Angles measure rotation. Degrees divide a full turn into 360 parts and are used in navigation, construction and everyday geometry. Radians measure the angle by the arc length on a circle of radius 1, so a full turn is 2π; mathematics, physics and programming functions such as sin() and cos() expect radians. Gradians split a right angle into 100 and are still found on surveying instruments and calculators.
Use the converter above for any pair. Degrees to radians and back have their own pages with worked examples and tables of common angles.