# How many 400KB files will fit on 1mm^2 surface of hard drive

• I
• Twodogs
In summary: This seems unbelievably high...What is unbelievable, is that mechanical parts move the head that reads this data, while hovering only few nanometers above it.Once you reach a certain threshold, humans stop seeing adding zeros as increases to the order of magnitude and simply start seeing it as a bigger number.We're also still several orders of magnitude from our theoretical limit. One bit,takes about a million atoms to store. About a billion atoms need to line up to make a mm, so in a square mm, you have a quadrillion atoms. A few hundred files a few KB each doesn't look like a lot when you think of it that way.But coming at it with those numbers
Twodogs
Gold Member
Given that 1.34Tbit of information can fit on a square inch of average hard drive surface, how many 400 KB files could be written on a square millimeter? I did the math and came up with about 634. This seems unbelievably high and I wonder if someone would have time to check it. I kind of need to get it right. My thanks.

Twodogs said:
This seems unbelievably high...
What is unbelievable, is that mechanical parts move the head that reads this data, while hovering only few nanometers above it.

Right, hard to imagine. Any clue as to the numbers?

Humans have a hard time imagining just how small things get. Once you reach a certain threshold, humans stop seeing adding zeros as increases to the order of magnitude and simply start seeing it as a bigger number.

We're also still several orders of magnitude from our theoretical limit. One bit,takes about a million atoms to store. About a billion atoms need to line up to make a mm, so in a square mm, you have a quadrillion atoms. A few hundred files a few KB each doesn't look like a lot when you think of it that way.

But coming at it with those numbers I get the capacity to store 3.125 400KB files in one mm^2.
That's compared to my first calculation of over 600. Still hard to imagine, but I wonder what number to go with. The smaller is sufficient to make my point.
Any other insights?

Just an anecdote...
As part of discovery in a legal case, I was once asked to print out three terabytes of ASCII (that's one byte per character!) documents and deliver the hard copy to the lawyers via FedEx overnight service. Eventually the phrase "one hundred fully loaded Boeing 747s" got through to them.

(I knew that I was up against a serious innumeracy problem when they started out by making it quite clear that they wanted everything printed double-spaced, because there was no reason to economize on paper consumption).

Jehannum, jbriggs444, mfb and 1 other person
Twodogs said:
Right, hard to imagine. Any clue as to the numbers?
In post #2 it was said your calc was pretty much correct.

mfb said:
You have some rounding error, but your result is a good approximation. Hard drives have a huge storage density.

If this is homework, it would fit better to our homework section.
Thanks, but no. The problem is I have been out of school for quite some time.

## 1. How do you calculate the number of 400KB files that can fit on a 1mm^2 hard drive surface?

To calculate the number of 400KB files that can fit on a 1mm^2 hard drive surface, you can use the formula: (1mm^2 / 400KB) = number of files. This will give you the maximum number of files that can fit on the hard drive, assuming no other data is stored on it.

## 2. Does the type of hard drive affect the number of 400KB files that can fit on a 1mm^2 surface?

Yes, the type of hard drive can affect the number of 400KB files that can fit on a 1mm^2 surface. Different hard drives have different storage capacities, so the number of files that can fit will vary.

## 3. Is the 1mm^2 surface of a hard drive the same as its storage capacity?

No, the 1mm^2 surface of a hard drive refers to its physical size, while its storage capacity is measured in bytes or kilobytes. The number of 400KB files that can fit on a 1mm^2 surface is determined by the storage capacity of the hard drive.

## 4. Can the number of 400KB files that fit on a 1mm^2 hard drive surface change over time?

Yes, the number of 400KB files that can fit on a 1mm^2 hard drive surface can change over time. As technology advances, hard drives with larger storage capacities are developed, allowing for more files to be stored on the same surface area.

## 5. Are there any other factors that can affect the number of 400KB files that can fit on a 1mm^2 hard drive surface?

Yes, there are other factors that can affect the number of 400KB files that can fit on a 1mm^2 hard drive surface. For example, if the hard drive has already been used to store other data, the available space for 400KB files will decrease. Additionally, the format and organization of the files can also impact the number that can fit on the surface.

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