“Distance” (or angular magnitude) between two quaternions?

Question

I want to find the \"distance\" between two quaternions. By \"distance\" I mean a single float or int, not another quaternion (that would be the difference, i.e. inverse(q

Answer 1

Find the difference quaternion qd = inverse(q1)*q2).

Than find the angle between q1 and q2 by angle = 2 * atan2(qd.vec().length(), qd.w()) // NOTE: signed

The "angle" here, is the angle of rotation from q1 to q2 by shortest arc.