Baud Rate Calculator
Baud rate and bit rate get used as synonyms everywhere, and that habit breaks the moment you leave simple serial links. In a 115200-baud UART link they really are equal, one symbol per bit. But 16-QAM Wi-Fi packs four bits into every symbol, so a link moving at 100 megabits per second only signals at 25 megabaud. Confuse the two and your bandwidth estimate is off by a factor of four.
The Baud Rate Calculator below converts in both directions, from bit rate to baud and from baud to bit rate, using the modulation scheme you pick. It also reports the Nyquist bandwidth, because the reason you care about baud in the first place is spectrum.
Quick Answer
Key takeaways
- Baud counts symbols per second; bit rate counts bits per second. They are equal only at 1 bit per symbol.
- Bits per symbol = log2(M): QPSK carries 2, 16-QAM carries 4, 64-QAM carries 6.
- The Nyquist minimum bandwidth is half the symbol rate: Rs/2.
- Higher-order modulation moves more bits per symbol, which is how Wi-Fi and 5G beat the bandwidth limit.
Baud vs. bit rate: the distinction that matters
A baud is one symbol change per second. A symbol is whatever the channel sends in one signaling interval: a voltage level, a phase shift, a frequency. The bit rate is how many data bits those symbols carry. The two are linked by one number, the bits per symbol, which comes from the modulation scheme. BPSK uses two phases, one bit per symbol, so baud equals bit rate. QPSK uses four phases, two bits per symbol, so the bit rate is twice the baud. 16-QAM encodes four bits per symbol, and 64-QAM encodes six.
Why anyone cares: baud is the number that sets bandwidth. The absolute minimum channel bandwidth is half the symbol rate (the Nyquist limit), and real pulse shaping needs a bit more, bandwidth = Rs × (1 + alpha) / 2 for roll-off alpha. When an engineer asks for the baud rate, they are really asking how much spectrum the link needs.
Worked example, checked against this exact tool
Enter the pre-filled defaults (bit rate to baud, 10 Mbps, QPSK) and click Calculate:
| Figure | Value |
|---|---|
| Bit rate | 10 Mbps |
| Bits per symbol | 2 (QPSK) |
| Baud rate | 5.0000 Mbaud (10 ÷ 2) |
| Nyquist bandwidth | 2.500 MHz |
Flip the direction and enter 5 Mbaud with 16-QAM: you get 20 Mbps, the exact inverse. Try the classic serial case, 115200 bps with BPSK: 115200 baud, because one bit per symbol makes the two numbers identical.
Where the confusion comes from
Early modems and serial ports really did send one bit per symbol, so "baud" and "bps" were interchangeable and datasheets used them loosely. The habit survived into an era where it is wrong. Modern links use forward error correction and high-order modulation: a 2400 bps link with QPSK is 1200 baud, and a Wi-Fi channel pushing hundreds of megabits might signal at a few tens of megabaud. Mismatching the two when configuring equipment is a classic failure: both ends must agree on the symbol rate, or the data comes out garbled.
Manchester encoding is the fun edge case. Each bit is sent as two symbol transitions, so the baud rate is twice the bit rate. It is the rare case where baud is the bigger number.
What competing baud calculators miss
We checked the top-ranking baud tools. Three gaps stood out.
One direction only. Most tools convert bit rate to baud and leave you to invert the formula yourself. This one has a direction switch that runs both ways and verifies they are exact inverses.
No bandwidth context. The whole point of computing baud is sizing the channel, but competitors stop at the number. The Nyquist bandwidth row connects the result to spectrum planning immediately.
Bits-per-symbol as a raw number. Several tools ask you to type log2(M) yourself, with no modulation picker. The scheme dropdown here carries the bits-per-symbol for you and shows which modulation you chose on every result.
Frequently asked questions
Baud rate = bit rate ÷ bits per symbol. A 10 Mbps link with QPSK (2 bits per symbol) is 5 Mbaud. Invert it for the reverse: bit rate = baud rate × bits per symbol.
Only when each symbol carries exactly one bit, as in BPSK or plain UART serial. With QPSK the bit rate is twice the baud, with 16-QAM it is four times. In Manchester encoding the relationship flips: the baud rate is twice the bit rate.
Four. Bits per symbol equals log2 of the modulation order: log2(16) = 4. Similarly, QPSK carries 2, 8-PSK carries 3, 64-QAM carries 6, and 256-QAM carries 8.
The theoretical minimum bandwidth for a symbol rate Rs, equal to Rs/2. A 5 Mbaud link needs at least 2.5 MHz. Real pulse shaping needs more: bandwidth = Rs × (1 + alpha) / 2, where alpha is the roll-off factor between 0 and 1.
FEC adds redundant symbols so the receiver can fix errors. With a code rate of 3/4, the channel must carry 4/3 as many symbols as the user data alone would need, so the required symbol rate rises. This calculator assumes an ideal channel; budget extra baud for FEC on real links.
9600, 115200, 230400, and 921600 are the classics for UART and RS-232, with 115200 the workhorse for Arduino and GPS modules. Both devices must be set to the same rate; a mismatch produces garbled data.
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References
- CopyProgramming, "What Is Bit Rate and Baud Rate? 2026 Guide" - bit rate vs. baud rate definitions, the bit rate = baud × bits per symbol relation, and common serial rates (9600, 115200, 921600). CopyProgramming: Bit Rate and Baud Rate Guide. Accessed October 19, 2026.
- TrueGeometry, "What is the formula to calculate the baud rate for a serial communication system?" - baud = bit rate / bits per symbol across NRZ, Manchester, BPSK, and QPSK encoding schemes. TrueGeometry: Baud Rate Formula by Encoding Scheme. Accessed October 19, 2026.
- BraveCalculator, "Symbol Rate Calculator" - symbol rate = bit rate / log2(M) with FEC code-rate adjustment and QPSK/16-QAM worked examples. BraveCalculator: Symbol Rate Calculator. Accessed October 19, 2026.
- Calculator Zilo, "Symbol Rate Calculator" - Rs = R / log2(M), FEC and overhead adjustments, and Nyquist bandwidth BW = Rs × (1 + alpha) / 2. Calculator Zilo: Symbol Rate Calculator. Accessed October 19, 2026.