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# Excel 2013

## Complex Formulas

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### Introduction

#### Video: Complex Formulas

Watch the video (5:10). Need help?

A simple formula is a mathematical expression with one operator, such as 7+9. A complex formula has more than one mathematical operator, such as 5+2*8. When there is more than one operation in a formula, the order of operations tells Excel which operation to calculate first. In order to use Excel to calculate complex formulas, you will need to understand the order of operations.

Optional: Download our Lesson 14 Practice Workbook.

#### Order of Operations

Excel calculates formulas based on the following order of operations:

1. Operations enclosed in parentheses
2. Exponential calculations (3^2, for example)
3. Multiplication and division, whichever comes first
4. Addition and subtraction, whichever comes first

A mnemonic that can help you remember the order is PEMDAS or Please Excuse My Dear Aunt Sally.

Click the arrows in the slideshow below to learn more about how the order of operations is used to calculate formulas in Excel.

• While this formula may look really complicated, we can use the order of operations step-by-step to find the right answer.

• First, we'll start by calculating anything inside the parentheses. In this case, there's only one thing we need to calculate: 6-3=3.

• As you can see, the formula already looks a bit simpler. Next, we'll look to see if there are any exponents. There's one: 2^2=4.

• Next, we'll solve any multiplication and division, working from left to right. Because the division operation comes before the multiplication, it is calculated first: 3/4=0.75.

• Now, we'll do our remaining multiplication operation: 0.75*4=3.

• Next, we'll calculate any addition or subtraction, again working from left to right. Addition comes first: 10+3=13.

• Finally, we have one remaining subtraction operation: 13-1=12.

• And now we have our answer: 12. This is the exact same result you would get if you entered the formula into Excel.

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#### Creating Complex Formulas

In the example below, we will demonstrate how Excel solves a complex formula using the order of operations. Here, we want to calculate the cost of sales tax for a catering invoice. To do this, we'll write our formula as =(D2+D3)*0.075 in cell D4. This formula will add the prices of our items together and then multiply that value by the 7.5% tax rate (which is written as 0.075) to calculate the cost of sales tax.

Creating a complex formula

Excel follows the order of operations and first adds the values inside the parentheses: (44.85+39.90) = \$84.75. Then, it multiplies that value by the tax rate: \$84.75*0.075. The result will show that the sales tax is \$6.36.

The completed formula and calculated value

It is especially important to enter complex formulas with the correct order of operations. Otherwise, Excel will not calculate the results accurately. In our example, if the parentheses are not included, the multiplication is calculated first and the result is incorrect. Parentheses are the best way to define what calculations will be performed first in Excel.

Result of an incorrect formula