DEGREES function

The DEGREES function in Excel is used to convert an angle from radians to degrees. This is particularly useful in trigonometric calculations where angles are usually represented in radians but need to be converted to degrees for certain applications or for easier interpretation.

Syntax

=DEGREES(radians)

Parameters

• radians: The angle in radians that you want to convert to degrees.

Return Value

The function returns the angle in degrees.

Conversion Formula

The function uses the following mathematical formula to convert radians to degrees:

$$\text{Degrees} = \text{Radians} \times \left( \frac{180}{\pi} \right)$$

Where:

• $\pi$ is approximately 3.14159.

Example 1: Convert 1 Radian to Degrees

If you want to convert 1 radian to degrees:

=DEGREES(1)

Result: 57.2958
(1 radian is approximately 57.2958 degrees.)

Example 2: Convert Pi Radians to Degrees

If you want to convert π (Pi) radians to degrees:

=DEGREES(PI())

Result: 180
(π radians is exactly 180 degrees.)

Example 3: Convert 3.14159 Radians to Degrees

To convert 3.14159 radians to degrees:

=DEGREES(3.14159)

Result: 180
(3.14159 radians is approximately 180 degrees.)

Important Notes

• The DEGREES function works with any valid numerical input that represents an angle in radians.
• If the input is not a valid number, the function will return a #VALUE! error.

Use Cases

• Trigonometry: When performing trigonometric calculations (like sine, cosine, tangent) in Excel, you often need to convert radians to degrees to interpret the result in a more familiar scale.
• Engineering and Physics: Angles are often given in radians in mathematical and physical formulas, but results may need to be presented in degrees for easier understanding, particularly in fields like navigation, astronomy, and mechanical engineering.