A tetrahedral interpolation calculation method and apparatus, a gamut conversion method and apparatus, and a medium are provided, the tetrahedral interpolation calculation method comprising: obtaining coordinates of an interpolation point in a sampling space, a side length of a cube formed of nearby eight sampling points surrounding the interpolation point in the sampling space, and mapping values of four vertices of a tetrahedron surrounding the interpolation point, wherein the four vertices are four out of the eight sampling points; calculating a volume of the tetrahedron, and volumes of four sub-tetrahedrons formed of the interpolation point and arbitrary three vertices in the tetrahedron, based on coordinates of the interpolation point in the sampling space, and the side length of the cube formed of nearby eight sampling points surrounding the interpolation point in the sampling space; and obtaining an interpolation value of the interpolation point, based on a tetrahedral interpolation theorem formula, the volume of the tetrahedron, volumes of four sub-tetrahedrons, and mapping values of the four vertices of the tetrahedron.