The paper presents a computationally accurate and efficient method for calculation of cloud droplets' collision efficiency in a turbulent flow with the properties typical of atmospheric clouds. According to Part III, the statistical properties of a turbulent flow are represented by a set of noncorrelated samples of turbulent velocity gradients and Lagrangian accelerations. Long series of these samples were generated for turbulent parameters typical of different atmospheric clouds. Each sample can be assigned to a certain point of the turbulent flow. Each such point can be surrounded by a small elementary volume with the linear length scale of the Kolmogorov length scale, in which the Lagrangian acceleration and the velocity gradient tensor can be considered uniform in space and invariable in time. For each sample (or an elementary volume), fluxes of droplets of one size onto droplets of another size are calculated both in the presence and absence of hydrodynamical droplet interaction (HDI). In each elementary volume, the collision efficiency is calculated as the ratio of these fluxes. Using a set of the collision efficiency and kernels, the probability distribution functions (PDFs) and the mean values of collision efficiency and collision kernels are calculated under different dissipation rates and Reynolds numbers. It is shown that turbulence significantly increases the collision efficiency, especially for droplets of close sizes and droplet pairs containing a few-microns-radius droplet. The results suggest that the main mechanism by means of which turbulence increases the rate of cloud droplets' collisions is its influence on HDI.