A unit of angular measure. There are 2π radians in a full circle or a full rotation.
There are many ways of measuring angle. The most common angle measure is 360 degrees for a full circle (with each degree divided into 60 minutes, and each minute into 60 seconds). A less common measure is the military method of grads, of which there are 100 in a right angle. Both of these are somewhat arbitrary, with 360 degrees being convenient because it is so easily divisible into so many fractions that are whole numbers of degrees (so that a right angle is 90 degrees, for instance). Radian measure is a more "natural" division in which the angle is designated by the length of the arc it subtends divided by the radius of the circle, so that full circle is 2πr/r = 2π. Radian measure is therefore a ratio of two lengths, and properly has no dimension.
Radian measure applies in a very natural way to calculations. it is only when angles are measured in radians, for instance, that the sin(θ) is very nearly equal to θ for small angles.
All such angular measures are proportional to each other. You can convert from radians to degrees by multiplying the angle as measured in radians by (180/π) . Consequently, one radian can be shown to be equal to 57.296 degrees.