I was clearing out and defragmenting my computer the other day, and I got to thinking about how cool it was that I’ve got so much stuff stored on my hard drive. Over 1000 mp3s, countless Word and Excel files etc etc, all on a disk I could fit into a (fairly large) pocket.
So I started wondering about how much physical space, say, a 5mg mp3 takes up. I realise that the data is often ‘scattered’, but if it was all consolidated? Is it possible to figure such a thing out? What units of measurements would be best to use? I’m not sure I know of one small enough. Nanometer?
I’ve tried a few Google searches, but can’t think of a search string that comes up with anything like what I’m wondering about.
Aereal density of hard drives progresses continuously, but we can go with some averages. The Western Digital 4th generation drives had densities of 4.3 GB per square inch of surface, while the 5th gen ones can be as high as 10.2 GB/square inch (using Giant Magnetoresitive Heads). So, figure if you have a new, top-of-the line drive, about 10.2 GBytes (not bits) per square inch.
So a 5 MB MP3 would take up about 4.9 x 10[sup]-4[/sup] square inches of area.
Use that info to calculate the unused area of a platter.
Subtrace value 4) from value 2) to get the used area of a platter.
Multiply 5) by two for the used area on boths sides of a platter.
Multiply 6) time the number of platters for total used area of all platters.
Divide total storage capacity by 7) to get the storage density.
Divide some file size by 8) to get the area used on the drive.
Be sure to keep your units straight. They can be whatever you want, just stay consistent.
I would recommend doing the physical size measurements in millimeters, and storage in kBytes. This of course will give a density measuremeant in kBytes per square millimeter.
Although the reference I used said “10.2 GBytes” per square inch, since the theoretical limit of magnetic media is near 20 GBits per square inch, I find it likely that instead it was 10.2 GBits per square inch. And thus, assuming 8 bits per byte and a formatted capacity we are talking about, your 5 MB MP3 takes up a larger 3.92x10[sup]-3[/sup] square inches.
Someone else will have to chip in with actual chip sizes for RAM or flash memory, unless I can get to it later on.
One complicating factor is the allocation block size. The various disk format architectures (FAT32, NTFS, HFS+, etc) have a minimum block size. You type one single character in a text file and save it to disk, it gets one of those minimum blocks allocated to the file. Reopen the file and type dozens of sentences and resave it and the file gets no larger on the hard drive because it is still within the bounds of the minimum allocation block size. Add some more and eventually you go over the block limit and the OS allocated the file another block and bang your file is suddenly twice its previous size. (You don’t notice this so much with large files like your single 5 MB mp3 file, but with text files and prefs files and tiny binary library files it makes a lot of difference. It’s also cumulative, if you’re talking about the physical space taken up by all the files on the hard drive, you get a completely different answer if you recalculate how much space would be taken up by the files as data as opposed to how much is taken up by the files as files (which is specific to the drive size and the formatting architecture you’re using, which in turn affects the minimum allocation block size).