# Overview of formulas

If you're new to Excel, you'll soon find that it's more than just a grid in which you enter numbers in columns or rows. Yes, you can use Excel to find totals for a column or row of numbers, but you can also calculate a mortgage payment, solve math or engineering problems, or find a best case scenario based on variable numbers that you plug in.

Excel does this by using formulas in cells. A formula performs calculations or other actions on the data in your worksheet. A formula always starts with an equal sign (=), which can be followed by numbers, math operators (such as a plus or minus sign), and functions, which can really expand the power of a formula.

For example, the following formula multiplies 2 by 3 and then adds 5 to that result to come up with the answer, 11.

=2*3+5

This next formula uses the **PMT** function to calculate a mortgage payment ($1,073.64), which is based on a 5 percent interest rate (5% divided by 12 months equals the monthly interest rate) over a 30-year period (360 months) for a $200,000 loan:

=PMT(0.05/12,360,200000)

Here are some additional examples of formulas that you can enter in a worksheet.

**=A1+A2+A3**Adds the values in cells A1, A2, and A3.**=SQRT(A1)**Uses the**SQRT**function to return the square root of the value in A1.**=TODAY()**Returns the current date.**=UPPER("hello")**Converts the text "hello" to "HELLO" by using the**UPPER**worksheet function.**=IF(A1>0)**Tests the cell A1 to determine if it contains a value greater than 0.

- The parts of a formula
- Using constants in formulas
- Using calculation operators in formulas
- Using functions and nested functions in formulas
- Using references in formulas
- Using names in formulas
- Using array formulas and array constants

## The parts of a formula

A formula can also contain any or all of the following: functions (function: A prewritten formula that takes a value or values, performs an operation, and returns a value or values. Use functions to simplify and shorten formulas on a worksheet, especially those that perform lengthy or complex calculations.), references (cell reference: The set of coordinates that a cell occupies on a worksheet. For example, the reference of the cell that appears at the intersection of column B and row 3 is B3.), operators (operator: A sign or symbol that specifies the type of calculation to perform within an expression. There are mathematical, comparison, logical, and reference operators.), and constants (constant: A value that is not calculated and, therefore, does not change. For example, the number 210, and the text "Quarterly Earnings" are constants. An expression, or a value resulting from an expression, is not a constant.).

**^**(caret) operator raises a number to a power, and the

*****(asterisk) operator multiplies numbers.

## Using constants in formulas

A constant is a value that is not calculated; it always stays the same. For example, the date 10/9/2008, the number 210, and the text "Quarterly Earnings" are all constants. An expression (expression: A combination of operators, field names, functions, literals, and constants that evaluates to a single value. Expressions can specify criteria (such as Order Amount>10000) or perform calculations on field values (such as Price*Quantity).) or a value resulting from an expression is not a constant. If you use constants in a formula instead of references to cells (for example, =30+70+110), the result changes only if you modify the formula.

## Using calculation operators in formulas

Operators specify the type of calculation that you want to perform on the elements of a formula. There is a default order in which calculations occur (this follows general mathematical rules), but you can change this order by using parentheses.

### Types of operators

There are four different types of calculation operators: arithmetic, comparison, text concatenation, and reference.

#### Arithmetic operators

To perform basic mathematical operations, such as addition, subtraction, multiplication, or division; combine numbers; and produce numeric results, use the following arithmetic operators.

Arithmetic operator |
Meaning |
Example |
---|---|---|

+ (plus sign) | Addition | 3+3 |

– (minus sign) | Subtraction Negation |
3–1 –1 |

* (asterisk) | Multiplication | 3*3 |

/ (forward slash) | Division | 3/3 |

% (percent sign) | Percent | 20% |

^ (caret) | Exponentiation | 3^2 |

#### Comparison operators

You can compare two values with the following operators. When two values are compared by using these operators, the result is a logical value — either TRUE or FALSE.

Comparison operator |
Meaning |
Example |
---|---|---|

= (equal sign) | Equal to | A1=B1 |

> (greater than sign) | Greater than | A1>B1 |

< (less than sign) | Less than | A1<B1 |

>= (greater than or equal to sign) | Greater than or equal to | A1>=B1 |

<= (less than or equal to sign) | Less than or equal to | A1<=B1 |

<> (not equal to sign) | Not equal to | A1<>B1 |

#### Text concatenation operator

Use the ampersand (**&**) to concatenate (join) one or more text strings to produce a single piece of text.

