The exciton-light coupling is an important characteristic quantitatively described by the radiative decay rate. Recent experimental studies of the radiative decay rate for high-quality quantum wells show a variance of the experimental data especially for narrow quantum wells. Therefore, the theoretical and numerical studies of the exciton-light coupling as an overlap of the light wave and the exciton wave function are of significant interest. In this paper, we present the radiative decay rates obtained for excitons in the GaAs-based quantum wells of various widths from 1 nm up to 100 nm. The exciton wave function is calculated by the direct numerical solution of the three-dimensional Schrödinger equation. The precise results for the lowest exciton state are obtained by the Hamiltonian discretization using the finite-difference scheme. The numerical results are compared with the experimental data extracted from the reflectance spectroscopy measurements for high-quality GaAs/AlGaAs and InGaAs/GaAs heterostructures.