  The treatment of angles within the SI is anomalous compared with other
quantities, and there is a case for removing this anomaly by declaring plane
angle to be an additional base quantity within the system. It is shown that
this could bring several benefits in terms of treating angle on an equal basis
with other metrics, removing potentially harmful ambiguities, and bringing SI
units more in line with concepts in basic physics, but at the expense of
significant upheaval to familiar equations within mathematics and physics. This
paper sets out the most important of these changes so that an alternative unit
system containing angle as a base quantity can be seen in the round,
irrespective of whether it is ever widely adopted. The alternative formulas and
units can be treated as the underlying, more general equations of mathematical
physics, independent of the units used for angle, which are conventionally
simplified by implicitly assuming that the unit used for angle is the radian.
