Nanofluids can enhance the thermophysical properties of base fluids to increase the efficiency of thermal systems. This study is to develop a new mathematical correlation to predict the thermophysical properties of the copper/damper oil (SAE10W oil) nanofluids. Also, experiments were conducted with varying concentrations of Cu nanoparticles and different temperatures. High-Resolution Scanning Electron Microscopy (HRSEM), Energy-Dispersive X-ray spectroscopy (EDX), and X-Ray Diffractometry (XRD) are done to characterize the Cu nanoparticles. After determining the structure of Cu nanoparticles, the Cu/damper oil nanofluid is prepared through a two-step method. The density and viscosity of the nanofluids are measured according to IS 1448-32 (1992) and ASTM D445-15 standards. The specific heat of nanofluids and thermal conductivity were measured using a thermal constant analyzer. The results demonstrate that Cu nanoparticles significantly improve the thermophysical properties of pure automotive damper oil, enhancing its thermal conductivity from 15.48% to 33.28%. Furthermore, the viscosity of automotive damper oil increases by 79% and 222% with 0.050% and 0.150% volume concentrations, respectively. The density and specific heat changes are also measured and reported. Based on the experimental findings, an empirical correlation is developed through a fitting method to predict the thermophysical properties of these nanofluids. This mathematical correlation accurately calculates the properties of Cu/damper oil nanofluid, with a margin of deviation ranging from −3.7% to 7%.