Hong Life CalculatorsUnderstanding the baud rate calculator — concept and principle
Baud rate and bit rate are often confused. Baud counts symbols per second, while bit rate counts bits. This calculator converts between them for serial ports (UART) and modulated links, works out UART framing overhead, characters per second and useful data rate, and estimates how long a message takes to send.
How it is calculated
Bit rate = baud × log₂M (M = number of symbol states)
Minimum noise-free bandwidth = bit rate ÷ (2 log₂M)
UART frame bits = 1 start + data bits + parity (0 or 1) + stop bits (1 or 2)
Characters per second = baud ÷ frame bits
Useful data rate = characters per second × data bits
Framing efficiency = data bits ÷ frame bits
Message time = bytes × frame bits ÷ baud (UART) or bytes × 8 ÷ bit rate
The principle
A symbol is one distinct signal state held for a fixed time. A UART line has only two states (high and low), so each symbol carries one bit and baud equals bit rate. Modems and radios use more states, such as 4 in QPSK or 16 in 16-QAM, so each symbol carries log₂M bits. A UART also wraps every character in a frame: a start bit tells the receiver a character is coming, and stop bits give it time to get ready for the next one. These overhead bits use line time but carry no data, which is why 8-N-1 framing turns 115,200 baud into 11,520 bytes per second.
Worked example
Default inputs: UART, 115,200 Bd, 8 data bits, no parity, 1 stop bit, 1,024-byte message.
- Bits per symbol = 1, so gross bit rate = 115,200 bit/s; minimum bandwidth = 57,600 Hz.
- Frame = 1 + 8 + 0 + 1 = 10 bits.
- Characters per second = 115,200 ÷ 10 = 11,520; useful data rate = 11,520 × 8 = 92,160 bit/s.
- Framing efficiency = 8 ÷ 10 = 80%; time per character = 10 ÷ 115,200 = 0.0868 ms.
- Message time = 1,024 × 10 ÷ 115,200 = 0.089 s.
| Baud rate (symbols per second, Bd) | Gross bit rate (bit/s) |
|---|---|
| 28,800 | 28,800 |
| 57,600 | 57,600 |
| 86,400 | 86,400 |
| 115,200 | 115,200 |
| 144,000 | 144,000 |
| 172,800 | 172,800 |
| 230,400 | 230,400 |
How to read the result
Both ends of a serial link must use the same baud rate and framing. Analog Dialogue notes that UART timing tolerates only a limited difference between the two clocks, about 10% at most. Real transfers add pauses between characters and protocol overhead, so measured throughput is usually lower than the calculated figure.
Common mistakes
- Using "baud" and "bits per second" interchangeably for modulated links.
- Forgetting start and stop bits when estimating UART throughput.
- Mismatched framing settings, such as 8-N-1 on one side and 8-E-1 on the other.
- Assuming characters are sent back to back with no gaps.
Frequently asked questions
What does 8-N-1 mean?
8 data bits, no parity, 1 stop bit, giving 10 bits per character including the start bit.
Is 9600 baud the same as 9600 bit/s?
On a UART, yes; on a modulated link it depends on bits per symbol.
Why use parity?
It detects single-bit errors at the cost of one extra bit per character.
What are common UART baud rates?
9,600, 19,200, 38,400, 57,600 and 115,200 are widely used.
Sources: L. Frenzel, "What's the Difference Between Bit Rate and Baud Rate?", Electronic Design (updated 2024) · E. Peña and M. G. Legaspi, "UART: A Hardware Communication Protocol", Analog Dialogue 54(4), Analog Devices, 2020