# Excel 2013

## Complex Formulas

### Introduction

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.

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#### The order of operations

Excel calculates formulas based on the following **order of operations**:

- Operations enclosed in
**parentheses** **E****xponential**calculations (3^2, for example)**M****ultiplication**and**division**, whichever comes first**A****ddition**and**subtraction**, whichever comes first

A mnemonic that can help you remember the order is **PEMDAS**, or **P**lease **E**xcuse **M**y **D**ear **A**unt **S**ally.

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

#### 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.

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

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 which calculations will be performed first in Excel.