  Let $L$ be a line bundle on a proper, geometrically reduced scheme $X$ over a
non-trivially valued non-Archimedean field $K$. Roughly speaking, the
non-Archimedean volume of a continuous metric on the Berkovich analytification
of $L$ measures the asymptotic growth of the space of small sections of tensor
powers of $L$. For a continuous semipositive metric on $L$ in the sense of
Zhang, we show first that the non-Archimedean volume agrees with the energy.
The existence of such a semipositive metric yields that $L$ is nef. A second
result is that the non-Archimedean volume is differentiable at any semipositive
continuous metric. These results are known when $L$ is ample, and the purpose
of this paper is to generalize them to the nef case. The method is based on a
detailed study of the content and the volume of a finitely presented torsion
module over the (possibly non-noetherian) valuation ring of $K$.
