IEC/SI-Units bits Bytes Meaning/purpose ============ ========== ========== ===================================== kb 1000 125 thousand bits (kilo bits) Kib 1024 128 2^10 bits (Kilo bits or Kibi bits) kB 8000 1000 thousand Bytes (kilo Bytes) KiB 8192 1024 2^10 Bytes (Kilo Bytes or Kibi Bytes) Mb 1000000 125000 million bits (mega bits) Mib 1048576 131072 2^20 bits (Mega bits or Mebi bits) MB 8000000 1000000 million Bytes (mega Bytes) MiB 8388608 1048576 2^20 Bytes (Mega Bytes or Mebi Bytes) Gb 1000000000 125000000 billion bits (giga bits) Gib 1073741824 134217728 2^30 bits (Giga bits or Gibi bits) GB 8000000000 1000000000 billion Bytes (giga Bytes) GiB 8589934592 1073741824 2^30 Bytes (Giga Bytes or Gibi Bytes) and so on ...
There is a big difference between b for bits and B for Bytes -- by a factor of 8 (since there's 8 bits in 1 byte). For a while, k and K were used interchangeably to mean 1024. Technically, it should have been the lower case; it is not a proper noun. It could have meant 1000 because kilo means 1000. Hence the KiloBinary ("kibi") unit was introduced to give "kilo" prefix its proper 10^3 meaning.
Storage devices like hard drives as well as communications speeds (like modem, ADSL, cable, Ethernet, etc) usually use units like kb, Mb, kB or MB.
Note: You should always use the correct unit and capitalisation to minimize confusion.
Speed vs. Amount of data
Internet transfer speeds are commonly denoted in bits and powers of 10 per second. E.g. 0.1Mb/s = 100kbps = 100kb/s = 12,5kB/s = 100 kilobits per second.
However, Vuze defaults to KibiBytes per second, this behavior can be changed under Options > Interface > Display options .
Powers of 2 are mostly used for data storage (e.g. filesizes, free space on a hard drive, amount of transfered data etc.). People often mean the file is 15MiB big if they say it's 15MB in size. Amounts of data are almost always noted in bytes, not in bits, thus you should use a capital B for sizes.
Read the Azureus FAQ