They are both angle measure units. To visualize a degree, think of a wheel with 360 evenly spaced spokes from the center to the rim. The angle in between each spoke measures one degree. The radian is a more naturally derived angle measure unit. One radian is the central angle cut out of a circle when the arc of that angle (on the circle) measures the same as the measure of the radius of the circle. In calculus involving trigonometry, radian measure is always used. Any rotational velocity or acceleration problems (angular velocity or acceleration) are well-done with radians. Since there is the length of 2*pi*radius around a circle, there is a radian measure of the central angle all around a circle equal to 2*pi radians. Also since halfway around the circle is either 180 degrees OR pi radians, you can say that the measure of one radian is equal to (180/pi) degrees. That's a little bit over 57 degrees.
