How to Calculate the Area Under a Curve in Excel

Understanding how to calculate the area under a curve in Excel is a valuable skill that can provide insights into trends, patterns, and overall performance across various fields. This is the total area covered between the curve and x-axis within a range of x-values, widely used in data science and relevant contexts. Excel offers multiple methods to perform this task efficiently, and we will explore two of them in this blog post. These methods will enable you to derive meaningful conclusions from your datasets, so let’s see how to find the area under a curve in Excel.

 

Calculating the Area Under a Curve with Trapezoidal Rule

Trapezoidal Rule, a numerical method, allows for an accurate approximation of this area by segmenting the curve into trapezoids, thereby simplifying complex curves into manageable calculations. Let’s see how to calculate the area under a curve in Excel, using this method:

Suppose you have this data table with its relevant curve.

 

You can divide the total area into multiple trapezoid areas like this:

 

Then add another column (Area) to calculate the area of each trapezoid between data points.

Now you only need to apply the mathematical formula used for calculating the area of ​​the trapezoid:

When applied to the aforementioned data table, the formula is adapted as follows:

 

Drag the fill handle through the rows except for the last one to calculate the area of all trapezoids.

 

Now you can sum up the values and calculate the total area under the curve using the SUM function:

 

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Calculating the Area Under a Curve with Excel Chart Trendline

Another way of calculating the area under a curve is through the use of its equation. You can use the chart trendline in Excel and access the curve’s equation. Let’s delve deeper into how to calculate area under a curve in Excel, using the trendline.

You only need to follow these steps for this purpose:

First, select the chart, go to the “Chart Design” tab > “Chart Layouts” and click on the “Add Chart Element” dropdown list.

Select “Trendline” and then “More Trendline Options”.

 

The “Format Trendline” pane will pop up.

In the “Trendline Options” section, select “Polynomial”.

 

Then check “Display Equation on Chart”.

 

Now you can see the related equation on the chart.

In this step, you need to get the definite integral of the equation. You can do it by yourself or use this online integral calculator.

In our example, the integral would be:

 F(x) = -0.0274 x ^ 3 + 0.35695 x ^ 2 + 3.2283 x + C

You should calculate the function value for two points, x=1 and x=10. (These are the beginning and the end of the curve.)

 

To find the area under the curve, calculate the difference between two values:

This is the final value as the area under the curve.

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Conclusion

In this blog post, we explained how to calculate area under a curve in Excel, using two straightforward methods. By understanding and applying these techniques, you can unlock deeper analytical capabilities within Excel, making it an even more powerful tool in your data analysis processes. Remember, the choice of method depends on your specific dataset and analytical needs, but either approach will equip you with the means to extract meaningful information from your data.

 

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