# How to Calculate Area Under Curve in Excel (3 Methods)

In this article, we will learn how to calculate the area under the curve in Excel according to three methods

- Calculate the Area Under the Curve by Trapezoidal method
- Calculate the Area Under the Curve by Integral method
- Calculate the Area Under the Curve by Simpson’s method

## Method 1. Calculate Area Under Curve by Trapezoidal Method in Excel

**Theory You should know to calculate the area by Trapezoidal Method**

**Step 01:** Create a data table containing the values of coordinates (X and Y) as shown below.

**Step 02:** Select both columns named “**Value of X**” and “**Value of Y**.”

**Step 03:** Then go to the **Insert **tab.

**Step 04:** From the **chart** section, select the** Scatter chart**

The result is

**Step 05: **Enter the following formula in the cell **D4**

`=0.5*(C3+C4)/(B4-B3)`

This formula will calculate the area of the marked trapezium in the image.

**Step 06:** Press **Enter** and **AutoFill** the remaining cell in column **D**

Here, we have taken into account the nine trapeziums that make up the entire area(to understand, see the image given below). No trapezium was made by the first ordinate alone. Therefore, we started the calculation in cell **D4**.

**Step 07: **Then to sum all the areas of trapeziums, enter the following formula in cell **D13**

`=SUM(D4:D12)`

## Method 2. Calculate Area Under Curve by Integral Method in Excel

**Step 01:** Double-click on the curve. The **Chart Design** tab will appear

**Step 02:** From the **Charts layouts** section, Click on **Add Chart Element**

**Step 03**: Keep the mouse pointer on the **Trendline **option

**Step 04:** Click on the **More Tradelines options**.

**Step 05:** **Format Trendline** tab will appear from the right side of your monitor

**Step 06**: Click on the** Trendline option**

**Step 07:** Select the **Polynomial** option, and set order** 2**

**Step 08:** Then, scroll down and check the **Display Equation on Chart** option.

The trendline and equation of the curve will be displayed with the curve.

**Step 09:** Find the integral of the polynomial equation.

The polynomial equation is,

y = -0.0341x^{2} + 1.2417x + 6.9833

According to the integration method, the integral of the polynomial equation is

**Step 10: **Let’s write the integrated polynomial equation in excel and enter into cell **D14**

`=(-0.0341*C14^3)/3 +( 1.2417*C14^2)/2 + 6.9833*C14`

Where **C14** contains the value of **X**

**Step 11: AutoFill** the formula to cell **D15**

**Step 12:** Now, in order to determine the area of the chart covered by the curve for** X = 1** to **X= 10**, we need to deduct the answer obtained by substituting** X = 1** into the equation we developed in step 10 from the result of substituting **X=10** into the equation obtained in step 10

So, enter **1** in cell **C14** and **10** in cell **C15**.

**Step 13:** Enter the following formula into cell **D16** to get the area under curve.

`=D15-D14`

## Method 3. Calculate Area Under Curve by Simpson’s method in Excel

**The theory you should know **

Here, we took the even ordinate (X = 10) number. So, we have to apply the Simpsons 1st rule

**Step 01:** Create a new column and input the Simpsons multiplier

**Step 02:** Then input the following formula into the cell **E3**Â and use **AutoFillÂ **

`=C3*D3`

**Step 03: **To get the sum of the products of Simpson’s multiplier and the value of Y, Apply the following formula in cell **E13**

`=SUM(E3:E12)`

**Step 04: **Finally, get the area by applying the formula given below in cell **E15**

`=(3/8)*E13`

## Comparison Between the Area Obtained From the Three Methods

Method | Trapezoidal Method | Integral Method | Simpsons method |

Result | 113 | 112.958 | 112.875 |

Reason of error | |||

By Trapezoidal and Simpson’s method, we considered the smaller division as a trapezium, but actually this region is not trapezoidal. Minor areas are left out of consideration. However, taking more ordinates can minimize the amount of error. |