Text operator |
Meaning |
Example |
---|---|---|

& (ampersand) | Connects, or concatenates, two values to produce one continuous text value | "North"&"wind" results in "Northwind" |

#### Reference operators

Combine ranges of cells for calculations with the following operators.

Reference operator |
Meaning |
Example |
---|---|---|

: (colon) | Range operator, which produces one reference to all the cells between two references, including the two references. | B5:B15 |

, (comma) | Union operator, which combines multiple references into one reference | SUM(B5:B15,D5:D15) |

(space) | Intersection operator, which produces one reference to cells common to the two references | B7:D7 C6:C8 |

### The order in which Excel performs operations in formulas

In some cases, the order in which a calculation is performed can affect the return value of the formula, so it's important to understand how the order is determined and how you can change the order to obtain the results you want.

#### Calculation order

Formulas calculate values in a specific order. A formula in Excel always begins with an equal sign (**=**). Excel interprets the characters that follow the equal sign as a formula. Following the equal sign are the elements to be calculated (the operands), such as constants or cell references. These are separated by calculation operators. Excel calculates the formula from left to right, according to a specific order for each operator in the formula.

#### Operator precedence

If you combine several operators in a single formula, Excel performs the operations in the order shown in the following table. If a formula contains operators with the same precedence — for example, if a formula contains both a multiplication and division operator — Excel evaluates the operators from left to right.

Operator |
Description |
---|---|

: (colon) (single space) , (comma) |
Reference operators |

– | Negation (as in –1) |

% | Percent |

^ | Exponentiation |

* and / | Multiplication and division |

+ and – | Addition and subtraction |

& | Connects two strings of text (concatenation) |

= < > <= >= <> |
Comparison |

#### Use of parentheses

To change the order of evaluation, enclose in parentheses the part of the formula to be calculated first. For example, the following formula produces 11 because Excel performs multiplication before addition. The formula multiplies 2 by 3 and then adds 5 to the result.

=5+2*3

In contrast, if you use parentheses to change the syntax, Excel adds 5 and 2 together and then multiplies the result by 3 to produce 21.

=(5+2)*3

In the following example, the parentheses that enclose the first part of the formula force Excel to calculate B4+25 first and then divide the result by the sum of the values in cells D5, E5, and F5.

=(B4+25)/SUM(D5:F5)

## Using functions and nested functions in formulas

Functions are predefined formulas that perform calculations by using specific values, called arguments, in a particular order, or structure. Functions can be used to perform simple or complex calculations.

### The syntax of functions

The following example of the **ROUND** function rounding off a number in cell A10 illustrates the syntax of a function.

**=**), followed by the function name, an opening parenthesis, the arguments for the function separated by commas, and a closing parenthesis.

**=ROUND(**and the tooltip appears. Tooltips appear only for built-in functions.

### Entering functions

When you create a formula that contains a function, you can use the **Insert Function** dialog box to help you enter worksheet functions. As you enter a function into the formula, the **Insert Function** dialog box displays the name of the function, each of its arguments, a description of the function and each argument, the current result of the function, and the current result of the entire formula.

To make it easier to create and edit formulas and minimize typing and syntax errors, use Formula AutoComplete. After you type an = (equal sign) and beginning letters or a display trigger, Excel displays, below the cell, a dynamic drop-down list of valid functions, arguments, and names that match the letters or trigger. You can then insert an item from the drop-down list into the formula.

### Nesting functions

In certain cases, you may need to use a function as one of the arguments (argument: The values that a function uses to perform operations or calculations. The type of argument a function uses is specific to the function. Common arguments that are used within functions include numbers, text, cell references, and names.) of another function. For example, the following formula uses a nested **AVERAGE** function and compares the result with the value 50.

**Valid returns** When a nested function is used as an argument, the nested function must return the same type of value that the argument uses. For example, if the argument returns a TRUE or FALSE value, the nested function must return a TRUE or FALSE value. If the function doesn't, Excel displays a #VALUE! error value.

