Bits, bytes and throughput
A size in every unit of both conventions with the bit count written out (1.5 GB is 12 000 000 000 bits and 1.397 GiB; read the 1024 way it would be 7.37 % more), a rate in bits and bytes per second and per minute, hour and day, and any two of size, rate and time giving the third, with the protocol efficiency of TCP over Ethernet applied if you ask. The connection table answers for a modem, T1, E1 and every Ethernet speed at once. Exact arithmetic; nothing is rounded until it is printed.
SieciWrite them the way you would say them: 1.5 GB, 700 MiB, 10K, 8 bits; 100 Mbit/s, 12.5 MB/s, 1 Gbps; 90 s, 2h 30min, 1 day. One field is explained on its own; two give the third (with all three, the time is recomputed from size and rate). b is a bit, B a byte; k and M are 1000s, Ki and Mi are 1024s.
Line rate counts every bit on the wire as payload. The presets count only the payload of full 1500-byte frames: 1460 of 1538 bytes on the wire for TCP over IPv4 (94.93 %), 1440 of 1538 for TCP over IPv6, 1472 of 1538 for UDP over IPv4; headers from RFC 791, RFC 8200 and RFC 9293, the frame, preamble and gap from RFC 2544 Appendix C.
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Transfer time
8,192 s
8,192 s, at 100 % efficiency.
The size, in every unit
bits 458 752 bytes 57 344
An IEC binary prefix (Ki, Mi, Gi, Ti) means a power of 1024 and nothing else; this reading is unambiguous.
Read as decimal (the SI meaning): 56 kB = 56 000 B. Read as binary (the 1024 convention some systems still label with the same letters): 56 KiB = 57 344 B. The gap is 2,4 %.
| Unit | Value | Convention |
|---|---|---|
| bit | 458 752 | binary (1024) |
| B | 57 344 | base unit |
| kbit | 458,752 | binary (1024) |
| KiB | 56 | binary (1024) |
| kB | 57,344 | decimal (1000) |
| Mbit | 0,458752 | binary (1024) |
| MiB | 0,054688≈ | binary (1024) |
| MB | 0,057344 | decimal (1000) |
| Gbit | 0,000459≈ | binary (1024) |
| GiB | 0,000053≈ | binary (1024) |
| GB | 0,000057≈ | decimal (1000) |
| Tbit | 0≈ | binary (1024) |
| TiB | 0≈ | binary (1024) |
| TB | 0≈ | decimal (1000) |
| PiB | 0≈ | binary (1024) |
| PB | 0≈ | decimal (1000) |
The rate, per second and over time
bit/s 56 000 B/s 7 000
At this rate: 420 kB a minute, 25,2 MB an hour, 604,8 MB a day.
| Unit | Per second |
|---|---|
| bit/s | 56 000 |
| kbit/s | 56 |
| Mbit/s | 0,056 |
| Gbit/s | 0,000056 |
| Tbit/s | 0≈ |
| B/s | 7 000 |
| kB/s | 7 |
| MB/s | 0,007 |
| GB/s | 0,000007 |
| TB/s | 0≈ |
| KiB/s | 6,835938≈ |
| MiB/s | 0,006676≈ |
| GiB/s | 0,000007≈ |
Over standard links, at 100 % efficiency
| Link | Nominal rate | Time |
|---|---|---|
| 56k modem (V.90, 56 000 bit/s)2004 | 56 000 bit/s | 8,192 s |
| ISDN, one B channel (64 kbit/s)2004 | 64 000 bit/s | 7,168 s |
| T1 (1 544 kbit/s)2004 | 1 544 000 bit/s | 0,297 s |
| E1 (2 048 kbit/s) | 2 048 000 bit/s | 0,224 s |
| Ethernet 10 Mb/s2004 | 10 000 000 bit/s | 0,046 s |
| Ethernet 100 Mb/s2004 | 100 000 000 bit/s | 0,005 s |
| Ethernet 1 Gb/s | 1 000 000 000 bit/s | 0,000 s |
| Ethernet 2.5 Gb/s | 2 500 000 000 bit/s | 0,000 s |
| Ethernet 5 Gb/s | 5 000 000 000 bit/s | 0,000 s |
| Ethernet 10 Gb/s | 10 000 000 000 bit/s | 0,000 s |
| Ethernet 25 Gb/s | 25 000 000 000 bit/s | 0,000 s |
| Ethernet 40 Gb/s | 40 000 000 000 bit/s | 0,000 s |
| Ethernet 100 Gb/s | 100 000 000 000 bit/s | 0,000 s |
| Ethernet 400 Gb/s | 400 000 000 000 bit/s | 0,000 s |
Nominal rates: ITU-T V.90 for the modem, ITU-T G.704 for T1 and E1, IEEE 802.3-2022 for Ethernet. The rows marked 2004 were in the connection table of the bits-and-bytes calculator on nutzmann.net in 2004 and ntz.com.br in 2013, the oldest ancestor of the tools here. Times are at the efficiency chosen above; a real link also carries acknowledgements and retransmissions.
The arithmetic is exact (BigInt decimals) and rounded only when printed, to six decimals. Not modelled: TCP window and round-trip limits, loss, compression, and the difference between a link's nominal rate and what a provider actually delivers. The two-readings line shows what a label means under each convention; which one a given operating system uses is that system's documentation to state.
Źródła
- NIST Reference on Constants, Units, and Uncertainty: Prefixes for binary multiples
- ls(1), GNU coreutils (man7.org)
- RFC 2544: Benchmarking Methodology for Network Interconnect Devices, Appendix C
- RFC 791: Internet Protocol
- RFC 9293: Transmission Control Protocol (TCP)
- RFC 8200: Internet Protocol, Version 6 (IPv6) Specification, section 8.3
- RFC 768: User Datagram Protocol
- ITU-T Recommendation V.90 (09/98)
- ITU-T Recommendation G.704 (10/98)
- IEEE Std 802.3-2022, IEEE Standard for Ethernet
- nutzmann.net, Calculadora de bits e bytes (2004-10-09), Internet Archive capture
- ntz.com.br, Calculadora e conversão de bits e bytes (2013), Internet Archive capture