Data sizes: decimal vs. binary
SI system (KB = 1,000 B) and IEC system (KiB = 1,024 B) explained
In information technology there are two systems for file sizes: the decimal SI system and the binary IEC system. In the SI system, all prefixes are powers of ten (kilo = 10³, mega = 10⁶, giga = 10⁹). In the IEC system they are powers of two (kibi = 2¹⁰ = 1,024, mebi = 2²⁰ = 1,048,576, gibi = 2³⁰ = 1,073,741,824). This seemingly small difference adds up significantly for large amounts of data: for a petabyte (PB decimal = 10¹⁵ bytes) compared to a pebibyte (PiB binary = 2⁵⁰ bytes), the difference is already about 12.6%.
Hard drive manufacturers use the decimal system because it makes capacity appear larger. Operating systems (Windows, macOS, Linux), on the other hand, traditionally display capacities in binary units – often mislabeled as "GB" even though GiB is meant. The IEC standard (IEC 80000-13) introduced its own prefixes for the binary system in 1998: KiB, MiB, GiB, TiB, PiB. macOS switched to the decimal system in 2009 (with Snow Leopard), which meant the same hard drive suddenly appeared "larger" on macOS than on Windows.
In practice this means: a hard drive advertised as 1 TB (1,000,000,000,000 bytes decimal) is shown by Windows as about 931 GiB. For a 256 GB SSD it would be 238 GiB. The difference grows with size: at 1 TB it is almost 70 GB – nearly 7% of the total capacity. On a 10 TB NAS, an apparently "missing" 680 GB is simply down to this unit difference – the storage capacity is actually present, just calculated differently.
For internet speed and data transfer, the decimal system is almost always used: 100 Mbit/s (megabits per second) means 100,000,000 bit/s = 12.5 MB/s (megabytes per second). Important: internet providers state speeds in Mbit/s, while file sizes are given in MB (megabytes). 1 byte = 8 bits, so: MB/s = Mbit/s ÷ 8. Downloading a 4K video file (about 50 GB) at 100 Mbit/s takes about 50,000 MB ÷ 12.5 MB/s = 4,000 seconds ≈ 66 minutes.
In the cloud and server world, precise data size figures are business-critical: cloud providers bill storage costs in GB (decimal). Database backups, log rotation and storage quotas on Linux systems frequently use GiB. IT administrators should know the difference: a backup script meant to stop at "50 GB" must be configured as 50 GB (decimal) or 46.6 GiB (binary) depending on the system. Our converter shows both systems side by side to help avoid such configuration errors.