What is the ROC curve?

The ROC (Receiver Operating Characteristic) curve plots the True Positive Rate (TPR, sensitivity) on the Y-axis against the False Positive Rate (FPR, 1-specificity) on the X-axis at every possible decision threshold. A curve that hugs the top-left corner indicates a strong classifier; the diagonal line represents random guessing.

AUC (Area Under the ROC Curve) is a single scalar that summarizes classifier performance across all thresholds. It equals the probability that the model will rank a randomly chosen positive example higher than a randomly chosen negative one. AUC = 1.0 is perfect; AUC = 0.5 is equivalent to random guessing; AUC < 0.5 means the model is predicting inversely.

Why does this tool compute a three-point ROC curve?

A single confusion matrix captures performance at one specific threshold, giving one (FPR, TPR) operating point. The full ROC curve requires scores for every sample. This tool approximates the curve using the three canonical points — (0,0), your operating point, and (1,1) — which is sufficient for estimating AUC from a reported confusion matrix.

How is AUC calculated here?

The tool applies the trapezoidal rule to the three-point ROC curve. The area under the piecewise-linear path from (0,0) → (FPR, TPR) → (1,1) equals: (FPR × TPR / 2) + ((1 - FPR) × (TPR + 1) / 2).

What is a good AUC score?

As a rough guide: AUC 0.90–1.00 is outstanding, 0.80–0.90 is excellent, 0.70–0.80 is acceptable, 0.60–0.70 is poor, and 0.50–0.60 is considered a failure. Context matters — a fraud detector with AUC 0.85 may be excellent, while a medical diagnostic tool may need AUC > 0.95.

Can AUC mislead on imbalanced datasets?

Yes. When negatives vastly outnumber positives, even a mediocre classifier can show a high AUC. In those cases, the Precision-Recall curve (and the area under it, AUPRC) is often a more informative complement to AUC.

ROC AUC Explainer

Name: ROC AUC Explainer
Availability: InStock
Author: Nham Vu

Enter TP, FP, TN, and FN to instantly plot the ROC curve, compute the AUC score, and understand model discrimination power.

Confusion Matrix Inputs

Enter the four counts from your classifier at one threshold.

TP — True Positive

Actual +, predicted +

FP — False Positive

Actual −, predicted +

FN — False Negative

Actual +, predicted −

TN — True Negative

Actual −, predicted −

Quick Examples

Enter confusion matrix values and click Plot ROC Curve.

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Summary

Enter TP, FP, TN, and FN to instantly plot the ROC curve, compute the AUC score, and understand model discrimination power.

How it works

Enter the four confusion matrix counts: TP (true positives), FP (false positives), FN (false negatives), and TN (true negatives).
The tool derives the true positive rate (TPR = recall) and false positive rate (FPR) from your inputs.
A three-point ROC curve is plotted — origin (0,0), your operating point (FPR, TPR), and (1,1) — representing the full threshold sweep.
The AUC is estimated using the trapezoidal rule over those three points.
Metric cards show TPR, FPR, AUC, and a plain-English interpretation of your model's discrimination ability.

Use cases

Quickly estimate AUC from a single reported confusion matrix without writing code.
Visualize where a binary classifier sits on the ROC space.
Compare multiple model checkpoints at a glance by changing the TP/FP/FN/TN counts.
Understand the trade-off between sensitivity and false positive rate for medical tests.
Explain ROC curves and AUC to stakeholders using the interactive chart.
Verify AUC estimates from research papers or model evaluation reports.
Identify whether a classifier performs better or worse than random chance (AUC = 0.5).
Explore how changing a threshold (adjusting TP/FP/FN/TN) shifts the operating point.

Frequently Asked Questions

Last updated: 2026-06-10 · Reviewed by Nham Vu