Calculus > Area under curve in Microsoft Excel
Note: This article is about finding the AUC in calculus. For finding areas under a normal distribution curve, see: Find the Area Under a Normal Curve.
How to Find the Area Under Curve in Microsoft Excel
Watch the video or read the steps below:
The area under a curve is the area between the curve and the x-axis. The curve may lie completely above or below the x-axis or on both sides. In calculus, you measure the area under the curve using definite integrals. Microsoft Excel does not have functions to calculate definite integrals, but you can approximate this area by dividing the curve into smaller curves, each tending to 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
Sample question: Find the area under curve in Microsoft 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.
Tip: When finding the area under curve in Microsoft 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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