  This paper describes the analysis of Lagrange interpolation errors on
tetrahedrons. In many textbooks, the error analysis of Lagrange interpolation
is conducted under geometric assumptions such as shape regularity or the
(generalized) maximum angle condition. In this paper, we present a new
estimation in which the error is bounded in terms of the diameter and projected
circumradius of the tetrahedron. Because we do not impose any geometric
restrictions on the tetrahedron itself, our error estimation may be applied to
any tetrahedralizations of domains including very thin tetrahedrons.
