Radian

lastmod 2018-08-17created 2014-09-114 edits

The radian is a dimensionless unit: the size of the central angle subtended by an arc on a circle whose length equals the radius. It is also called circular measure (弧度) and is abbreviated as rad. More generally, the radian value equals the ratio of the arc length to the radius of a circle. That is, θ = s /r, where θ is the angle in radians, s is the arc length, and r is the radius.

When writing an angle in radians, rad or c is appended to the number, or sometimes nothing is written. In that case, ° is appended to degree values so they are not confused with them.

Simple rules and formulas

• 1rad = 180° / π ≒ 57.2958°
• 1° = π / 180° ≒ 0.0175rad
• 360° = 2π rad ≒ 6.2832rad

Radian - sexagesimal relationship and conversion

The following formulas hold.

• 1 rad = 180 / π
• x rad = θ° × π / 180°
• θ° = x rad × 180° / π
  (θ° : x rad = 360° : 2π)

== Why is 2π rad = 360°? == Considering that pi (π) is the ratio of a circle's circumference to its diameter, the circumference of a circle with diameter 1 is π. So the circumference of a circle with radius 1 is 2π. A circle is 360°, so 2π rad = 360° holds.
(Usually rad is omitted, giving 2π = 360°.)

Favorite site

• Navercast: summary of radians ¹
• Daum blog: understanding radians (circular measure)
• Radian and degree

References