| Bits per second (bit/s) | Exbibits per second (Eibit/s) |
|---|---|
| 1 Bit per second | 8.67361737988 × 10-19 Eibit/s |
| 2 Bits per second | 1.73472347598 × 10-18 Eibit/s |
| 3 Bits per second | 2.60208521397 × 10-18 Eibit/s |
| 4 Bits per second | 3.46944695195 × 10-18 Eibit/s |
| 5 Bits per second | 4.33680868994 × 10-18 Eibit/s |
| 10 Bits per second | 8.67361737988 × 10-18 Eibit/s |
| 20 Bits per second | 1.73472347598 × 10-17 Eibit/s |
| 25 Bits per second | 2.16840434497 × 10-17 Eibit/s |
| 50 Bits per second | 4.33680868994 × 10-17 Eibit/s |
| 100 Bits per second | 8.67361737988 × 10-17 Eibit/s |
| Reference | Bits per second (bit/s) | Exbibits per second (Eibit/s) |
|---|---|---|
| A dial-up modem | 56000 bit/s | 4.85723 × 10-14 Eibit/s |
| Typical home broadband | 100000000 bit/s | 8.67362 × 10-11 Eibit/s |
| Gigabit Ethernet | 1 × 109 bit/s | 8.67362 × 10-10 Eibit/s |
| Streaming a 4K film | 25000000 bit/s | 2.1684 × 10-11 Eibit/s |
The bit per second is the fundamental unit of data transfer rate. Its symbol is bit/s, often written bps. It counts how many binary decisions a channel carries in one second, and every other unit of transmission speed is a multiple of it.
Because it is a rate, it has the form of a quantity divided by time, exactly like metres per second or litres per second. That makes the arithmetic straightforward: a link running at a given number of bits per second, multiplied by a duration in seconds, gives the total number of bits transferred, and dividing by eight converts that to octets.
The unit must be distinguished from the baud, which counts symbols per second rather than bits. Early modems transmitted one bit per symbol, so the two numbers were the same and the words were used interchangeably. Modern schemes encode several bits in each symbol — by varying phase and amplitude together — so a channel running at 3,000 baud may carry 33,600 bits per second. Only the bit rate describes how much information moves.
Claude Shannon established the theoretical ceiling in 1948. The capacity of a channel in bits per second depends on its bandwidth and on the ratio of signal to noise, and no coding scheme can exceed it. Every advance in modem and radio design since has been an attempt to approach that limit more closely, and modern systems come within a fraction of a decibel of it.
In practice the raw bit rate of a link is never the rate at which useful data arrives. Protocol headers, error-correcting codes, acknowledgements and retransmissions all consume capacity, and the usable fraction is typically 90 to 95 per cent on a wired link and considerably less on a shared wireless one.
Single bits per second are rarely quoted, because almost every channel is faster. The exceptions are deep-space communication, where a probe billions of kilometres away may return data at a few tens of bits per second, and certain low-power sensor networks that transmit a handful of bits at long intervals to preserve battery life.
One bit per second equals 0.125 octets per second, 0.001 kilobits per second, or about 0.0009766 kibibits per second.
The exbibit per second is a unit of data transfer rate equal to two to the sixtieth power bits per second, which is 1,024 pebibits per second. Its symbol is Eibit/s. It is the binary counterpart of the exabit per second, and the two differ by 15.3 per cent.
That fifteen per cent is more than the margin most engineering work allows anywhere. A quantity stated in the wrong convention at this level is not slightly imprecise but plainly wrong, and no amount of context recovers the intended figure once it has been written ambiguously. This is the situation the IEC prefixes were introduced to prevent.
No physical link approaches this rate. The unit describes aggregates: the total instantaneous traffic of the whole internet is roughly an exabit per second, so a binary exbibit per second is fifteen per cent more than everything moving on every network on the planet at a given moment.
Where a binary figure of this size arises naturally is in address arithmetic rather than in transmission. Two to the sixtieth is a number that appears throughout the design of 64-bit systems, and any rate derived from filling or traversing such an address space in a fixed time is naturally binary. Those calculations are theoretical, but they are the reason the unit is defined rather than left unnamed.
In octets an exbibit per second is 144,115,188,075,855,872, or 128 pebioctets per second. That is more storage moved per second than the world manufactures in several years, which is a way of saying that no source and no destination for such a flow could exist.
For a converter the treatment is mechanical and must be exact. Eibit/s and Ebit/s differ by an eighth, and a tool that treats them as interchangeable has introduced an error larger than the difference between many neighbouring units. The lowercase i is not decoration.
One exbibit per second equals 1,024 pebibits per second, 144,115,188,075,855,872 octets per second, or about 1.153 exabits per second.