# Calculate Area Between Two Curves Excel

In this article, we will learn how to calculate the area between two curves in Excel. We will divide the total steps into three sections:

- Plotting curves from the equations
- Calculating the intersecting point of two curves
- Find the integral of the equations of two curves
- Calculate the area between two curves

**The theory you should know before jumping into the steps:**

## Section A. Plotting Curves from the Equations

Suppose you need to calculate the areas between two curves given below:

**Step 1: ** Take some random value of x to plot the curves.

**Step 2:** Write the equations of curves in Excel and enter them into the cells** C2** and **D2**

- For curve
**y1**

`=B2^2+3`

- For curve
**y2**

`=-(B2^2)+20`

Where **B2 **contains the values of x,

**Step 3: AutoFill** the remaining cells in columns **C** and **D** to get the values for **y1** and **y2** which correspond to the values of **x**

**Step 4:** Select the range **B1:D12**, go to the **Insert** tab

**Step 5:** From the **chart **section, choose the **Scatter** chart

The result is

## Section B. Calculating the Intersecting Point of Two Curves in Excel

We will use Excel’s built-in option named “**Goal Seek**” to find the intersection point.

Goal Seek has three options

**Set cell:**The reference cell containing the formula**To value:**The target value**By changing cell:**the reference cell acts as a variable for the formula. Changing the value of the “**By changing cell’s**” reference cell,**Goal Seek**will check for which value the formula will result in the target value.

The Goal seek will run a check by tanking random values starting from the initially entered value to the the “**By changing cell’s**” reference cell and terminate if the formula entered in the** “set cell’s” **reference meets the **target **value.

**Step 1:** It’s clear from the chart we created in **Section A**, the intersection points will be any points closer to **-2** and** 2**.

So, enter **-2** and **2** in cells **C16** and **C17**, respectively.

**Step 2:** Enter the following formula in cell **D16** and AutoFill to the cell **D17**

`=-(C16^2)+20-(C16^2+3) //returns the value of (y2-y1)`

where, cell **C16** contains the value of x

**Step 2:** Select cell** D16** and go to the **Data** tab.

**Step 3:** From the **Forecast** Section, Click on **What-If Analysis **

**Step 4: **Click on the **Goal Seek** option.

**Step 5:** Enter the values in the fields of the Goal Seek window, as shown below. And click on** OK**

**Note: **At the intersection point, the value of **y2-y1 (cell D16)** will be zero for any particular value of **x (cell C16)**. So, we set the target value in the Goal Seek to **Zero**

**Step 6: **After clicking **Ok**, we got the value of x for the intersection **point1**

Similarly, find the value of x for the intersection **point2**

## Section C. Find the integral of the equations of two curves

**Step 1: **Enter the values of x at intersection points (obtained from section B) in cell **C21**, **C22**

**Step 2:** Theoretically the integration of the curve equation is

**Step 3: **Write the integrated equations in Excel and input them in cells **D21** and **E21**, respectively.

`=(C21^3)/3+3*C21`

`=-(C21^3)/3+20*C21`

Where **C21 **contains the value of x for the intersection **point1**,

**Step 4:** Select **D21**, **E21 **and AutoFill to the **row 22**

## Section E. Calculate the Area Between Two Curves

To find the enclosed area by curve **y1** between **X = -2.91545** and **X = -2.91545**, we need to find the difference between the values obtained in section C by substituting **X = -2.91545** and **X = 2.91545** in the integrated equation.

And similar calculation applicable to find the enclosed area by curve **y2**

**Step 1: **Input the following formulas in cells **E25** and **E26**, respectively

`=D22-D21 //returns the enclosed area by curve y1`

`=E22-E21 // returns the enclosed area by curve y2.`

**Step 2:** Finally to get the area enclosed by the curve **y1** and** y2**, apply the following formula in cell **E27**

`=E26-E25`