Baud Rate Calculator
Convert between bit rate and baud rate (symbol rate) for any digital modulation. Estimate bandwidth with roll‑off factor.
Bit → Baud
Baud → Bit
Bandwidth
Bits/Symbol
Baud: 0 Bd
Mod: QPSK
bps
kbps
Mbps
Bits per symbol = log₂(M)
Common Modulation Schemes
Baud Rate (Symbol Rate)
500 Bd
Formula
Rₛ = Rᵦ / log₂(M)
Bits per symbol
2
Bandwidth (α=0.35)
675 Hz
Baud Rate & Bandwidth Formulas
Rₛ = Rᵦ / log₂(M) | Rᵦ = Rₛ · log₂(M)
BW = Rₛ · (1 + α) (raised‑cosine)
Rᵦ: bit rate (bps)
Rₛ: baud rate / symbol rate (Bd)
M: modulation order (number of symbols)
k = log₂(M): bits per symbol
α: roll‑off factor (0…1)
BW: required bandwidth (Hz) for raised‑cosine filter
People Also Ask
📡 What is baud rate and how is it different from bit rate?
Baud rate (symbol rate) is the number of symbol changes per second. Bit rate is data rate. With multi‑level modulation, one symbol carries multiple bits, so baud rate ≤ bit rate.
🔢 How to calculate baud rate from bit rate and modulation?
Baud rate = Bit rate / log₂(M). Example: 1 Mbps with 16QAM (4 bits/sym) → 1e6/4 = 250 kBd.
📊 What is the bandwidth of a QPSK signal at 1 Msym/s?
Minimum bandwidth = symbol rate (Nyquist). With raised‑cosine roll‑off α, BW = Rₛ·(1+α). For α=0.35, BW = 1.35 MHz.
🔧 Why do we use higher‑order modulation like 64QAM?
To transmit more bits per second without increasing bandwidth. However, higher order requires better SNR to maintain low error rate.
Reference – Common Modulations
| Modulation | Order M | Bits/symbol | Example bit rate @ 1 MBd |
|---|---|---|---|
| BPSK | 2 | 1 | 1 Mbps |
| QPSK / 4QAM | 4 | 2 | 2 Mbps |
| 8PSK | 8 | 3 | 3 Mbps |
| 16QAM | 16 | 4 | 4 Mbps |
| 32QAM | 32 | 5 | 5 Mbps |
| 64QAM | 64 | 6 | 6 Mbps |
Nyquist bandwidth = symbol rate (for ideal sinc pulses). Practical filters increase occupied bandwidth by roll‑off factor.
Frequently Asked Questions
What is the relationship between baud rate and bandwidth?
For baseband transmission, the minimum required bandwidth equals the baud rate (Nyquist). For modulated signals (passband), the bandwidth is twice the baud rate for double‑sideband (e.g., QPSK). With raised‑cosine filtering, occupied bandwidth = symbol rate × (1 + α).
How does roll‑off factor affect spectrum efficiency?
Roll‑off α (0…1) controls the excess bandwidth beyond Nyquist. Lower α gives sharper cut‑off but more complex filtering. α=0 is ideal but unrealizable. Common values: 0.2–0.35 in satellite, 0.1 in some high‑speed links.