A universal function is proposed to describe REAPDOR dephasing curves of an observed spin-1/2 nucleus dipole-recoupled to a spin-1 quadrupolar nucleus (2H or 14N). Previous work had shown that, in contrast to REDOR, the shape of the dephasing curve depends on a large number of parameters including the quadrupolar coupling constant and asymmetry parameter, the sample rotation speed, the RF amplitude, and the relative orientations of the quadrupole tensor and the internuclear vector. Here we demonstrate by numerical simulations that the actual dispersion of REAPDOR dephasing curves is quite small, provided the rotation speed and the RF amplitude applied to the quadrupolar nucleus satisfy an adiabaticity condition. The condition is easily met for 2H and is also practically achievable for virtually any 14N-containing compound. This allows the REAPDOR curves to be approximated by a simple universal gaussian-type function, comparison of which with experimental data yields internuclear distances with less than 4% error. The spin dynamics of the recoupling mechanism is discussed. The critical importance of a stable spinning speed for optimizing the signal-to-noise ratio of the 13C echoes is demonstrated and practical suggestions for achieving high stability are presented. Examples of applications of the universal curve are given for 2H/13C and 14N/13C REAPDOR in alanine.