Reverend Jim thought that you were talking about 4K as in 4 kilobytes (or 4KB), and by that measure, the size of a 4KB file is, well, 4 * 1024
bytes. He simply did not realize you were talking about that new ultra-high-definition format for video and televisions that is commonly called "4K", which refers to the fact that it has 4 times the resolution of 1080p video.
Since 4K is 4 times more pixels than 1080p, then a rough approximation of the file sizes will be 4 times that of an equivalent 1080p video file. But, of course, most video compression methods aim to achieve as much compression as possible without negatively affecting the quality of the picture, i.e., it merges frames or parts of the frames that are static of several video frames (e.g., a static background), and also compresses groups of pixels that have nearly identical color values (e.g., making bigger pixels). So, when the resolution is as high as 4K, there is probably a lot more opportunity for compression too, i.e., when the resolution is higher quality than what you can perceive with your naked eyes, it can compress a lot before you notice any difference. So, I would say that it might not be as much as 4 times the size of 1080p video, maybe as low as 2 times bigger, or even less, depending on the encoding quality settings.