What is the transmission rate?

The baud rate is the symbol rate of a link; that is, the number of symbols or signal changes per second. It is distinct from the bit rate unless each individual symbol represents exactly one bit. Simple binary signaling satisfies this condition, while schemes such as QPSK and QAM do not.

What is the difference between transfer rate and bit rate?

The bit rate counts the number of information units (bits) transferred per second, while the baud rate counts the number of symbols transferred per second. The bit rate is the product of the baud rate and the number of bits that each symbol represents. In a binary signaling system both values are identical since one symbol represents exactly one bit. However, a single 16-QAM symbol can represent 4 bits, making the bit rate four times as high as the baud rate.

How do you calculate transmission rate from bit rate?

The baud rate is divided by the number of bits each symbol represents, or log2 of the number of signal states. For example, an 8-PSK modulation with 3 bits per symbol and a data rate of 4800 bit/s results in 1600 baud, computed as 4800 divided by 3.

Why is serial throughput lower than baud rate?

Serial connections add a start bit, optional parity bits and at least one stop bit to each byte. In a typical format such as 8N1, it takes 10 bits to transmit each data byte, of which 8 bits are actual data. So a 9600 baud connection transmits 960 bytes per second, for an efficiency of 80 percent.

What baud rate should be used for a serial connection?

Use a baud rate that is suitable for both devices. 9600 is a safe and universal default value while 115200 is typically used for faster debug consoles. Standard rates are evenly divisible by common crystal frequencies, ensuring that both ends remain within their respective timing margins.

Baud Rate Calculator

Baud rate calculator

What do you want to work out?

Symbol rate ↔ bit rate

Serial / UART throughput

Channel capacity (Nyquist & Shannon)

Modulation scheme

Symbol rate (baud)

Baud unit

Bit rate

Bit-rate unit

Please input values into the fields

Bits per symbol
Constellation size (levels)

Visualise it

The chart below reacts to your inputs — switch modes to see a different view.

The baud rate calculator tool links three values that can be easily confused when transferring data: the symbol rate, bit rate and actual amount of data transferred. This tool allows you to perform three different calculations: convert baud rate and bit rate for any modulation scheme, calculate effective throughput of a serial or UART connection given frame overhead, and determine the Nyquist limit and Shannon limit of a channel.

By selecting a mode above the corresponding fields change. In the first mode you can do a bidirectional calculation: if you enter either the symbol rate or the bit rate and leave the other field blank the calculator tool will automatically fill in the blank field.

The baud rate is not the same as the bit rate.

The baud rate is the number of symbols or signal changes per second while the bit rate is the number of data bits transmitted per second.

Both values are only equal when each symbol represents exactly one bit. This is the case for simple binary signals like traditional serial ports. When a symbol represents more than one bit, the bitrate is higher than the baud rate.

Basic formula:

The bit rate is the product of symbol rate and number of bits that each symbol represents. The "number of bits per symbol" is a logarithm to base 2 of the total number of states.

\text{Bit rate} = \text{Baud rate} \times \log_2(M)

Here M is the number of states used for modulation. By rearranging this equation we can see that baud rate is equal to bit rate divided by the number of bits per symbol. This is a common way to calculate baud rate. If a data stream is transmitted at 4500 bps and each symbol represents 9 bits, then the baud rate would be 500 which is 4500 divided by 9.

Modulation	States (M)	Bits per symbol	Bit rate vs baud
Binary / BPSK	2	1	equal
QPSK / 4-QAM	4	2	2 times
8-PSK	8	3	3 times
16-QAM	16	4	4 times
64-QAM	64	6	6 times
256-QAM	256	8	8 times

Thus a modem transmitting 1000 symbols per second using a 16-QAM constellation is transmitting 4000 bits per second, which is four times the baud rate. This allows faster data streams to be transmitted over narrow channels by increasing not the symbol transmission rate but rather the number of bits represented by each symbol.

Throughput of serial and UART connections

In serial or UART connections the data rate is equal to the baud rate since the signal is binary. What really matters is the amount of useful data transmitted but this value will always be less than the baud rate because each byte has framing bits added to it.

Each character is sent as a frame. A start bit is followed by data bits, optionally a parity bit, and one or more stop bits. In a typical 8N1 configuration there are 8 data bits, no parity, and 1 stop bit, for a total of 10 bits on the line, of which 8 bits are data.

