Angles are, by convention, considered to be dimensionless quantities (although the wisdom of this is contested ). As an example, consider again the projectile problem in which a point mass is launched from the origin (x, y) = (0, 0) at a speed v and angle θ above the x -axis, with the force of gravity directed along the negative y -axis. It is desired to find the range R, at which point the mass returns to the x -axis. Conventional analysis will yield the dimensionless variable π = R g / v, but offers no insight into the relationship between R and θ.