We say that two groups are orbit equivalent (OE) if they both act on a same probability space with the same orbits. A famous result of Ornstein and Weiss states that all infinite amenable groups are orbit equivalent to Z. In other words: orbit equivalence does not take into account the geometry of groups. For this reason Delabie, Koivisto, Le Maître and Tessera suggested to refine this relation with a quantitative version of OE. They obtain obstructions to the existence of such equivalence using isoperimetric profile. After defining the quantitative version of OE we will focus in this talk on the ?inverse problem?, namely: can we find a group that is OE to a prescribed group with prescribed quantification? Using the diagonal products introduced by Brieussel and Zheng we will answer this question in the case of a prescribed OE with Z. If times permits we will also discuss the optimality of the quantification and talk about measure equivalence.