Bits to Bytes Converter
Convert bits to bytes — eight to one, and b and B are not the same symbol.
Updated
bytes
1.00B
8 bit = 1.00 B
In short
How many bits are in a byte?
Eight. Divide bits by 8 to get bytes, so 64 bits is 8 bytes and 1,024 bits is 128 bytes. The symbols matter: lowercase b means a bit and uppercase B means a byte, which is why 100 Mbps and 100 MB/s differ by a factor of eight.
One character of difference in the symbol, eight times the difference in the quantity.
bits to bytes — quick reference
| bits (bit) | bytes (B) |
|---|---|
| 1 bit | 0.13 B |
| 8 bit | 1.00 B |
| 16 bit | 2.00 B |
| 32 bit | 4.00 B |
| 64 bit | 8.00 B |
| 128 bit | 16.00 B |
| 1,024 bit | 128.00 B |
| 8,000 bit | 1,000.00 B |
The formula, worked line by line
Divide by eight. There is no constant to choose and no convention to resolve, which makes this the one page on the data shelf with a single unambiguous answer. The care required is entirely in reading the units on either side of it.
“One character of difference in the symbol, eight times the difference in the quantity. No other pair of units is this close in writing and this far apart in size.”
That asymmetry is the argument for care. Most notation errors produce a figure that is obviously wrong; this one produces a figure that is plausible, in the right units, and eight times out. It survives review precisely because it does not look like a mistake.
bytes = bits / 8
bits = bytes x 8
1 byte = 8 bits = 1 octet
256 bits / 8 = 32 bytes
100 Mbps / 8 = 12.5 MB/s- Advertised line speed
- 200 Mbps
- Divided by 8
- 25 MB/s
- A 4 GB file at that rate
- 160 seconds
- If read as 200 MB/s
- 20 seconds
- The factor
- eight, before any overhead
The eight-fold difference is the whole of the surprise, and it happens before protocol overhead is considered at all. Overhead then removes a further few percent, but it is a small correction on top of a factor that has already been applied.
Where bits are the natural unit
Anything to do with a link or a signal is counted in bits: connection speeds, modem rates, sampling depths, error rates. Anything to do with storage is counted in bytes: file sizes, memory, disk capacity. Cryptographic key lengths sit with the bit camp because their security depends on the number of possible values, which is two to the power of the bit count.
The prefixes apply to both
- 1 kilobit, kb
- 1,000 bits = 125 bytes
- 1 megabit, Mb
- 10^6 bits = 125,000 bytes
- 1 gigabit, Gb
- 10^9 bits = 125,000,000 bytes
- 1 kilobyte, kB
- 1,000 bytes = 8,000 bits
- 1 megabyte, MB
- 10^6 bytes = 8,000,000 bits
In bit rates the prefixes are always decimal — there is no binary reading of a megabit. That makes the rate pages simpler than the storage pages, because only one of the two ambiguities on this shelf applies to them.
It is worth stating that last point plainly, because it is the one piece of good news on this subject. Whatever confusion surrounds megabytes, a megabit is a million bits everywhere, in every standard and every specification, with no second definition waiting to be discovered.
How to use the bits to bytes converter
Eight bits make a byte, so the conversion is a division by eight. The reason this comes up as often as it does has nothing to do with the arithmetic and everything to do with notation: the symbols for the two units differ by the case of a single letter, and that letter is routinely typed wrong, read wrong, or dropped entirely.
The convention is that lowercase b means a bit and uppercase B means a byte. IEEE Standard 1541 sets it out explicitly. So 100 Mb is a hundred megabits and 100 MB is a hundred megabytes, which is eight times more data, and the two are written a shift key apart. Nothing else in measurement is quite so easy to get wrong so quietly.
8
Bits in a byte
the octet, universally
b
Symbol for the bit
lowercase, always
B
Symbol for the byte
uppercase, always
The split has a logic behind it. Communications engineering counts bits because a link carries individual signal transitions and the byte is not a meaningful unit on the wire. Storage counts bytes because that is the smallest independently addressable unit of memory. Both conventions are correct in their own domain, and the friction appears exactly where the two domains meet.
The word octet exists to remove the remaining doubt. ISO/IEC 2382 defines it as exactly eight bits, and networking specifications use it for that reason. A byte is eight bits on every machine anyone is likely to meet, but the term carries historical baggage that the octet does not, which is why standards reach for the second word.
