How to Calculate Accuracy From an ROC Curve

Find a point on the ROC curve that you wish to determine the accuracy of. The horizontal axis of the ROC curve shows the rate of true-positives in the detection system, and the vertical axis shows the rate of false-positives.

Familiarize yourself with the accuracy equation for ROC curves. This equation is the ratio of true-positives plus true-negatives to actual positives plus actual negatives. The equation looks like this, where TP is true-positive, TN is true-negative, P is actual positive, and N is actual negative. P + N is also equal to the total number of measurements taken by the system. If you don't have the exact values for P or N, you can fall back on total number of measurements and use it in place of (P + N).

ACC = (TP + TN) / (P + N)

Add the number of true-positives to the number of true-negatives. For example, suppose the number of true-positives is 46 and true-negatives is 23. Adding these two together yields a value of 69.

Add the number of actual positives to the number of actual negatives. For example, suppose there were actually 50 positives and 30 negatives. Adding these together results in a value of 80.

Divide the sum of true-positives and true-negatives by the sum of actual positives and negatives. Continuing with the examples above, you would divide 69 by 80, resulting in an accuracy of 0.8625.

Analyze the accuracy value. The closer the accuracy is to 1.00, the more accurate the system is at predicting true-positives and true-negatives.