\text{Frame bits} = 1 + \text{data} + \text{parity} + \text{stop}

\text{Bytes per second} = \frac{\text{Baud rate}}{\text{Frame bits}}

At a baud rate of 9600 and the format 8N1, each byte takes up 10 bit times, resulting in a transfer rate of 960 bytes per second, which is an efficiency of 80 percent. Adding a parity bit increases the frame size to 11 bits, further reducing the effective transfer rate. This explains why file transfers over serial connections often appear slower than one would expect based on the stated baud rate.

Common serial transmission rates:

Use standard baud rates whenever possible. These are chosen to be divisible by the frequency of the crystal oscillator in microcontrollers, which provides a sufficient time buffer for reliable bit synchronization at both ends.

Baud rate	Typical use
300 to 2400	legacy terminals and dial-up modems
9600	the long-standing default, still everywhere
19200 to 57600	faster sensors and modules
115200	the usual speed for microcontroller debug consoles
230400 and up	high-speed links that need a precise clock

Nyquist and Shannon - limits of the channel:

There are two important results that determine the maximum data rate of a channel. The Nyquist theorem shows that a channel with a given bandwidth can transmit at most twice that bandwidth in symbols per second. The actual bit rate depends on how many levels are used for each symbol.

\text{Max baud} = 2B \qquad \text{Max bit rate} = 2B\,\log_2(M)

Nyquist assumes that the channel is free of noise so in theory the number of levels can be increased indefinitely. In reality channels are subject to noise and Shannon has defined a strict limit here; the capacity of a channel increases with bandwidth and signal-to-noise ratio, and no transmission technique can exceed this limit.

C = B\,\log_2\!\left(1 + \mathrm{SNR}\right)

For an audio channel with a bandwidth of 3 kHz and a signal-to-noise ratio (SNR) of 30 dB, the SNR ratio is one thousand times larger, and the Shannon capacity is about 30 kbit/s. This explains why dial-up modems were limited to about 33 to 56 kbit/s; it was not a limitation of hardware but rather the physical limits of the phone line.

Frequently asked questions

What is the transmission rate?: The baud rate is the symbol rate of a link; that is, the number of symbols or signal changes per second. It is distinct from the bit rate unless each individual symbol represents exactly one bit. Simple binary signaling satisfies this condition, while schemes such as QPSK and QAM do not.
What is the difference between transfer rate and bit rate?: The bit rate counts the number of information units (bits) transferred per second, while the baud rate counts the number of symbols transferred per second. The bit rate is the product of the baud rate and the number of bits that each symbol represents. In a binary signaling system both values are identical since one symbol represents exactly one bit. However, a single 16-QAM symbol can represent 4 bits, making the bit rate four times as high as the baud rate.
How do you calculate transmission rate from bit rate?: The baud rate is divided by the number of bits each symbol represents, or log2 of the number of signal states. For example, an 8-PSK modulation with 3 bits per symbol and a data rate of 4800 bit/s results in 1600 baud, computed as 4800 divided by 3.
Why is serial throughput lower than baud rate?: Serial connections add a start bit, optional parity bits and at least one stop bit to each byte. In a typical format such as 8N1, it takes 10 bits to transmit each data byte, of which 8 bits are actual data. So a 9600 baud connection transmits 960 bytes per second, for an efficiency of 80 percent.
What baud rate should be used for a serial connection?: Use a baud rate that is suitable for both devices. 9600 is a safe and universal default value while 115200 is typically used for faster debug consoles. Standard rates are evenly divisible by common crystal frequencies, ensuring that both ends remain within their respective timing margins.

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Disclaimer: This calculator is provided for general informational and educational purposes only. Our calculators are under active development, and results may be inaccurate, incomplete, or unsuitable for your situation. Always verify the figures independently and seek advice from a qualified professional before relying on them. We make no warranties and accept no liability for any loss or decision arising from use of this tool.

References

Baud — Wikipedia
Definition of the baud as the symbol rate and its relation to bit rate.
Symbol rate — Wikipedia
Symbol rate, bits per symbol, and gross bit rate for M-ary modulation.
Nyquist–Shannon sampling theorem — Wikipedia
The Nyquist rate: maximum symbol rate for a given channel bandwidth.
Shannon–Hartley theorem — Wikipedia
Channel capacity from bandwidth and signal-to-noise ratio.
Asynchronous serial communication — Wikipedia
Start, data, parity, and stop bits in a UART frame.