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Radians

Excel use of Radians

Radians are a system of measuring angles. A full rotation in radians is equal to 2π where a full rotation in degrees is 360°. In Excel, the trigonometric functions such as COS, SIN and TAN, expect input provided in radians.

Convert Degrees to Radians

To convert an angle in degrees to radians, multiply the angle by PI()/180 or use the RADIANS function. For example, to convert 60 degrees to radians, you can use either formula below:

=60*PI()/180 // Returns 1.047 radians
=RADIANS(60) // Returns 1.047 radians

Definition of Radians

Radians Definition

Geometrically, the angle formed by one radian is equal to the amount of rotation required to travel the length of the radius along the circumference of the circle. The angle formed by this system is independent of the size of the circle. A full rotation in radians is equal to 2π or approximately 6.283. In Excel, the value of a full rotation is given by the formula below:

=2*PI() // Returns 6.2831853071

The value for a full rotation in radians can be calculated by dividing the circumference of any circle by its radius. See wumbo.net for a more detailed explanation of radians and other math concepts.

Common Angles

Common Angles Degrees and Radians

The PI or RADIANS function can be used to measure equivalent angles in the degrees and radians systems. The geometric constant π, whose value is returned from the PI function, represents a half-rotation in radians. Some common angles are shown below in the formulas:

=RADIANS( 90)=PI()/2
=RADIANS(180)=PI()
=RADIANS(270)=3*PI()/2
=RADIANS(360)=2*PI()

Notes

  • The RADIANS function converts degrees to radians
  • The DEGREES function converts radians to degrees
  • One full rotation in radians is equal to 2*PI()