What is a confusion matrix?

A confusion matrix is a table used to evaluate the performance of a classification model. It compares the actual class labels against the predicted labels and organises the results into four cells: true positives (TP) where the model correctly predicted the positive class, true negatives (TN) where it correctly predicted the negative class, false positives (FP) where it incorrectly predicted positive when the actual class was negative, and false negatives (FN) where it incorrectly predicted negative when the actual class was positive. These four values are used to derive all standard classification performance metrics.

What is the difference between precision and recall?

Precision measures how often the model is right when it predicts positive: TP / (TP + FP). A high precision means few false alarms. Recall (also called sensitivity) measures how many actual positives the model correctly identified: TP / (TP + FN). A high recall means few positive cases are missed. There is often a trade-off between the two: tuning a model to be more conservative reduces false positives (raises precision) but may miss more true positives (lowers recall). The F1 score is the harmonic mean of both and balances them into a single metric.

When should I use the F1 score versus accuracy?

Accuracy is the proportion of all predictions that are correct: (TP + TN) / (TP + FP + FN + TN). It is most useful when the classes in your dataset are roughly balanced. When classes are imbalanced (for example, a fraud detection model where 99% of transactions are legitimate), a model that always predicts the majority class can achieve very high accuracy while being useless. In imbalanced scenarios, the F1 score or Matthews correlation coefficient (MCC) are better indicators because they account for both false positives and false negatives relative to the class distribution.

Confusion Matrix Calculator

Enter your confusion matrix values - true positives, false positives, false negatives and true negatives - to instantly calculate accuracy, precision, recall, specificity, F1 score, MCC and a plain-language performance verdict.

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Standard formulas Based on standard binary classification evaluation metrics used in statistics and machine learning.

1. Enter Confusion Matrix Values

True Positives (TP) correct positive predictions

False Positives (FP) predicted positive, actually negative

False Negatives (FN) predicted negative, actually positive

True Negatives (TN) correct negative predictions

Please enter valid non-negative numbers (total must be greater than zero).

2. Matrix Visualisation

Predicted → / Actual ↓

Predicted Positive

Predicted Negative

Actual Positive

Actual Negative

Total observations: 100

Classification Performance Metrics

Accuracy
-
(TP + TN) / Total

Precision

TP / (TP + FP)

Recall (Sensitivity)

TP / (TP + FN)

Specificity

TN / (TN + FP)

F1 Score

Harmonic mean of P & R

MCC

Matthews Correlation Coeff.

Full Metric Breakdown

True Positives (TP)50

False Positives (FP)10

False Negatives (FN)5

True Negatives (TN)35

Total observations100

Predicted positives60

Predicted negatives40

Actual positives55

Actual negatives45

Derived Metrics

Accuracy85.00%

Precision (PPV)83.33%

Recall / Sensitivity (TPR)90.91%

Specificity (TNR)77.78%

F1 Score86.96%

MCC0.698

False Positive Rate (FPR)22.22%

False Negative Rate (FNR)9.09%

Negative Predictive Value (NPV)87.50%

Summary: Enter your values above to see a performance summary.

Understanding Confusion Matrix Metrics

A confusion matrix is the starting point for evaluating any binary classification model. It records four counts that describe how well a model separates the positive class from the negative class, and from those four numbers every standard classification metric can be derived.

The Four Core Counts

Term	Symbol	Meaning
True Positives	TP	The model predicted positive and the actual label is positive. Correct positive predictions.
False Positives	FP	The model predicted positive but the actual label is negative. Also called Type I errors or false alarms.
False Negatives	FN	The model predicted negative but the actual label is positive. Also called Type II errors or misses.
True Negatives	TN	The model predicted negative and the actual label is negative. Correct negative predictions.

Formulas Used in This Calculator

Metric	Formula	Interpretation
Accuracy	(TP + TN) / (TP + FP + FN + TN)	Proportion of all predictions that are correct.
Precision (PPV)	TP / (TP + FP)	Of all predicted positives, what fraction are actually positive.
Recall / Sensitivity (TPR)	TP / (TP + FN)	Of all actual positives, what fraction did the model detect.
Specificity (TNR)	TN / (TN + FP)	Of all actual negatives, what fraction did the model correctly reject.
F1 Score	2 * (Precision * Recall) / (Precision + Recall)	Harmonic mean of precision and recall. Balances both metrics into one.
MCC	(TPTN - FPFN) / sqrt((TP+FP)(TP+FN)(TN+FP)(TN+FN))	A balanced measure even for imbalanced classes. Ranges from -1 to +1.
False Positive Rate (FPR)	FP / (FP + TN)	Proportion of actual negatives that are incorrectly classified as positive.
False Negative Rate (FNR)	FN / (FN + TP)	Proportion of actual positives that are incorrectly classified as negative.
Negative Predictive Value (NPV)	TN / (TN + FN)	Of all predicted negatives, what fraction are actually negative.

Worked Example

Using the calculator defaults: TP = 50, FP = 10, FN = 5, TN = 35 (total = 100 observations).

Accuracy: (50 + 35) / 100 = 85.00%
Precision: 50 / (50 + 10) = 50 / 60 = 83.33%
Recall: 50 / (50 + 5) = 50 / 55 = 90.91%
Specificity: 35 / (35 + 10) = 35 / 45 = 77.78%
F1 Score: 2 * (0.8333 * 0.9091) / (0.8333 + 0.9091) = 86.96%
MCC: (50*35 - 10*5) / sqrt(60 * 55 * 45 * 40) = 1700 / sqrt(5,940,000) = 0.698

Choosing the Right Metric

Accuracy is intuitive but misleading when classes are imbalanced. For example, if 95% of samples are negative, a model that always predicts negative achieves 95% accuracy while being entirely useless for detecting positives.

Precision is critical when false positives are costly (for example, a spam filter that mistakenly blocks legitimate emails). Recall matters more when false negatives are costly (for example, a cancer screening test that misses actual cases). The F1 score balances the two. The MCC is widely considered the most reliable single-value summary for binary classification because it takes all four quadrants of the confusion matrix into account symmetrically.

Related Calculators

Sources and method: Formulas sourced from Fawcett T. (2006), "An introduction to ROC analysis", Pattern Recognition Letters 27(8):861-874; Powers D.M.W. (2011), "Evaluation: From Precision, Recall and F-Measure to ROC, Informedness, Markedness and Correlation", Journal of Machine Learning Technologies 2(1):37-63. MCC formula as defined by Matthews B.W. (1975), Biochimica et Biophysica Acta 405(2):442-451.

This calculator applies standard binary classification evaluation formulas to the values you enter. Results are valid for two-class (binary) problems only. For multi-class classification, an extended confusion matrix and macro/micro-averaged metrics are required.