Three-dimensional table interpolation techniques are now widely used in color management systems. These techniques are practical because complicated color conversions such as gamma conversion, matrix masking, under color removal, or gamut mapping can be executed at once by use of a three-dimensional lookup table (3D LUT). However, in some cases, the resultant interpolated reproduction of gradation has visible artifacts that degrade neutral and color gradations. Several research works concerning interpolation accuracy have been published. However, those articles have focused on an average color difference derived from experiments based on very few types of color conversions with no theoretical explanation. This paper describes a theoretical evaluation of errors and reproduced gradation curves using three-dimensional interpolation for several nonlinear color conversions. Two types of errors; conventional error and ripple error that is difference between piece-wise linear approximation and interpolated curves are defined, and gray gradation is used for an input image. The errors with a tetrahedral interpolation technique are also examined. Several nonlinear color conversions are tested and significant ripples have been found in case of the matrix-gamma with negative coefficients and minimum (MIN) function. The error goes down with decreasing of the distance between the lattice points (D), however, the decreasing rate is quite different. From these analyses we can get useful information about optimal 3D LUT sizes and which conversions are suitable for three-dimensional interpolation.