1. A projection system comprising: a plurality of projection units configured to project an image on a projection body; a taken image preparation unit configured to prepare a plurality of calibration-use images; an extraction unit configured to extract, from each of the plurality of calibration-use images, at least grating points indicating a distortion in a projected image of one of the plurality of projection units and alignment points of the projected image of the one of the plurality of projection units or a projected image of another one of the plurality of projection units; a conversion unit configured to convert, onto a common coordinate system, the grating points of the projected images of the plurality of projection units extracted from the plurality of calibration-use images by the extraction unit, based on alignment points common to the plurality of calibration-use images; and a geometric correction coefficient calculation unit configured to calculate a geometric correction coefficient for providing a projection image to be projected from the plurality of projection units, based on the grating points on the common coordinate system.