A system and method for making custom boxes for objects of random size or shape includes physical measurement apparatus having two or more mutually orthogonal surfaces, each surface including a plurality of computer-readable codes representing distances to one of the other surfaces. At least one object is placed or transferred into apparatus so as to contact as many of the surfaces as possible. The codes are read on each surface to determine the greatest physical extent of the object in multiple dimensions, and the dimensions are delivered to a carton making machine to construct a custom carton to accommodate the object in the multiple dimensions. The physical measurement apparatus preferably includes a primary horizontal surface and two upstanding vertical surfaces, and the computer-readable codes are scannable bar codes arranged as matrices on each surface.