Sometimes we need to calculate the area under the curve in Excel to make the dataset more efficient. It helps us in different fields of data science. We cannot calculate the area under the curve directly in Excel. In this article, we are going to learn about some quick methods to calculate the area under the curve in Excel with some examples and explanations.
Download the following workbook and exercise.
2 Suitable Methods to Calculate Area Under Curve in Excel
First, we need to create a Scatter chart. For that, we are going to use the below dataset which contains different points on the X & Y axes in columns B & C respectively. In the first method, we are adding a helper column (Area) in column D. See the screenshot to get a clear idea.
1. Calculate Area Under Curve with Trapezoidal Rule in Excel
As we know, it is not possible to calculate directly the area under the curve. So we can break the whole curve into the trapezoids. After that, adding the areas of the trapezoids can give us the total area under the curve. So let’s follow the procedure below.
- First, select the range B4:C11 from the dataset.
- Next, go to the Insert tab.
- Further, select the Insert Scatter (X, Y) option from the Charts section.
- Now, from the drop-down, select Scatter with Smooth Lines and Markers option.
- Consequently, this will open a chart like the one below.
- Further, we will calculate the area of our very first trapezoid which is between X = 1 & X = 3 under the curve.
- For that, write the below formula in cell D5:
- Then press Enter.
- Use the Fill Handle tool till the second last cell to get the area of the trapezoids.
- After that, we will add all the areas of the trapezoids.
- For that, in cell D13, write down the below formula:
Here, we use the SUM function, to add up the cell range D5:D10.
- Finally, hit Enter to see the result.
2. Use Excel Chart Trendline to Get Area Under Curve
Excel Chart Trendline helps us to find an equation for the curve. We use this equation to get the area under the curve. Suppose, we have the same dataset containing different points on the X & Y axes in columns B & C respectively. We use the chart trendline to get the equation from which we can get the area under the curve. Follow the below steps.
- In the beginning, select the chart that we plotted from:
First selecting range B4:C11 > Then Insert tab > After that Insert Scatter (X, Y) drop-down > Finally Scatter with Smooth Lines and Markers option
- Secondly, go to the Chart Design tab.
- Further, select Add Chart Element drop-down from the Chart Layouts section.
- From the drop-down, go to the Trendline option.
- Next, select More Trendline Options.
- Or you can simply click on the Plus (+) sign on the right side of the chart after selecting it.
- Consequently, this will open the Chart Elements section.
- From that section, let the cursor hover over the Trendline section and click on More Options.
- Here, this will open the Format Trendline window.
- Now, select Polynomial from the Trendline Options.
- Also, give a tick mark on the Display Equation on chart option.
- Finally, we can see the polynomial equation on the chart.
- The polynomial equation is:
y = 0.0155×2 + 2.0126x – 0.4553
- Thirdly, we need to get the definite integral of this polynomial equation which is:
F(x) = (0.0155/3)x^3 + (2.0126/2)x^2 – 0.4553x+c
- Fourthly, we are going to put the value x = 1 in the definite integral. We can see the below calculation in cell F8:
F(1) = (0.0155/3)*1^3 + (2.0126/2)*1^2 - 0.4553*1
- After that, hit Enter to see the result.
- Again, we are going to input x = 10 in the definite integral. The calculation looks like the below in cell F9:
F(10) =(0.0155/3)*10^3 + (2.0126/2)*10^2 - 0.4553*10
- After hitting Enter, we can see the result.
- Then we are going to calculate the difference between the calculations of F(1) & F(10) to find the area under the curve.
- So, in cell F10, write down the below formula:
- In the end, hit Enter to see the result.
By using these methods, we can quickly calculate the area under the curve in Excel. There is a practice workbook added. Go ahead and give it a try. Visit the ExcelDemy website for more articles like this. Feel free to ask anything or suggest any new methods.