AUC Calculator
Enter curve points, choose a method, and convert units before calculating the area under the curve.
Formula Used
For the trapezoidal rule, each segment uses this formula:
For left step area, the calculator uses Σ [(xi+1 - xi) × yi]. For right step area, it uses Σ [(xi+1 - xi) × yi+1]. Baseline subtraction changes each y value before the segment area is calculated.
How to Use This Calculator
- Select whether you want to enter x,y pairs or y values with equal x spacing.
- Paste your curve data into the matching field.
- Choose trapezoidal, left step, or right step calculation.
- Enter scale factors if you need unit conversion before integration.
- Add a baseline only when a reference value must be removed.
- Press the calculate button and review the segment table.
Understanding AUC
AUC means area under the curve. It measures the accumulated value of a plotted line over a chosen x range. The idea is simple. Each segment adds a small area. The total area shows the overall exposure, response, quantity, or performance. Many fields use it. AUC appears in pharmacokinetics, machine learning, chemistry, finance, and signal review.
Why This Calculator Helps
Manual AUC work can be slow. It also becomes risky when points are unevenly spaced. This calculator accepts ordered or unordered points. It can sort them by x value. It can subtract a baseline. It can also apply unit scale factors. These options help you make a clean conversion from raw curve data to a useful numeric area.
Point Data and Spacing
You can enter x and y points directly. Each line should contain one pair. You may separate values with commas, spaces, tabs, or semicolons. You can also enter only y values. In that mode, the tool creates x values from a start value and equal spacing. This is helpful when samples are taken at fixed time intervals.
Trapezoid Method
The trapezoidal rule is the default method. It joins each pair of nearby points with a straight line. Then it finds the area of a trapezoid. The formula works well for many smooth curves. It is also transparent. You can view each segment and see how the final value was built.
Step Area Options
Some data should not be interpolated with a sloped line. A reading may stay constant until the next sample. For that reason, left step and right step methods are included. Left step uses the starting y value of a segment. Right step uses the ending y value. These choices are useful for dose, inventory, and digital signal data.
Baseline and Absolute Area
A baseline changes the meaning of the result. When you subtract a baseline, the calculator measures area above or below that reference. A negative segment can reduce the total. The absolute area option changes that behavior. It counts every segment as positive. This can help when the size of deviation matters more than direction.
Units and Conversion
AUC units combine the x unit and the y unit. For example, concentration over time may produce mg hour per liter. The calculator lets you scale x and y values before integration. That supports conversions such as minutes to hours or small concentration units to larger units. The final label reminds you what the area represents.
Interpreting the Result
A larger AUC usually means more total effect, exposure, or accumulated amount. A smaller value means less total area. For ROC work, x and y values normally run from zero to one. Then AUC often stays between zero and one. Always check that your x order, units, baseline, and method match your study plan before using the result. Document assumptions with every saved result too.
Frequently Asked Questions
What does AUC mean?
AUC means area under the curve. It shows the total accumulated value across an x range. The result combines the y quantity with the x quantity, so the final unit is usually y unit multiplied by x unit.
Which method should I choose?
Choose the trapezoidal rule for smooth continuous curves. Choose left step or right step when values stay constant between samples. Step methods are common for inventory, digital signals, and dose records.
Can this calculator handle ROC AUC?
Yes. Enter false positive rate as x and true positive rate as y. Keep both axes between zero and one. Use the trapezoidal method for most ROC calculations.
Why should points be sorted?
AUC needs a path from left to right. Sorting places x values in increasing order. This prevents negative widths caused by unordered points and makes the segment table easier to check.
What does baseline subtraction do?
Baseline subtraction removes a reference value from every y value before calculation. It measures area above or below that reference instead of area above zero.
What is absolute segment area?
Absolute segment area turns each segment area positive. Use it when total deviation matters. Leave it off when positive and negative portions should cancel each other.
How do scale factors work?
The x scale factor multiplies each x value. The y scale factor multiplies each y value. Use them to convert units before AUC is calculated, such as minutes to hours.
What if my x spacing is equal?
Select the equal spacing mode. Enter y values only, then set x start and x spacing. The calculator will build the x values automatically and calculate the final area.
Can AUC be negative?
Yes. Signed AUC can be negative when adjusted y values are below the baseline or below zero. Turn on absolute segment area if you want all segment sizes counted as positive.
What units does the result use?
The result uses y unit multiplied by x unit. For example, concentration over time may become mg hour per liter. Your entered labels are shown beside the result.
How many points do I need?
You need at least two valid points. More points usually improve accuracy because the curve shape is captured in smaller segments. Very uneven spacing should be reviewed carefully.