All spacecraft are subject to the possibility of high-speed particle impacts during their mission life. Such high-speed impacts on spacecraft surfaces create debris clouds that travel towards and eventually impact other downstream spacecraft components. In addition to the impulsive load that such debris clouds would deliver, the largest fragment in these debris clouds also poses a significant threat to those spacecraft elements. In order to be able to assess the severity of the threat posed by such a fragment, it is important to be able to predict the size of this largest fragment and its associated velocity. In this paper, we develop empirical equations that can be used to predict these quantities in terms of the material properties of the surface that sustains the initial impact, the characteristics that define the impact event and the material properties of the impacting projectile.