1. A density calculating apparatus comprising: an image data acquisition section that acquires print image data representing a print image to be printed by a first printing system, the first printing system setting print densities of color materials having a plurality of colors and printing an image based on the image data by using the color materials in the print densities; a density acquisition section that acquires the print densities in a second printing system different from the first printing system, the second printing system setting print densities of the color materials having the plurality of colors and printing an image based on the image data by using the color materials in the print densities; a place designating section that designates a place on the print image represented by the print image data acquired by the image data acquisition section; a first color guess section that guesses a print color to be printed by the first printing system on the basis of the print densities of the color materials having the plurality of colors and the image data; a second color guess section that guesses a print color to be printed by the second printing system on the basis of the print densities of the color materials having the plurality of colors and the image data; a target color acquisition section that acquires a print color of the place designated by the place designating section as a target color of the place in the first printing system, by providing the print image data acquired by the image data acquisition section and the print densities acquired by the density acquisition section to the second color guess section; a density calculation section that calculates the print densities of the color materials having the plurality of colors by using the first color guess section so that the target color acquired by the target color acquisition section is achieved at the place by the first printing system based on the print image data; and a storage section that stores a reference color of each patch which is obtained by printing the chart image while setting the print density of the first printing system to a standard print density when a print color of an image to be printed on the basis of a predetermined image data becomes a predetermined standard color, as well as stores a corresponding relationship between a color difference and a density difference, the color difference being a difference between the reference color and a color of each patch obtained by printing the chart image while setting the print density of the first printing system to a series of print densities changed from the standard print density for each of the color materials having the plurality of colors, and the density difference being a difference between the print density and the standard print density, wherein the first color guess section receives the designation of a tentative print density of each of the color materials having the plurality of colors and the place, acquires a relating portion according to the place of the corresponding relationship stored in the storage section, and guesses a print color at the place by performing interpolation processing which uses the reference color of each patch and the relating portion, wherein the interpolation processing includes calculation according to: print color R of a patch approximately obtained as follows: 
 R=R ( std )+ RΔC+RΔM+RΔY+RΔK (1) wherein R(std) is print color of the standard print density, a difference between the colorimetric value of the patch when print density of only C color ink is changed and the colorimetric value of the patch printed with the standard print density is R ΔC , a difference between the colorimetric value of the patch when the print density of only M color ink is changed and the colorimetric value of the patch printed with the standard print density is R ΔM , a difference between the colorimetric value of the patch when the print density of only Y color ink is changed and the colorimetric value of the patch printed with the standard print density is R ΔY , and a difference between the colorimetric value of the patch when the print density of only K color ink is changed and the colorimetric value of the patch printed with the standard print density is R ΔK .