The optimization of grating couplers is usually realized by multiple simulations using specific computational software for this task. Many grating parameters must be analyzed and designed to get the maximum coupling efficiency and the transmission spectrum centred at the wavelength of operation. However, these simulations may take a long time and consume high computational resources depending on the simulation resolution. This work is focused on finding a method to optimize the grating parameters with the lowest number of simulations. In this way, closed-form expressions are presented to get the optimal values for the period and fill-factor, which are the main parameters in the grating design. The usefulness of the proposed approach is shown for the design of silicon grating couplers operating at 1.31 µm and 1.55 µm and both TE and TM polarizations.