Excel has a number of built-in trigonometric functions that make it easy to find:

of a right-angled triangle (a triangle containing an angle equal to 90^{o}).

The only problem is that these functions require the angles to be measured in *radians* rather than *degrees*, and while radians are a legitimate way of measuring angles - based on the radius of a circle - they are not something most people work with on a regular basis.

To help the average spreadsheet user get around this problem, Excel has the RADIANS function, which makes it easy to convert degrees to radians.

And to help that same user convert the answer from radians back to degrees, Excel has the DEGREES function.

### Historical Note

Apparently, Excel's trig functions use radians rather than degrees because when the program was first created, the trig functions were designed to be compatible with the trig functions in the spreadsheet program Lotus 1-2-3, which also used radians and which dominated the PC spreadsheet software market at the time.

### The DEGREES Function's Syntax and Arguments

A function's syntax refers to the layout of the function and includes the function's name, brackets, and arguments.

The syntax for the DEGREES function is:

*= DEGREES ( Angle )*

**Angle **- (required) the angle in degrees to be converted to radians. Options for this argument are to enter:

- the size of the angle in radians can be entered for this argument - as shown in row three of the image above;
- the cell reference to the location of this data in the worksheet - row two above.

### Excel's DEGREES Function Example

As shown in the image above, this example will use the DEGREES function to convert an angle of 1.570797 radians into degrees.

Options for entering the function and its arguments include:

- Typing the complete function:
*=DEGREES(A2)*or*=DEGREES(1.570797)*into cell B2 - Selecting the function and its arguments using the DEGREES function dialog box

Although it is possible to just enter the complete function manually, many people find it easier to use the dialog box as it takes care of entering the function's syntax - such as brackets and, for functions with multiple arguments, the comma separators located between arguments.

The information below covers using the dialog box to enter the DEGREES function into cell B2 of the worksheet.

- Click on cell B2 in the worksheet - this is where the function will be located
- Click on the
*Formulas*tab of the ribbon menu - Choose
*Math & Trig*from the ribbon to open the function drop down list - Click on
*DEGREES*in the list to bring up the function's dialog box - In the dialog box, click on the
*Angle*line; - Click on cell A2 in the worksheet to enter the cell reference as the function's argument;
- Click
*OK*to complete the function and return to the worksheet; - The answer 90.0000 should appear in cell B2;
- When you click on cell B1 the complete function
*= DEGREES ( A2 )*appears in the formula bar above the worksheet.

### PI Formula

Alternatively, as shown in row four in the image above, the formula:

=A2*180/PI()

that multiplies the angle (in radians) by 180 and then divide the result by the mathematical constant *Pi *can also be used to convert the angle from radians to degrees.

Pi, which is the ratio of a circle's circumference to its diameter, has a rounded value of 3.14 and is usually represented in formulas by the Greek letter π.

In the formula in row four, Pi is entered using the PI() function, which gives a more accurate value for Pi than 3.14.

The formula in row five of the example:

*=DEGREES( PI() )*

results in an answer of 180 degrees because the relationship between radians and degrees is:

π radians = 180 degrees.