**Nesting level limits** A formula can contain up to seven levels of nested functions. When one function (we'll call this Function B) is used as an argument in another function (we'll call this Function A), Function B acts as a second-level function. For example, the **AVERAGE** function and the **SUM** function are both second-level functions if they are used as arguments of the **IF** function. A function nested within the nested **AVERAGE** function is then a third-level function, and so on.

## Using references in formulas

A reference identifies a cell or a range of cells on a worksheet, and tells Excel where to look for the values or data you want to use in a formula. You can use references to use data contained in different parts of a worksheet in one formula or use the value from one cell in several formulas. You can also refer to cells on other sheets in the same workbook, and to other workbooks. References to cells in other workbooks are called links or external references (external reference: A reference to a cell or range on a sheet in another Excel workbook, or a reference to a defined name in another workbook.).

### The A1 reference style

**The default reference style** By default, Excel uses the A1 reference style, which refers to columns with letters (A through XFD, for a total of 16,384 columns) and refers to rows with numbers (1 through 1,048,576). These letters and numbers are called row and column headings. To refer to a cell, enter the column letter followed by the row number. For example, B2 refers to the cell at the intersection of column B and row 2.

To refer to |
Use |
---|---|

The cell in column A and row 10 | A10 |

The range of cells in column A and rows 10 through 20 | A10:A20 |

The range of cells in row 15 and columns B through E | B15:E15 |

All cells in row 5 | 5:5 |

All cells in rows 5 through 10 | 5:10 |

All cells in column H | H:H |

All cells in columns H through J | H:J |

The range of cells in columns A through E and rows 10 through 20 | A10:E20 |

**Making a reference to another worksheet** In the following example, the **AVERAGE** worksheet function calculates the average value for the range B1:B10 on the worksheet named Marketing in the same workbook.

### The difference between absolute, relative and mixed references

**Relative references** A relative cell reference in a formula, such as A1, is based on the relative position of the cell that contains the formula and the cell the reference refers to. If the position of the cell that contains the formula changes, the reference is changed. If you copy or fill the formula across rows or down columns, the reference automatically adjusts. By default, new formulas use relative references. For example, if you copy or fill a relative reference in cell B2 to cell B3, it automatically adjusts from =A1 to =A2.

**Absolute references** An absolute cell reference in a formula, such as $A$1, always refer to a cell in a specific location. If the position of the cell that contains the formula changes, the absolute reference remains the same. If you copy or fill the formula across rows or down columns, the absolute reference does not adjust. By default, new formulas use relative references, so you may need to switch them to absolute references. For example, if you copy or fill an absolute reference in cell B2 to cell B3, it stays the same in both cells: =$A$1.

**Mixed references** A mixed reference has either an absolute column and relative row, or absolute row and relative column. An absolute column reference takes the form $A1, $B1, and so on. An absolute row reference takes the form A$1, B$1, and so on. If the position of the cell that contains the formula changes, the relative reference is changed, and the absolute reference does not change. If you copy or fill the formula across rows or down columns, the relative reference automatically adjusts, and the absolute reference does not adjust. For example, if you copy or fill a mixed reference from cell A2 to B3, it adjusts from =A$1 to =B$1.

### The 3-D reference style

**Conveniently referencing multiple worksheets** If you want to analyze data in the same cell or range of cells on multiple worksheets within a workbook, use a 3-D reference. A 3-D reference includes the cell or range reference, preceded by a range of worksheet names. Excel uses any worksheets stored between the starting and ending names of the reference. For example, =SUM(Sheet2:Sheet13!B5) adds all the values contained in cell B5 on all the worksheets between and including Sheet 2 and Sheet 13.

- You can use 3-D references to refer to cells on other sheets, to define names, and to create formulas by using the following functions: SUM, AVERAGE, AVERAGEA, COUNT, COUNTA, MAX, MAXA, MIN, MINA, PRODUCT, STDEV.P, STDEV.S, STDEVA, STDEVPA, VAR.P, VAR.S, VARA, and VARPA.
- 3-D references cannot be used in array formulas (array formula: A formula that performs multiple calculations on one or more sets of values, and then returns either a single result or multiple results. Array formulas are enclosed between braces { } and are entered by pressing CTRL+SHIFT+ENTER.).
- 3-D references cannot be used with the intersection operator (operator: A sign or symbol that specifies the type of calculation to perform within an expression. There are mathematical, comparison, logical, and reference operators.) (a single space) or in formulas that use implicit intersection (implicit intersection: A reference to a range of cells, instead of a single cell, that is calculated like a single cell. If cell C10 contains the formula =B5:B15*5, Excel multiplies the value in cell B10 by 5 because cells B10 and C10 are in the same row.).

