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## What is an “Area Under the Curve?”

The **area under a curve** is the area between the line of a graph (which is often curved) and the x-axis.

In calculus, you find the area under the curve using definite integrals.

Watch the video for an overview of definite integrals:

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## How to Find the Area Under Curve in Excel

Watch the video or read the steps below:

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Microsoft Excel doesn’t have functions to calculate definite integrals, but you can approximate this area by dividing the curve into smaller curves, each resembling a line segment. Use the following steps to calculate the area under a curve in Excel as the total area of the trapezoids under these line segments:

## How to Find the Area Under Curve in Microsoft Excel: Steps

Example question: Find the area under curve in Excel for the graph below, from x = 1 to x = 6.

Step 1: Choose a few data points on the** x-axis **under the curve (use a formula, if you have one) and list these values in Column A in sequence, starting from Row 1. In this example from the graph on the left, your x-values are 1, 2, 3, 4, 5 and 6. Ensure that the first and last data points chosen on the curve are its starting and ending points respectively.

Step 2: List the corresponding **y-axis** data points in Column B, aligning them row-wise with the values in Column A. For this example, I’m going to assume that you *don’t have the formula*. In other words, I’m guessing where the values lie based on the graph. I’ll use y = 1, 0.5, 0.33, 0.225, 0.2 and 0.19.

Step 3: Type the following** formula** into cell C1

**=(B1+B2)/2*(A2-A1)**

and copy this for all Column C cells till the second-last row of data. To copy, click cell C1 and then click and drag the little black box in the right hand corner. In this example, you have 6 data points so you would drag the formula to cell C5.

Step 4: Calculate the **sum of the totals** in Column C. In this example, click cell C6 and then click the summation sign “Σ” on the ribbon. The solution will appear in cell C6.

Step 5: Delete the last row in column c (not the total!—see the image below). The correct approximation will not show in the summation cell.

For this example, the solution is **1.85**.

*That’s it!*

## Tip

When finding the area under curve in Excel, keep the x-axis increments as small as possible. This improves the curve’s approximation and the accuracy of the area under the curve. In other words, *the more values you input into columns A and B, the more accurate your results will be*. By using trapezoids of equal width, i.e. equidistant data points on the x-axis, you can do away with the first column; the formula in Column C is simply C1=(B1+B2)/2. The total sum of the values in Column C can then be multiplied by this constant width to give the total area under the curve.

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## References

“Area under a curve” image created at Desmos.com.

**CITE THIS AS:**

**Stephanie Glen**. "Area Under the Curve Excel, Graphs: Find in Easy Steps" From

**CalculusHowTo.com**: Calculus for the rest of us! https://www.calculushowto.com/problem-solving/area-under-the-curve-excel/

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