What Are Radians?
What Are Radians?
Radians are a unit of measurement of an angle.
There are 2π radians in a full rotation.
Dictionary Definition
The Oxford English Dictionary defines a degree as "a unit of angle, equal to the angle subtended at the centre of a circle by an arc equal in length to the radius."
Definition of a Radian
1 radian is the angle found when the radius is wrapped around the circle.
More generally, the angle in radians is equal to:

the arc length divided by the radius.

arc length of a circle with radius 1 (the unit circle).
A Formula to Define a Radian
We have seen that the angle in radians is equal to the arc length divide by the radius. We can use this to define a formula.
The angle in radians is found using the formula:
In this formula, θ is the angle in radians, s is the arc length and r is the radius. The image below shows what we mean by angle, arc length and radius:
2π Radians in a Circle
There are 2π radians in a full rotation (a circle).
Using the definition of radians, can you work out why there are 2π radians in a circle?
See the Note to find out why.