We construct a covariant bound on the energy-momentum of the M-fivebrane wh
ich is saturated by all supersymmetric configurations. This leads to a gene
ralised notion of a calibrated geometry for M-fivebranes when the worldvolu
me gauge field is non-zero. The generalisation relevant for Dp-branes is al
so given. (C) 1999 Published by Elsevier Science B.V. All rights reserved.