We propose a new way to determine weak repulsive forces operative between colloidal particles by measuring the rate of slow coagulation. The rate of slow coagulation is directly related to the competition of the repulsion with thermal motion. Since the thermal forces are weak, measurements of the coagulation rate can lead to precise information on repulsive potentials having a magnitude of just a few kT. We demonstrate this novel way by studying colloidal spherical polyelectrolyte brush (SPB) particles in aqueous solution containing trivalent La3+ counterions. The particles consist of a monodisperse polystyrene core of 121 nm radius from which linear sodium poly(styrenesulfonate) (PSS) chains are densely grafted (contour length 48 nm). We determine the rate of coagulation by time-resolved simultaneous static and dynamic light scattering in the presence of LaCl3 (0.2 to 150 mM). Direct measurements of the repulsive force between macroscopic brush layers demonstrate that the potential is decaying exponentially with distance. This is in good agreement with a simple theoretical treatment that furthermore leads to the effective surface potential Psi0. The good agreement of data obtained by the novel microscopic method with direct macroscopic measurements underscores the general validity of our approach.