No lesson in how to calculate pixel count here or its relevance to a computer screen size; plenty of websites exist that do a fine job.
Remember that the primary reason I make compressed copies of an already compressed Jpeg is for ease of e-mailing. Here, the extra "compression" I am talking about is actually a combination of resizing and sacrificing some quality (removing detail). This is because absolute quality is not important for the casual viewing performed on e-mailed photos to friends and family, but being able to cram a ton of photos in to a single e-mail without killing someone's in-box, is. A fair amount of quality loss is therefore acceptable so long as the photo still looks "nice" on screen; reasonable colours and textures, no easily seen pixelation, and no huge black borders around the edge when seen native size. I have chosen a default "long edge" of 1280 pixels since this will reasonably fill large monitors without being too wasteful on tiny ones of lower horizontal pixel count than this. In this case Jpegs that start out at 6-11 MB end up between 90 and 150 kb depending on the amount of detail in the photograph. A massive reduction. This file size is much the same either using the "RW" tool I mentioned above that I have been using for batch compression or the XP Powertoy Jpeg resizer.
Another reason for compressing is the speed of 802.11g WiFi browsing (through that massively lower file size) that I mentioned. It's my wife that does this most often and she is running a Asus 1000H netbook with 10" 1024x600 pixel screen of distinctly average colour and texture rendering ability. Here, those teeny weeny resized photos with a ton of detail removed look indistinguishable from the massive originals. On my HD 1920x1080 monitor of course they look poor compared to the the originals, but this is an irrelevance!
If you are using MS Windows and have similar needs to those described above, download the Power Toy suite from
here and try the image resizer. It works from right mouse button in Windows Explorer.
HTH