In this article, we propose a simple method to calculate electrical permittivity and refractive index of surface agents of gold nanoparticles (Au NPs), in which it is possible to find the refractive index of surface agents shell by using the absorption peak of the gold nano-colloid. One of the usual tests for detection of surface agents is colorimetric methods based on the change of color of Au NPs. The color change is mainly due to the shift of localized surface plasmon resonance which is related to electrical interactions of surface agents. Although there are many mathematical models for simulating the absorption spectrum and calculating the plasmonic peak, using them is not simple and possible for everyone due to the need for programming. Here, the necessary simulations have been performed for different values of refractive index of surface agents and particle size, and absorption peaks have been obtained. Using numerical methods, a simple formula is obtained between the wavelength of plasmonic peak, the ratio of hydrodynamic diameter to Feret size of the particles, and the refractive index of the surface agents. This method can help researchers to obtain the refractive index and consequently the type or concentration of surface agents around Au NPs without the need for programming or complex mathematical operations. It can also open new horizons in analyzing colorimetric diagnosis of biological agents such as viral antibodies, antigens, and other biological agents.