Fragment velocity is an important parameter for fragmentation warheads, but for an asymmetrically initiated warhead, formulas for calculating the fragment velocity in the aiming direction are rare. In this work, new formulas for calculating fragment velocities in the aiming direction and the initiation side of an asymmetrically initiated warhead were established by taking the long element from the warhead section and applying one-dimensional gas dynamics. Accounting for the assumptions made during the formulas establishing, three experimentally verified warheads modelling of different charge ratios were used to verify the formulas. It is found that the velocity ratios of the modelling to the formulas' calculations of different warheads are very similar. Hence the fitted curves for the velocity ratios versus the warhead charge ratios were used as correction factors for the established formulas. Finally experiments were designed and conducted to validate the revised formulas, which shows acceptable relative errors of 2.8% and 9.9%, better than already existing formulas. The established formulas could be a good reference for the damage evaluation of aimable warheads and for fragment velocity distribution research.