  In the asymptotic limit of a large Ginzburg-Landau parameter, we give a new
asymptotic formula for the $L^2$-norm of the Ginzburg-Landau order parameter.
The formula is valid in the bulk regime where the intensity of the applied
magnetic field is of the same order as the Ginzburg-Landau parameter and
strictly below the second critical field. Our formula complements the
celebrated one of Sandier-Serfaty for the $L^4$-norm.
