Abstract In this paper we calculate the field equations for Scalar-Tensor from a variational principle, taking into account the Gibbons-York-Hawking type boundary term. We do the same for the theories f ( R ), following (Guarnizo (2010), Gen. Rel. Grav. 42 , 2713–2728). Then, we review the equivalences between both theories in the metric formalism. Thus, starting from the perturbations for Scalar-Tensor theories, we find the perturbations for f ( R ) gravity under the equivalences. Working with two specific models of f ( R ), we explore the equivalences between the theories under conformal-Newtonian gauge. Further, we show the perturbations for both theories under the sub-horizon approach.