What is the radian equivalent of 360 degrees?

The radian equivalent of 360 degrees is 2π radians. This relationship stems from the definition of the radian, which is the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle. Since a full circle encompasses 360 degrees and also corresponds to 2π radians, it follows that 360 degrees and 2π radians represent the same angular measurement.

In the context of converting degrees to radians, the conversion factor is π radians for every 180 degrees. Therefore, to convert 360 degrees to radians:

360 degrees × (π radians / 180 degrees) = 2π radians.

This clear mathematical relationship showcases why 2π is the correct radian equivalent of a full circle measured in degrees.