||In order to study the hardness of material, it is possible to use Vickers or Knoop tests. This tests differ by the shape of their indenters, square base pyramid for Vickers and lozenge base for Knoop. The hardness numbers, which are obtained, are nearly the same but may differ substantially for high hardness. In order to explain this difference some authors have proposed various expressions associated to the elastic properties of the material. Unfortunately, this methodology is not correct. In fact, Vickers hardness is based on the ratio between the applied load and the true area of contact when the Knoop hardness considers the projected area. Here, we propose to modify the Knoop expression in accordance with the Vickers definition. In these conditions, the conversion relation, which is obtained between the two expressions, allows to represent much better the true behavior of the material. This procedure is applied and validated on various literature and laboratory experimental data.