Clinching is an economical sheet joining technique that does not require any consumables. Besides, after its usage, the joints can be recycled without much difficulty, making clinching one of the most sustainable and eco-friendly manufacturing processes and a topic of high research potential. In this work, the influence of surface roughness on the load-bearing capacity (strength) of joints made by the mechanical clinching method in cross-tensile and lap-shear configuration is explored. Additionally, a correlating mathematical model is established between the joint strength and its surface parameters, namely, friction coefficient and wrap angle, based on the belt friction phenomenon. This correlation also explains the generally observed higher strength in lap-shear configuration compared to cross-tensile in clinching joints. From the mathematical correlation, through friction by increasing the average surface roughness, it is possible to increase the strength of the joint. The quality of the thus produced joint is analyzed by cross-sectional examination and comparison with simulation results. Experimentally, it is shown that an increment of >50% in the joint strength is achieved in lap-shear configuration by modifying the surface roughness and increasing the friction coefficient at the joint interface. Further, the same surface modification does not significantly affect the strength in cross-tensile configuration.