I want to calculate the angle between two vectors a and b. Lets assume these are at the origin. This can be done with theta = arccos(a . b / |a| * |b|) However arccos gives you the angle in [0, pi], i.e. it will never give you an angle greater than 180 degrees, which is what I want. So how do you find out when the vectors have gone past the 180 degree mark? In 2D I would simply let the sign of the y-component on one of the vectors determine what quadrant the vector is in. But what is the easiest way to do it in 3D?