  Let $X$ be a smooth projective toric variety over $Spec(Z)$. Let
$\bar{\mathcal{O}(D)}$ be an equivariant hermitian line bundle on $X$, equipped
with a positive metric and invariant under the action of the compact torus of
$X(C)$, we provide a formula for the arithmetic volume in term of
Fenchel-Legendre transform attached to the metric.
