False Positives Fp, False Negatives Fn through MCC, F1 & Confusion Matrix Formula.
Matthews Correlation Coefficie: 0.841 MCC (−1 to + MCC, F1 & Confusion Matrix • Invariants & Metrics Matthews Correlation Coeffic 0.841 MCC (−1 to +1) F1-Score (Harmonic Precision 0.872 F1 Balanced Accuracy ((Sens + S 92.885 % Youden’s J Statistic (Sens + 0.858 J
Graph 2 • Matthews Correlation Coefficient (MCC) Across True Positives Tp Sweep (40% → 160%) Evaluates MCC = (TP·TN − FP·FN) / √((TP+FP)(TP+FN)(TN+FP)(TN+FN)); F1 = 2·TP / ( across 7 operating points (current input highlighted).
0 MCC (− 0.550 MCC (− 1.10 MCC (− 0.702 34TP 0.773 51TP 0.814 68TP 0.841 85TP 0.860 102TP 0.874 119TP 0.885 136TP
Graph 3 • Joint Sensitivity: True Positives Tp × False Positives Fp Compares Matthews Correlation Coefficient (MCC) when False Positives Fp is shifted +25% (solid) vs. −25% (dashed).
0 MCC (− 0.550 MCC (− 1.10 MCC (− --- False Positives Fp @ 75% 0.772 -30% 0.800 -15% 0.821 +0% 0.837 +15% 0.850 +30%
Summary: MCC is 0.8412, F1-Score is 0.8718 (87.18%), Balanced Accuracy is 92.88%, and Youden’s J Index is 0.8577.
Summary: MCC is 0.8412, F1-Score is 0.8718 (87.18%), Balanced Accuracy is 92.88%, and Youden’s J Index is 0.8577.
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Formula & Mathematical Methodology: MCC, F1 & Confusion Matrix Formula

MCC = (TP·TN − FP·FN) / (TP+FP(TP+FN)(TN+FP)(TN+FN))
F1 = 2·TP / (2·TP + FP + FN)
MCC = (TP·TN − FP·FN) / √((TP+FP)(TP+FN)(TN+FP)(TN+FN)); F1 = 2·TP / (2·TP + FP + FN)
  • truePositivesTp: True Positives Tp (TP)
  • falsePositivesFp: False Positives Fp (FP)
  • falseNegativesFn: False Negatives Fn (FN)
  • trueNegativesTn: True Negatives Tn (TN)

Rounding: Internal floating-point calculations run in 64-bit IEEE-754 double precision; display values round to 2–4 decimal places.

Worked Example: Worked Mathematical Example: MCC, F1 & Confusion Matrix

Evaluate imbalanced binary classifiers via MCC, F1, Precision, Recall, Specificity, and Youden’s J.

  1. Specify the function parameters, matrix entries, or confusion matrix counts.
  2. Apply the closed-form or iterative formula: MCC = (TP·TN − FP·FN) / √((TP+FP)(TP+FN)(TN+FP)(TN+FN)); F1 = 2·TP / (2·TP + FP + FN).
  3. Examine the primary result, error bounds, and 3 interactive SVG plots.
Result: Computes MCC, F1 & Confusion Matrix via MCC = (TP·TN − FP·FN) / √((TP+FP)(TP+FN)(TN+FP)(TN+FN)); F1 = 2·TP / (2·TP + FP + FN).

Frequently Asked Questions

How does the Matthews Correlation Coefficient (MCC), F1-Score, Cohen’s Kappa & Youden’s J Calculator compute the solution?

It evaluates MCC = (TP·TN − FP·FN) / √((TP+FP)(TP+FN)(TN+FP)(TN+FN)); F1 = 2·TP / (2·TP + FP + FN) directly in your browser and updates three custom SVG visualizations in real time.

Can I solve backwards for an input parameter using Goal Seek?

Yes. Click "🎯 Goal Seek" in the results toolbar to solve backwards for any numeric input field.

Does this calculator run locally offline?

Yes. All calculations run 100% locally in your browser and work offline via the CalculatorGraph PWA.

Mathematics & Statistics · Machine Learning & Classification Metrics

Matthews Correlation Coefficient (MCC), F1-Score, Cohen’s Kappa & Youden’s J Calculator: inputs, method, and how to read the result

Evaluate imbalanced binary classifiers via MCC, F1, Precision, Recall, Specificity, and Youden’s J.

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • True Positives Tp: True Positives (TP).
  • False Positives Fp: False Positives (FP / Type I Error).
  • False Negatives Fn: False Negatives (FN / Type II Error).
  • True Negatives Tn: True Negatives (TN).

What the calculation includes

With the default values shown, Matthews Correlation Coefficient (MCC) is 0.841 MCC (−1 to +1). The calculation follows MCC, F1 & Confusion Matrix Formula; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing True Positives Tp from 85 TP to 94 TP changes Matthews Correlation Coefficient (MCC) from 0.841 MCC (−1 to +1) to 0.852 MCC (−1 to +1). This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses exact analytical or standard numerical analysis formulations from NIST DLMF.
  • Double-precision floating-point arithmetic has ~15–17 significant decimal digits of precision.

Scope: Global Mathematical & Statistical Standard Check the assumptions and limitations against your situation before relying on the estimate.

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