The baud rate is the number of signal changes – symbols – a line sends per second. It is not the same as the bit rate unless each symbol carries exactly one bit. A modem that sends 2,400 symbols per second using 16 different signal states (16-QAM) carries 4 bits per symbol and therefore 9,600 bit/s.
Serial ports (UART) use simple two-level signalling, so there the “baud rate” setting – 9,600, 115,200 and so on – equals the bit rate including the start, stop and parity bits. Radio and DSL systems pack more bits into each symbol with phase and amplitude modulation, which is why they quote both numbers.
Choose a method: bit rate and bits per symbol (the usual case), the bandwidth of an amplitude-shift keyed (ASK) signal with its modulation (filtering) factor d, the bandwidth of a frequency-shift keyed (FSK) signal with its carrier separation, or a direct baud ↔ frequency conversion. The bits-per-symbol field then gives the matching bit rate and the number of signal levels M = 2ⁿ.
How to use the Baud Rate Calculator
- Calculate baud rate from
- Bit rate
- Signal bandwidth (B)
- Modulation (filtering) factor d — 0 for an ideal filter, 1 for the widest practical filter.
- Carrier frequency separation Δf (f₁ − f_c)
- Frequency
- Bits per symbol (n) — 1 for BPSK/FSK/UART, 2 for QPSK, 4 for 16-QAM, 6 for 64-QAM, 8 for 256-QAM.
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Pick the method and enter its values. The calculator divides the bit rate by the bits per symbol, or applies the textbook ASK and FSK bandwidth relations, and then derives the symbol period and the bit rate for the chosen bits per symbol.
Worked example
A link sends 4,500 bit/s with 9 bits per symbol (512 signal levels): baud = 4,500 ÷ 9 = 500 Bd, and each symbol lasts 1 ÷ 500 = 2 ms. For an ASK signal occupying 3 kHz with d = 0.5 the baud rate is 3,000 ÷ 1.5 = 2,000 Bd; an FSK signal in the same 3 kHz with Δf = 500 Hz gives (3,000 − 1,000) ÷ 1.5 ≈ 1,333 Bd.
Bits per symbol for common modulations
| Modulation | Levels M | Bits per symbol |
|---|---|---|
| BPSK, binary FSK, UART | 2 | 1 |
| QPSK | 4 | 2 |
| 8-PSK | 8 | 3 |
| 16-QAM | 16 | 4 |
| 64-QAM | 64 | 6 |
| 256-QAM | 256 | 8 |
| 1024-QAM (Wi-Fi 6) | 1024 | 10 |
Inputs explained
| Field | What to enter |
|---|---|
| Calculate baud rate from | Choose one: Bit rate and bits per symbol, ASK bandwidth, FSK bandwidth, Frequency (1 baud = 1 Hz) |
| Bit rate | Units: bit/s, kbit/s, Mbit/s |
| Signal bandwidth (B) | Units: Hz, kHz, MHz |
| Modulation (filtering) factor d | A number. 0 for an ideal filter, 1 for the widest practical filter. |
| Carrier frequency separation Δf (f₁ − f_c) | Units: Hz, kHz, MHz |
| Frequency | Units: Hz, kHz, MHz |
| Bits per symbol (n) | A number. 1 for BPSK/FSK/UART, 2 for QPSK, 4 for 16-QAM, 6 for 64-QAM, 8 for 256-QAM. |
What each result means
- Bit rate = [Baud rate]×[Bits per symbol (n)]
- Signal levels M = 2ⁿ = 2^[Bits per symbol (n)]
- Symbol duration = 1÷[Baud rate]
- Equivalent frequency = [Baud rate]
Formula
Baud = bit rate ÷ bits per symbol · ASK: baud = B ÷ (1 + d) · FSK: baud = (B − 2Δf) ÷ (1 + d) · Bit rate = baud × log₂(M) · Symbol time = 1 ÷ baud
Worked example
Inputs — Calculate baud rate from: Bit rate and bits per symbol; Bit rate: 4,500 bit/s; Bits per symbol (n): 9.
Results — Baud rate = 500 Bd (symbols/s); Bit rate = 4,500 bit/s; Signal levels M = 2ⁿ = 512; Symbol duration = 2 ms; Equivalent frequency = 500 Hz.
Key terms
- Baud (Bd)
- One symbol (signal change) per second.
- Symbol
- A distinct signal state that carries one or more bits.
- Bits per symbol
- log₂ of the number of signal levels M.
- Modulation factor d
- A number from 0 to 1 that describes how much extra bandwidth the filtering needs.
Frequently asked questions
What is the difference between baud and bit rate?
Baud counts symbols per second; bit rate counts bits. Bit rate = baud × bits per symbol, so they are equal only with 1 bit per symbol.
What is the baud rate for 4,500 bit/s at 9 bits per symbol?
4,500 ÷ 9 = 500 baud.
What are common serial baud rates?
300, 1,200, 2,400, 4,800, 9,600, 19,200, 38,400, 57,600, 115,200 and 230,400 Bd.
How many bytes per second is 9,600 baud on a serial port?
With 8N1 framing each byte takes 10 bits, so 960 bytes per second.
What is the ASK bandwidth formula?
B = (1 + d) × baud, so baud = B ÷ (1 + d). With B = 3 kHz and d = 0.5 the baud rate is 2,000.
What does the FSK formula add?
Two carriers are used, so the bandwidth also includes 2Δf: B = (1 + d) × baud + 2Δf.
Is 1 baud the same as 1 Hz?
Both mean one event per second, so numerically they match; strictly a baud is a symbol per second.