Conventional formula for a Gaussian beam propagating in a homogeneous slab waveguide can be derived by solving the Helmoholtz equation with the paraxial approximation. Based on the Kirchhoff diffraction theory, a more accurate formula is derived. The quantitative error of the conventional formula is analyzed and a modification is given to improve the accuracy. The accuracy of the modified formula is verified by a numerical simulation with finite difference-beam propagation method (FD-BPM). The modified formula can be used to simplify the design and simulation for integrated photonic devices such as arrayed waveguide grating (AWG) and etched diffraction grating (EDG).