Calculate image height using file size and width

I'm not very hopeful that this is actually even possible because JPG is a lossy compression format, but I'll ask anyway.

I have some incomplete metadata about an image, and need to figure out the dimensions without loading the file into memory, or using command-line tools like imagemagick.

This is what I know:

• file format is JPG (JPG is an 8-bit image format).
• total file size is 96284 bytes.
• image width is 600 pixels.

Assuming the height could be variable, is there a mathematical equation I can use to calculate the height predictably?

No, there is no relation between the number of pixels and the compressed size.

You can try your luck by analyzing the file header to get the width/height tags. A library like jpeglib allows you to read just the header, but it takes some effort to integrate it.