ROC Curve Calculator

A Receiver Operating Characteristic (ROC) curve is a graphical representation of a binary classifier's performance across all discrimination thresholds. It plots the True Positive Rate (sensitivity) on the Y-axis against the False Positive Rate (1 − specificity) on the X-axis. A perfect classifier hugs the top-left corner, while a random classifier follows the diagonal line.

AUC stands for Area Under the ROC Curve. It ranges from 0 to 1: an AUC of 1.0 indicates a perfect classifier, 0.5 indicates no discriminative ability (equivalent to random guessing), and values below 0.5 suggest the model is performing worse than chance. Generally, AUC ≥ 0.8 is considered good and AUC ≥ 0.9 is considered excellent.

ROC curves are used whenever you need to evaluate the performance of a binary classification model — for example, in medical diagnostics (disease vs. no disease), fraud detection, or spam filtering. They are especially useful when the class distribution is imbalanced, because they are independent of the class prevalence.

Using the geometric method by Zhang and Mueller (2005), the AUC can be bounded from a single operating point. The lower bound is the area of the quadrilateral formed between (0,0), the point (FPR, TPR), (1,1), and (1,0), equal to (sensitivity + specificity) / 2. The upper bound depends on which region the point falls in relative to the diagonal. The midpoint estimate averages these bounds.

The optimal threshold depends on the relative costs of false positives and false negatives. In cost-sensitive applications (e.g., medical diagnosis where missing a disease is far more costly than a false alarm), the threshold should be shifted to favor sensitivity. The cost-weighted slope at your operating point in this calculator helps quantify that trade-off.

Sensitivity (True Positive Rate) measures the proportion of actual positives correctly identified by the model. Specificity (True Negative Rate) measures the proportion of actual negatives correctly identified. Together, they characterize the operating point on the ROC curve. High sensitivity is critical when missing a positive is costly; high specificity matters when false alarms carry high cost.

Enter your sensitivity value (between 0 and 1) and specificity value (between 0 and 1) representing a single operating point of your classifier. You can also adjust the confidence level and the relative costs of false positives and false negatives. The calculator will compute the AUC bounds and display the ROC curve chart and coordinate table automatically.

The AUC confidence interval gives a range within which the true AUC likely falls, given the uncertainty from a single operating point. A 95% confidence interval means that if you repeated your measurement many times, 95% of the resulting intervals would contain the true AUC. Wider intervals indicate more uncertainty; more data points reduce this uncertainty.