Based on the results of sediment hidden degree research, an incipient velocity formula with hidden degree as its parameter was deduced in this paper using the rolling model of sediment incipient motion. The formula was applied in limit analysis and monotonicity analysis to theoretically expound the physical phenomena of incipient motion and to demonstrate the starting characteristic of broadly graded non  uniform cohesionless sediment. The numerical relations between hidden degree and non-dimensional incipient shear stress were established via the analysis on incipient motion criterion and the characteristic of hidden degree distribution of cohesionless sediment particles. Finally, former research achievements are taken to manifest the applicability of this incipient velocity formula.