- 8 bits
- 1 byte
- 64 bits
- 8 bytes, one 64-bit word
- 128 bits
- 16 bytes, a UUID or an AES block
- 256 bits
- 32 bytes, a SHA-256 digest
- 1,024 bits
- 128 bytes
Cryptographic sizes are quoted in bits by convention, which is why a "256-bit key" is a 32-byte value. Reading those figures as bytes overstates the size by eight and makes the numbers sound far larger than they are.
Apply the same eight to download speeds
The practical payoff of this conversion is turning an advertised connection speed into the transfer rate you will actually see. That page runs it directly.
Open Mbps to MB/s →Bits converted to bytes at eight bits per byte, with the contexts in which each size is normally quoted in bits rather than bytes.
| Bits | Bytes | Where the figure appears |
|---|---|---|
| 1 bit | 0.125 bytes | |
| 8 bits | 1 byte | one character in ASCII |
| 16 bits | 2 bytes | a 16-bit integer |
| 32 bits | 4 bytes | an IPv4 address |
| 64 bits | 8 bytes | a 64-bit word |
| 128 bits | 16 bytes | a UUID, an AES block |
| 160 bits | 20 bytes | a SHA-1 digest |
| 256 bits | 32 bytes | a SHA-256 digest |
| 512 bits | 64 bytes | a SHA-512 digest |
| 1,024 bits | 128 bytes | |
| 2,048 bits | 256 bytes | a common RSA key size |
| 8,000 bits | 1,000 bytes | one kilobyte |
Why eight, and why it was not always eight
Eight is a convention that won rather than a mathematical necessity. It is a power of two, which makes bit-addressing within a byte clean; it holds one character in the encodings that dominated early computing; and it divides evenly into the word sizes that followed. None of those reasons is decisive on its own, and together they were enough.
Before that settled, byte width varied by machine. The DEC PDP-10 had a 36-bit word and its byte instructions operated on fields of any width up to that word, so a byte on a PDP-10 was whatever the programmer declared it to be. Six-bit and nine-bit bytes were both in ordinary use.
- A SHA-256 digest
- 256 bits
- Divided by 8
- 32 bytes
- Written as hexadecimal
- 64 characters
- Because each hex digit is
- 4 bits
- One digest
- 256 b = 32 B = 64 hex characters
Three different counts of one value, and each is used in a different context. The bit count is how the algorithm is named, the byte count is how much storage it needs, and the character count is what you actually see when it is printed.
Telling the two symbols apart in practice
The safest habit is to treat any lowercase b as a warning to check. Rates are usually bits, so Mbps, Gbps and kbps all mean bits per second. Sizes are usually bytes, so MB, GB and KB mean bytes. When a figure crosses from one world to the other, the factor of eight applies and it applies in full.
Do
- Write Mbps for bit rates and MB/s for byte rates
- Divide by eight when turning a link speed into a transfer rate
- Read cryptographic key sizes as bits unless told otherwise
- Say octet when the audience might read byte as something else
Don't
- Write MBps when you mean megabits per second
- Compare a connection speed against a file size without converting
- Assume a bare number carries its unit with it
- Expect an advertised rate to arrive intact after protocol overhead
MBps is the notation to avoid entirely. Written strictly it means megabytes per second, but it is used so often as a careless spelling of megabits that the symbol has lost its reliability. MB/s and Mbps are both unambiguous, and using them costs nothing.
Every bits value, worked out
141 common bits figures each get their own page, with the answer at full precision, the arithmetic, what rounding costs, and the nearest real-world reference point on the scale.
10 to 99 bit
100 to 999 bit
Questions people ask
Sources
Where the constants and formulas on this page come from. Each line names the figure it backs.
The symbol b denotes the bit and the symbol B denotes the byte.
IEEE Std 1541-2021 — Standard for Prefixes for Binary Multiples — IEEE Standards Association
The octet is defined as an ordered sequence of eight bits considered as a unit, equivalent to an eight-bit byte.
ISO/IEC 2382:2015 Information technology — Vocabulary — International Organization for Standardization
The PDP-10 provided byte instructions operating on fields of any width within its 36-bit word.
PDP-10 System Reference Manual, DEC-10-HGAA-D — Digital Equipment Corporation
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