It is generally observed in the literature, that the Knoop hardness number is lower than the Vickers hardness number, in particular for ceramics. This difference is due, on the one hand to the elastic recovery occurring during the removal of the Knoop indenter, and on the other hand to the difference between the representatives areas considered in each hardness calculation formula. In this work, conventional hardness tests with Knoop and Vickers indenters were carried out in order to show how Knoop hardness test can give the same hardness number obtained by Vickers hardness test. This is obtained when Knoop hardness number is calculated based on the residual plastically deformed area whether projected or true. Complementary hardness data obtained from the literature were used in this work in order to validate the method we proposed. A revision of the wellknown relation of Marshall is also proposed in order to determine the elastic modulus by means of one Knoop hardness test when the Vickers hardness is unknown.