# Why is an angle dimensionless? [duplicate]

I was trying out Dimensional Analysis on a few equations and realized that angles have no dimension. Otherwise equations such as $s=r\theta$ are not dimensionally consistent.

Further, why don't trigonometric ratios have any dimension?

PS: I couldn't find any appropriate tag for this question. Could someone re tag as appropriate? Thanks.

-

## marked as duplicate by Zev Chonoles, Amzoti, Andrey Rekalo, Danny Cheuk, Alex WertheimJul 12 '13 at 18:56

When doing dimensional analysis on a problem which has an angle as a parameter, you generally find that the solution can involve an arbitrary function of the angle, as in e.g. the problem of how far a ball travels under a gravitational field $g$ if thrown with velocity $v$ at angle $\theta$ (the dimensional analysis solution is $x\propto v^2/g \times f(\theta)$ – Chris Taylor Jan 30 '12 at 10:34