  We introduce a new measurable quantity, $R_{\Delta \phi}$, for studies of the
rapidity and transverse momentum dependence of dijet azimuthal decorrelations
in hadron-hadron collisions. In pQCD, $R_{\Delta \phi}$ is computed as a ratio
of three-jet and dijet cross sections in which the parton distribution
functions cancel to a large extent. At the leading order, $R_{\Delta \phi}$ is
proportional to $\alpha_s$, and the transverse momentum dependence of can
therefore be exploited to determine $\alpha_s$. We compute the NLO pQCD theory
predictions and non-perturbative corrections for $R_{\Delta \phi}$ at the LHC
and the Tevatron and investigate the corresponding uncertainties. From this, we
estimate the theory uncertainties for $\alpha_s$ determinations based on
$R_{\Delta \phi}$ at both colliders. The potential of $R_{\Delta \phi}$
measurements for tuning Monte Carlo event generators is also demonstrated.
