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Radian

A unit for measuring angles. 180° = π radians, and 360° = 2π radians. The number of radians in an angle equals the number of radii it takes to measure a circular arc described by that angle.

Note: 360° equals 2π radians because a complete circular arc has length equal to 2π times the radius.

 

Formula: θ = s/r

θ = measure of the central angle in radians
s = arc length
r = radius of the circle

Example:

s = 10
r = 5

θ = 10/5 = 2 radians

 

Commonly used angles in degrees and radians

 

See also

Special angles

 


  this page updated 21-feb-16
Mathwords: Terms and Formulas from Algebra I to Calculus
written, illustrated, and webmastered by Bruce Simmons
NCTM Web Bytes December 2004 Web Bytes March 2005 Web Bytes