**What occurs when you move, copy, insert, or delete worksheets** The following examples explain what happens when you move, copy, insert, or delete worksheets that are included in a 3-D reference. The examples use the formula =SUM(Sheet2:Sheet6!A2:A5) to add cells A2 through A5 on worksheets 2 through 6.

**Insert or copy**If you insert or copy sheets between Sheet2 and Sheet6 (the endpoints in this example), Excel includes all values in cells A2 through A5 from the added sheets in the calculations.**Delete**If you delete sheets between Sheet2 and Sheet6, Excel removes their values from the calculation.**Move**If you move sheets from between Sheet2 and Sheet6 to a location outside the referenced sheet range, Excel removes their values from the calculation.**Move an endpoint**If you move Sheet2 or Sheet6 to another location in the same workbook, Excel adjusts the calculation to accommodate the new range of sheets between them.**Delete an endpoint**If you delete Sheet2 or Sheet6, Excel adjusts the calculation to accommodate the range of sheets between them.

### The R1C1 reference style

You can also use a reference style where both the rows and the columns on the worksheet are numbered. The R1C1 reference style is useful for computing row and column positions in macros (macro: An action or a set of actions that you can use to automate tasks. Macros are recorded in the Visual Basic for Applications programming language.). In the R1C1 style, Excel indicates the location of a cell with an "R" followed by a row number and a "C" followed by a column number.

Reference |
Meaning |
---|---|

R[-2]C | A relative reference (relative reference: In a formula, the address of a cell based on the relative position of the cell that contains the formula and the cell referred to. If you copy the formula, the reference automatically adjusts. A relative reference takes the form A1.) to the cell two rows up and in the same column |

R[2]C[2] | A relative reference to the cell two rows down and two columns to the right |

R2C2 | An absolute reference (absolute cell reference: In a formula, the exact address of a cell, regardless of the position of the cell that contains the formula. An absolute cell reference takes the form $A$1.) to the cell in the second row and in the second column |

R[-1] | A relative reference to the entire row above the active cell |

R | An absolute reference to the current row |

When you record a macro, Excel records some commands by using the R1C1 reference style. For example, if you record a command, such as clicking the **AutoSum** button to insert a formula that adds a range of cells, Excel records the formula by using R1C1 style, not A1 style, references.

You can turn the R1C1 reference style on or off by setting or clearing the **R1C1 reference style **check box under the **Working with formulas** section in the **Formulas** category of the **Options** dialog box. To display this dialog box, click the **File** tab.

## Using names in formulas

You can create defined names (name: A word or string of characters that represents a cell, range of cells, formula, or constant value. Use easy-to-understand names, such as Products, to refer to hard to understand ranges, such as Sales!C20:C30.) to represent cells, ranges of cells, formulas, constants, or Excel tables. A name is a meaningful shorthand that makes it easier to understand the purpose of a cell reference, constant, formula, or table, each of which may be difficult to comprehend at first glance. The following information shows common examples of names and how using them in formulas can improve clarity and make formulas easier to understand.

Example Type |
Example with no name |
Example with a name |
---|---|---|

Reference | =SUM(C20:C30) | =SUM(FirstQuarterSales) |

Constant | =PRODUCT(A5,8.3) | =PRODUCT(Price,WASalesTax) |

Formula | =SUM(VLOOKUP(A1,B1:F20,5,FALSE), —G5) | =SUM(Inventory_Level,—Order_Amt) |

Table | C4:G36 | =TopSales06 |

### Types of names

There are several types of names that you can create and use.

**Defined name** A name that represents a cell, range of cells, formula, or constant value. You can create your own defined name. Also, Excel sometimes creates a defined name for you, such as when you set a print area.

