Matthews Correlation Coefficient Calculator - MCC from a Confusion Matrix

The Matthews correlation coefficient calculator converts the four cell counts of a binary confusion matrix into a single, comparable correlation score plus the usual classification metrics. You enter true positives, false negatives, false positives, and true negatives, and the tool returns the MCC score, also known as the phi coefficient, alongside accuracy, precision, recall, specificity, and F1. In machine learning and statistics courses this number is the go-to summary when you need one value that reflects both classes honestly.

• • Grading a student classifier: Compare a logistic regression homework model against a target matrix without retyping the formula by hand.
• • Evaluating a rare-disease screen: Report MCC where false negatives are dangerous and the positive class is a small fraction of patients.
• • Comparing two model thresholds: Read off the four cells at each candidate cutoff and watch how MCC trades off against raw accuracy.
• • Writing a research methods section: Quote a single defensible summary statistic instead of cherry-picking the metric that flatters the model.

Most evaluation reports print a 2x2 matrix of TP, FN, FP, and TN, but the derived metrics live on different dashboards. A single page that takes the four counts and turns them into one correlation score makes reading a model quicker and keeps the comparison fair.

The top row covers actual positive cases (TP and missed FN), and the bottom row covers actual negative cases (FP and correct TN). MCC respects all four of these cells at once, so it does not reward a model that simply predicts the majority class.

If you need the full set of classification metrics, the Confusion Matrix Calculator builds accuracy, precision, recall, F1, specificity, and MCC from the same four counts.

The calculator reads the four cell counts, sums them into a total, and combines them with one formula. Denominators of zero are treated as undefined so the page never silently reports a metric that has no meaning for your matrix.

• TP: True positives: actual positives the model predicted positive.
• FN: False negatives: actual positives the model predicted negative.
• FP: False positives: actual negatives the model predicted positive.
• TN: True negatives: actual negatives the model predicted negative.
• N: Total samples: TP + FN + FP + TN.

The numerator is TP times TN minus FP times FN, the signed agreement between predictions and reality. The denominator is the square root of the product of the four marginal sums, which normalizes the score so it always lands between minus one and one.

For binary classification this is mathematically the same as Pearson's phi coefficient, the correlation between two binary variables. That equivalence is why MCC behaves like a correlation: it can be negative when predictions and labels disagree systematically.

According to Wikipedia: Matthews correlation coefficient, the MCC is a correlation between observed and predicted binary classifications ranging from -1 to +1.

After you have the MCC, the Statistics Calculator reports mean, median, variance, and standard deviation on the raw score list.

Four ideas explain why the Matthews correlation coefficient behaves the way it does. Read the names first, then return to them once you have a score to interpret.

Once these four ideas click, the rest of the classifier vocabulary - balanced accuracy, Cohen's kappa, F-beta - reads as a small rearrangement of the same four cells.

Because MCC is a correlation, it is symmetric: swapping which class you call positive flips the sign of the numerator but squares cancel in the denominator, so the magnitude is unchanged. That symmetry is handy when the 'positive' label is a matter of convention.

To test whether the association behind the MCC is significant, the Chi-Square Calculator turns the same 2x2 table into a chi-square statistic and p-value.

Four steps cover the typical workflow: pull the four counts from your report, type them in, read the MCC and companion metrics, then screen for undefined values.

1. 1 Locate the four counts: Open the classification report or library output that shows TP, FN, FP, and TN. If you only have rates, multiply them back by the sample size to recover the counts.
2. 2 Enter the four counts: Type each integer into the matching input. Decimals are truncated to whole numbers so the matrix always matches a real count.
3. 3 Read the result panel: Watch the MCC update alongside accuracy, precision, recall, specificity, and F1. The score is the headline number; the companions tell you which cells drove it.
4. 4 Check for undefined metrics: If MCC shows nothing, at least one marginal sum is zero, meaning a whole row or column of the matrix is empty. Inspect the denominator before quoting the score.
5. 5 Save and compare to a baseline: Copy the row of metrics into your notebook or pull request and run the same matrix from a baseline model. The side-by-side makes it easy to argue a new threshold actually moved the metric you care about.

Example: read TP = 50, FN = 10, FP = 5, TN = 100 from a confusion matrix image, type them in, and the panel reports MCC 0.8018, accuracy 0.9091, precision 0.9091, recall 0.8333, F1 0.8696 - the same numbers you would get by hand.

When comparing MCC from two models, the T-Test Calculator checks whether the difference is larger than chance.

These are the concrete benefits students, instructors, and machine learning practitioners get from one focused page.

• • One honest number for imbalanced data: MCC summarizes the full matrix, so a model that scores 99 percent accuracy on a rare-event dataset cannot hide behind that number.
• • Fewer formula mistakes: Typing the four cells once beats hand-computing a four-term square root in a spreadsheet, the most common source of sign and order errors.
• • Faster model reviews: A teammate pastes a confusion matrix in a pull request and you confirm the MCC within seconds instead of reconstructing it from partial metrics.
• • Comparable across datasets: Because MCC is always bounded from minus one to one, scores from unrelated projects can be ranked on the same axis.
• • Reinforces the matrix layout: Entering counts by hand forces you to remember which cell is TP and which is FN, the bug that most often corrupts student code.

The biggest payoff is the first time you build a model that looks 95 percent accurate on a rare-disease screen and then watch the MCC fall to 0.66, revealing that precision on the rare class is weak.

For instructors, linking the page in a course site lets students verify homework without handing them the answer key.

For summarizing the distribution of several MCC scores across folds, the Descriptive Statistics Calculator gives the full five-number summary.

Three factors move the MCC you see, and two caveats remind you when the single number should not be quoted alone.

• • This tool is built for binary classification. Multi-class problems must be collapsed into one-versus-rest counts before the four cells make sense.
• • Counts are entered as integers and truncated. If your pipeline reports fractional counts, normalize to the nearest whole number first, because the formula assumes discrete events.

If you need a single number to summarize a binary classifier on an imbalanced dataset, prefer the Matthews correlation coefficient over accuracy. It uses every cell, so it cannot be inflated by a dominant negative class.

The matrix is only as honest as the labels you started with. Noisy ground truth, common in medical imaging or user-tagged datasets, propagates straight into the score.

According to scikit-learn: Model evaluation, MCC is identical to phi and handles imbalanced data better than accuracy, precision, and F1.

If your counts came from a fixed trial count, the Binomial Distribution Calculator shows how unusual the observed false-negative total is under the null.