When using Camera Calibration Toolbox or OpenCV camera calibration, we are asked to provide the size of width and height of a grid in the the chessboard. So we measure the length with a ruler (in millimeter or meter) and type the length into the program.
When the measured width and height of a grid are 25 mm and 25 mm, what will happen if we provide the width and height as 2500 mm and 2500 mm (which are wrong and hundred times bigger than the real size) respectively to the program. The answer is that it does not make any difference to the intrinsic parameter values and this implies the unit of focal length as the output of calibration software above is NOT mm or meter BUT pixels. (Actually it affects only translation, that is, part of extrinsic parameters of each camera frame, which is unimportant calibration results). This also implies that if the image size (resolution) is big enough, it is OK to use a small chessboard such as the one printed on a A4 paper sheet.
This also means it is up to scale, that is, when the actually measured width and height are 25 and 50 mm respectively, it is okay to provide such a pair of scaled values (250, 500), (25000, 50000) , (1, 2) or (0.001, 0.002) as long as the ratio of width and height is the same as that of the real size (here 1 : 2).
What if, we provide the width and height value whose ratio is not the same as the measured one? In other words, if we provide 250 and 750 as the width and height of grid (ratio 1 : 3), the program will not run properly giving complain or very strange intrinsic parameters. Because with a chessboard of grid ratio 1 : 3, it might be impossible to get such images (of chessboard with ratio 1 : 2) taken by the camera to be calibrated.