**Table name** A name for an Excel table, which is a collection of data about a particular subject that is stored in records (rows) and fields (columns). Excel creates a default Excel table name of "Table1", "Table2", and so on, each time you insert an Excel table, but you can change these names to make them more meaningful.

For more information about Excel tables, see Using structured references with Excel tables.

### Creating and entering names

You create a name by using the:

**Name box on the formula bar**This is best used for creating a workbook level name for a selected range.**Create a name from selection**You can conveniently create names from existing row and column labels by using a selection of cells in the worksheet.**New Name dialog box**This is best used for when you want more flexibility in creating names, such as specifying a local worksheet level scope or creating a name comment.

** Note ** By default, names use absolute cell references (absolute cell reference: In a formula, the exact address of a cell, regardless of the position of the cell that contains the formula. An absolute cell reference takes the form $A$1.).

You can enter a name by:

**Typing**Typing the name, for example, as an argument to a formula.**Using Formula AutoComplete**Use the Formula AutoComplete drop-down list, where valid names are automatically listed for you.**Selecting from the Use in Formula command**Select a defined name from a list available from the**Use in Formula**command in the**Defined Names**group on the**Formula**tab.

For more information, see Define and use names in formulas.

## Using array formulas and array constants

An array formula can perform multiple calculations and then return either a single result or multiple results. Array formulas act on two or more sets of values known as array arguments. Each array argument must have the same number of rows and columns. You create array formulas in the same way that you create other formulas, except you press CTRL+SHIFT+ENTER to enter the formula. Some of the built-in functions are array formulas, and must be entered as arrays to get the correct results.

Array constants can be used in place of references when you don't want to enter each constant value in a separate cell on the worksheet.

### Using an array formula to calculate single and multiple results

When you enter an array formula (array formula: A formula that performs multiple calculations on one or more sets of values, and then returns either a single result or multiple results. Array formulas are enclosed between braces { } and are entered by pressing CTRL+SHIFT+ENTER.), Excel automatically inserts the formula between { } (braces).

**To calculate a single result** This type of array formula can simplify a worksheet model by replacing several different formulas with a single array formula.

For example, the following calculates the total value of an array of stock prices and shares, without using a row of cells to calculate and display the individual values for each stock.

When you enter the formula ={SUM(B2:D2*B3:D3)} as an array formula, it multiples the Shares and Price for each stock, and then adds the results of those calculations together.

**To calculate multiple results** Some worksheet functions return arrays of values, or require an array of values as an argument. To calculate multiple results with an array formula, you must enter the array into a range of cells that has the same number of rows and columns as the array arguments.

For example, given a series of three sales figures (in column B) for a series of three months (in column A), the **TREND** function determines the straight-line values for the sales figures. To display all the results of the formula, it is entered into three cells in column C (C1:C3).

When you enter the formula =TREND(B1:B3,A1:A3) as an array formula, it produces three separate results (22196, 17079, and 11962), based on the three sales figures and the three months.

### Using array constants

In an ordinary formula, you can enter a reference to a cell containing a value, or the value itself, also called a constant. Similarly, in an array formula you can enter a reference to an array, or enter the array of values contained within the cells, also called an array constant. Array formulas accept constants in the same way that non-array formulas do, but you must enter the array constants in a certain format.

Array constants can contain numbers, text, logical values such as TRUE or FALSE, or error values such as #N/A. Different types of values can be in the same array constant — for example, {1,3,4;TRUE,FALSE,TRUE}. Numbers in array constants can be in integer, decimal, or scientific format. Text must be enclosed in double quotation marks — for example, "Tuesday".

Array constants cannot contain cell references, columns or rows of unequal length, formulas, or the special characters $ (dollar sign), parentheses, or % (percent sign).

When you format array constants, make sure you:

- Enclose them in braces (
**{****}**). - Separate values in different columns by using commas (
**,**). For example, to represent the values 10, 20, 30, and 40, you enter {10,20,30,40}. This array constant is known as a 1-by-4 array and is equivalent to a 1-row-by-4-column reference. - Separate values in different rows by using semicolons (
**;**). For example, to represent the values 10, 20, 30, and 40 in one row and 50, 60, 70, and 80 in the row immediately below, you enter a 2-by-4 array constant: {10,20,30,40;50,60,70,80}.