Passive micro-mixers are indispensable components within microfluidic systems, and this research delves into the nuanced interplay of various design parameters on the mixing efficiency of a Koch fractal micro-mixer with rounding corners (RCSM). The study systematically examines cross-sectional shapes, inlet angles, obstacles, and 3D printing methods to unravel their collective impact. The Design of Experiment (DoE) methodology proves instrumental, allowing for the simultaneous exploration of these parameters. Computational Fluid Dynamics (CFD) simulations serve as the experimental platform, showcasing that the RCSM micro-mixer, characterized by a trapezoid cross-section and a 180° inlet angle, attains peak mixing efficiency (0.976) when devoid of obstacles and utilizing the SLA 3D printing method. Notably, the research underscores the preeminent influence of the 3D printing method on mixing efficiency, followed by the inlet angle, cross-sectional shape, and the presence of obstacles. This comprehensive exploration advances our understanding of passive micro-mixer dynamics, offering valuable insights for optimizing microfluidic systems in diverse applications, from medical diagnostics to chemical analyses.