Abstract: Fragmentation velocity increments were an important character for breakup events intensity which decided the fragmentation debris orbit distribution and breakup nature. In this paper two means were given for the fragmentation velocity increments. One is orbit position propagation means, the other is orbit plane intersection means which was introduced in details. Orbit position propagation means is that velocity increments are computed by orbit velocity changes before and after the breakup; Orbit plane intersection means is that the velocity increments are computed with breakup spherical triangle for the parent and debris, the changes of breakup debris inclination and right ascension of ascending node, and the parent orbit's inclination and argument of perigee at the breakup epoch. The breakup epoch and velocity increment is then obtained. Compared with the two means, orbit position propagation means is suitable to fragmentation events with high quality data and high fragmentation altitude; orbit plane intersection means is suitable even if the fragmentation altitude is low and the orbit data is lagged more. This paper introduced the means and principle of computing breakup velocity increments, compared and discussed the applicability of the two means in detail. Based on the two means, fragmentation epoch and three velocity increments components in space were given for three past breakup events with two-line element data.