We introduce a jet shape observable defined for an ensemble of jets in terms of two-particle angular correlations and a resolution parameter R. This quantity is infrared and collinear safe and can be interpreted as a scal- ing exponent for the angular distribution of mass inside the jet. For small R it is close to the value 2 as a consequence of the approximately scale invariant QCD dynamics. For large R it is sensitive to non-perturbative effects. We describe the use of this correlation function for tests of QCD, for studying underlying event and pile-up effects, and for tuning Monte Carlo event generators. Show Partial Abstract