In this paper, we have synthesized zinc oxide (ZnO) nanoparticles using the sol–gel method. Zinc acetate dihydrate ({text{Zn(C}}{{{text{H}}}_{3}}{text{C}}{{{text{O}}}_{2}}{{{text{)}}}_{2}}cdot2{{{text{H}}}_{2}}{text{O}}), sodium hydroxide (NaOH) were used as a basic precursors for the synthesis. The synthesized crystalline powder was characterized by X-ray diffraction (XRD). The XRD studies explain that zinc oxide nanoparticles have a single phase with a wurtzite hexagonal structure. The theoretically calculated lattice parameters have obtained using the famous Scherrer equation and agree well accordance with the standard JCPDS card number. Various relevant physical parameters such as micro-strain, stress, energy density, and crystalline size have calculated by using the modified Williamson–Hall (W–H) assuming uniform deformation (UD) model, uniform stress deformation (USD) model and uniform deformation energy density (UDED) model. The root mean square (rms) lattice strain (leftlangle {{{varepsilon }_{{{text{rms}}}}}} rightrangle ) theoretically calculated from the interplanar spacing and strain estimated obtained the USD and UDED models are different due to consideration of anisotropic crystal nature. The obtained results shows that the average particle size of zinc oxide nanoparticles from Scherrer’s formula and the W–H method are the best intercorrelated. All the calculated physical parameters from the Willamson–Hall plot are tabulated, compared, and found to match well the value of bulk zinc oxide. Similarly for the synthesized ZnO nanoparticles, the optical properties were analyzed by UV-vis spectroscopy which confirmed the bandgap energy.