Data Speed and Size Calculation

From Retro Arcade Guides

Usually, data connection speeds are measured in bits (and its multiples) and file sizes are measured in bytes (and its multiples).

Bits and Bytes

The bit is the smallest unit of information. A bit can have only two different values, commonly called "0" and "1".

With 4 bits, there are only 16 different possible values (remember that 24 = 16):

Bit 1 Bit 2 Bit 3 Bit 4 Value
0 0 0 0 0
0 0 0 1 1
0 0 1 0 2
0 0 1 1 3
0 1 0 0 4
0 1 0 1 5
0 1 1 0 6
0 1 1 1 7
1 0 0 0 8
1 0 0 1 9
1 0 1 0 10
1 0 1 1 11
1 1 0 0 12
1 1 0 1 13
1 1 1 0 14
1 1 1 1 15

One byte is a set of 8 bits. Thus, a byte can have only 256 different values (remember that 28 = 256).


Two examples of calculations follow:

Example 1
My internet download speed is 100 megabits per second. I can download up to 12.5 megabytes per second (because 100 / 8 = 12.5).
Example 2
To download at my hard disk's top speed, which is 55 megabytes per second, my internet download connection must be of at least 440 megabits per second (because 55 x 8 = 440).


Multiples

In most units, multiples are in powers of 10. For example, 1 kilometer = 1,000 meters (note that 1,000 = 103).

But for binary data, multiples are in powers of 2. For example, 1 megabyte = 1,024 kilobytes (note that 1,024 = 210).

On the table below, the byte multiples are listed with their absolute values in bytes:

Unit Unit
Abbreviation
Bytes
(in powers of 2)
Bytes
(full number)
Byte B 20 1
Kilobyte KB 210 1,024
Megabyte MB 220 1,048,576
Gigabyte GB 230 1,073,741,824
Terabyte TB 240 1,099,511,627,776
Petabyte PB 250 1,125,899,906,842,624
Exabyte EB 260 1,152,921,504,606,846,976
Zettabyte ZB 270 1,180,591,620,717,411,303,424
Yottabyte YB 280 1,208,925,819,614,629,174,706,176

The abbreviations of bit multiples are just like the abbreviations of byte multiples of the table above, but with lowercase B instead. Example: megabit → Mb.

Also from the table above, note that each unit times 1,024 is equal to the next larger unit. A simpler table can be written as below:

Byte Multiples Bit Multiples
1 kilobyte = 1,024 bytes 1 kilobit = 1,024 bits
1 megabyte = 1,024 kilobytes 1 megabit = 1,024 kilobits
1 gigabyte = 1,024 megabytes 1 gigabit = 1,024 megabits
1 terabyte = 1,024 gigabytes 1 terabit = 1,024 gigabits
1 petabyte = 1,024 terabytes 1 petabit = 1,024 terabits
1 exabyte = 1,024 petabytes 1 exabit = 1,024 petabits
1 zettabyte = 1,024 exabytes 1 zettabit = 1,024 exabits
1 yottabyte = 1,024 zettabytes 1 yottabit = 1,024 zettabit


Some examples of calculations:

Example 1
A certain torrent collection is 3.19 terabytes. That's equal to 3,266.56 gigabytes (that's 3.19 x 1,024) or 0.003115234 petabyte (that's 3.19 / 1,024).
Example 2
I have 900 GB uploaded, so I need to upload more 124 GB to get to 1.0 TB of upload (because 1,024 GB - 900 GB = 124 GB).
Example 3
I have 9.90 TB uploaded, so I need to upload more 102.4 GB to get to 10.00 TB of upload (because 0.10 TB x 1,024 = 102.4 GB).
Example 4
I have uploaded 10 TB and downloaded 100 GB. Because Share Ratio is the Upload divided by the Download and I can only divide numbers of the same multiple, my Ratio is 10 x 1,024 / 100 = 102.4.


Media Sizes

Follows a table with the most common media and their approximate capacities:

Media Capacity
(in bytes)
Capacity
(readable)
3.5-inch High Density Floppy Disk 1,457,664 1.39 MB
CD 737,280,000 703 MB
DVD - 1 layer 4,707,319,808 4.38 GB
DVD - 2 layers 8,543,666,176 7.96 GB
Blu-ray - 1 layer 25,025,314,816 23.31 GB
Blu-ray - 2 layers 50,050,629,632 46.61 GB
Blu-ray - 3 layers 100,103,356,416 93.23 GB
Blu-ray - 4 layers 128,001,769,472 119.21 GB

The table above can be used with simple Mathematics concepts to plan how many media is needed to backup data:

Example
Question: How many 2-layer Blu-ray discs do I need to backup 3.19 TB of data?
Answer: Because 3.19 x 1,024 / 46.61 = 70.08, you would need 71 discs.


Online Calculators

There are multiple calculators of bandwidth and file transfers on the internet. Some are linked below:


https://coderstoolbox.net/network/bandwidth.php

https://techinternets.com/copy_calc

https://www.calculator.net/bandwidth-calculator.html

https://www.expedient.com/file-transfer-time-calculator/


Reference