Degrees and Radians

The Radian describes the plane angle subtended by a circular arc as the length of the arc divided by the radius of the arc.

The number of radians in 1 complete revolution = Circumference / radius

The circumference of a circle of radius r = 2 π r

Therefore: 2 π r / r = 2 π

so: 2 π radians = 360 ° π radians = 180° π radians / 2 = 90°

so: 1 radian = 57.296 °

and there are roughly 6.283 radians in 360°

because π radians(180°) = 3.1416 and

2π radians(360°) = 6.283

Degrees to Radian terms of π

Take the number of degrees you wish to convert: e.g 120°

multiply by: 120 x π / 180 120π / 180

Simplify / reduce by dividing by the largest common factor : 2π / 3

Radians to Degrees

Take the radian value in terms of π you wish to convert: e.g (4 / 9) π

multiply by: 180 / π

Simplify: 4π x 180 / 9π 4 x 180 / 9 80 °

take the radian value you wish to convert: e.g. 1.396

Multiply by: 180/π

Simplify: 1.396 x 180 / π 80 ° (rnd up)