Is there any formula calculates the width and height given the resolution

i would like to know please whether there is a formula through which i can find the width and height of the requested .tiff file given the resolution resx and resy and conversely

This isn’t a question specific to Sentinel Hub. So I would also encourage you to ask on for example.

A quick answer to your question: No, it is not possible. You at least need the bounding box and width and height to be able to deduce the resolution. Read up on the affine transform to learn more how those parameters interplay.

To go from bouding box and width and height to resolution there’s for example this function in rasterio: rasterio.transform module — rasterio 1.4dev documentation

The closest you can get with Sentinel Hub utilities is the bbox_to_dimensions function of the sentinelhub Python library. Please check this first example in the library documentation.