The Vickers microhardness H-V of the (110) and (111) as-grown faces of lithium dihydrogen phosphate (LDP) crystals was investigated as a function of applied load P. The microhardness H-V of the two faces increases with load P i.e. reverse indentation size effect (reverse ISE) and the hardness of the (110) face is somewhat lower than that of the (111) face but this difference is not easily recognized for these planes due to large scatter in the data. The origin of observed ISE was analyzed using different approaches. It was found that: (1) Hays-Kendall's and Begley-Hutchinson's relations do not explain the origin of reverse ISE but Meyer's law describes the reverse ISE satisfactorily and its constants provide a link between ISE and formation of radial cracks with applied indentation load P, (2) reverse ISE is associated with tensile surface stresses, (3) despite its failure to explain reverse ISE, Begley-Hutchinson's relation is reliable to obtain load-independent hardness H-0, is 2337 MPa for LDP, and (4) the value of fracture toughness K-C of LDP crystals lies between 4.7 and 12 MPa m(1/2). The load-independent hardness H-0 of LDP is higher by a factor of 1.5 than that reported for undoped KDP and ADP crystals whereas its fracture toughness K-C is higher by factor of about 20 than that of undoped KDP crystals. (C) 2015 Elsevier B.V. All rights reserved.