Macro for degree symbol

Maybe it’s a good alternative to use siunitx

\documentclass{minimal}
\usepackage{siunitx}
\begin{document}
    Works in text \ang{45} an in math $\ang{2.4}$.
    Even with minutes and seconds: \ang{40;12;08}.
\end{document}

It also gives you the oportunity to set all numbers in the same style an change it globally if it’s requested, e. g. changing from period to comma: 1.234 --> 1,234

Edit: To type radians just use the \radian unit. One may likes to define an own macro.

\documentclass{scrartcl}
\usepackage{siunitx}
\newcommand{\rad}[1]{\SI{#1}{\radian}}
\begin{document}
    \SI{\pi}{\radian}
    \rad{\pi/2}
\end{document}

Anything wrong with textcomp's \textdegree?

I prefer this solution

\renewcommand{\deg}{\ensuremath{^{\circ}}\xspace}

because it also works in math mode. (At least for me, \textdegree does not work in math mode, i.e.

$> 30\textdegree$

does not work, but

$> 30\deg$

does.