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AUC Calculator

Paste scores and labels and get the area under the ROC curve.

Try:
Format: score,label with label 1 (positive) or 0 (negative). A header line is fine.
Curve shown

Scores at or above the threshold are predicted positive.

Area under the ROC curve (AUC)

0.75

An AUC of 0.75 means a randomly chosen positive gets a higher score than a randomly chosen negative 75% of the time (ties count half): fair separation.

Average precision
0.8333
base rate 0.5
Positives
2
Negatives
2
Best threshold
0.8
Youden J 0.5

ROC curve

Confusion matrix at threshold 0.45

Actual \ PredictedPositiveNegative
Positive11
Negative02
Accuracy
0.75
Precision
1
Recall (TPR)
0.5
False positive rate
0
F1
0.6667
MCC
0.5774

How the numbers are computed

AUC, trapezoid rule

AUC=∑i(FPRi−FPRi−1)(TPRi+TPRi−1)2\mathrm{AUC} = \sum_i \frac{(\mathrm{FPR}_i-\mathrm{FPR}_{i-1})(\mathrm{TPR}_i+\mathrm{TPR}_{i-1})}{2}AUC=∑i​2(FPRi​−FPRi−1​)(TPRi​+TPRi−1​)​

Average precision

AP=∑n(Rn−Rn−1) Pn\mathrm{AP} = \sum_n (R_n - R_{n-1})\,P_nAP=∑n​(Rn​−Rn−1​)Pn​

Scores are sorted from high to low. Each distinct score is a threshold; tied scores move together, so a tie between a positive and a negative cuts a diagonal step and counts half.

Curve points

ThresholdFPRTPR (recall)Precision
0.800.51
0.40.50.50.5
0.350.510.6667
0.1110.5
  1. Tools
  2. Machine Learning
  3. ROC Curve and AUC Calculator
  4. AUC Calculator

About AUC Calculator

This AUC calculator returns the area under the ROC curve of your scores using the trapezoid rule, and explains the value in plain English. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.

The page opens on the classic four-point example: scores 0.1, 0.4, 0.35 and 0.8 with labels 0, 0, 1, 1. Of the four positive-negative pairs, the positive scored 0.35 beats the negative 0.1 but loses to the negative 0.4, so three of four pairs are ranked correctly and the AUC is 0.75.

That pair-counting view is the easiest way to understand AUC: it is the chance that a random positive outranks a random negative, with ties counted as half.

How to use AUC Calculator

  1. 1Paste your data as score,label lines. A label is 1 for the positive class and 0 for the negative class; true and false also work.
  2. 2Or tap an example to load a good model, a weak model, an imbalanced set or the classic four-point example.
  3. 3Read the AUC and average precision in the result card.
  4. 4Switch between the ROC curve and the precision-recall curve.
  5. 5Move the threshold slider, or press the best-threshold button, to see the confusion matrix and metrics at that cut-off.
  6. 6Open the curve points table to see every threshold, false positive rate, true positive rate and precision.

Features

  • ROC curve with the chance diagonal, shaded area and a marker for your chosen threshold.
  • AUC by the trapezoid rule, with ties between a positive and a negative counted as half.
  • Precision-recall curve with the no-skill baseline, and average precision.
  • A threshold slider with the live confusion matrix, accuracy, precision, recall, false positive rate, F1 and MCC.
  • The best threshold by Youden's J statistic in one tap.
  • Up to 20,000 rows, with a table of the curve points.
  • A plain-English reading of what the AUC means for your model.

Worked examples

  • scores 0.1, 0.4, 0.35, 0.8 and labels 0, 0, 1, 1 → gives AUC 0.75

    Average precision for the same data is 0.8333.

Privacy: how it works

  • Your scores and labels are processed by code running in your browser tab. They are never sent to Ulkaa or anyone else.

Tips

  • Scores need not be probabilities. Any number where higher means more likely positive works, because only the ranking matters.
  • The AUC depends only on the order of the scores. Multiplying all scores by a constant changes nothing.
  • Tied scores are handled as one step. A tie between a positive and a negative cuts a diagonal and counts half.
  • Both classes must appear in the data, or the rates are undefined and the tool asks for more.

Frequently asked questions

Is it really free?

Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.

Do I need an account?

No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.

Does it run in my browser?

Yes. Your scores and labels are processed by code running in your browser tab, on your own device.

Is my data uploaded?

No. Your scores and labels are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.

What is a good AUC?

Above 0.9 is excellent, 0.8 to 0.9 good, 0.7 to 0.8 fair and near 0.5 is no better than chance. Compare with a simple baseline on your data.

Does AUC depend on the threshold?

No. It summarises performance over all thresholds, which is why it is useful for comparing models before you pick a cut-off.

More ROC Curve and AUC Calculator pages

  • ROC Curve and AUC CalculatorPaste model scores and true labels to draw the ROC curve, find the AUC and explore thresholds.
  • ROC Curve CalculatorPaste scores and labels to plot the ROC curve and move along it with a threshold slider.
  • Precision-Recall Curve CalculatorSee precision against recall for every threshold, and compare it with the no-skill line.
  • Average Precision CalculatorGet the average precision of a ranked list of predictions.
  • Optimal Classification Threshold FinderFind the cut-off that best balances true positives and false positives.
  • ROC AUC for Imbalanced DataCheck what a ROC AUC means when only a few cases are positive.

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