How this calculator works
A symbol is one distinguishable signalling state, such as a phase, a frequency pair or an amplitude level. The baud rate is how many of those states pass each second. Each state can encode several bits: QPSK has four phases and therefore two bits per symbol, 16-QAM has sixteen states and four bits. Multiplying the baud rate by the bits per symbol gives the bit rate. The symbol rate also sets the minimum signal bandwidth. Binary ASK needs roughly twice the baud rate, and FSK needs about twice the sum of the baud rate and the peak deviation, which is Carson's rule applied to a two-tone signal.
Formula
bit rate = baud rate x bits per symbol. baud rate = bit rate / bits per symbol. baud rate = 1 / symbol duration. ASK bandwidth = 2 x baud rate. FSK bandwidth = 2 x (peak deviation + baud rate).
Worked example
A 9600 bit/s modem using two bits per symbol runs at 9600 / 2 = 4800 baud. Each symbol lasts 1 / 4800 seconds, about 208.3 microseconds. Sending 1200 baud with 600 Hz peak deviation in FSK needs about 2 x (600 + 1200) = 3600 Hz of bandwidth.
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Frequently asked questions
Is baud rate the same as bit rate?
Only when each symbol carries exactly one bit, as in binary ASK or BPSK. With QPSK the bit rate is twice the baud rate, and with 64-QAM it is six times. People often say baud when they mean bits per second, which is why modem speeds were quoted as bits per second even though the symbol rate was lower.
Why is ASK bandwidth twice the baud rate?
A binary ASK signal is a carrier multiplied by a rectangular pulse train. That multiplication produces two sidebands around the carrier, each as wide as the baseband pulse train, so the total occupies about twice the symbol rate. Real hardware filters the pulses and needs a little extra.
Is Carson's rule exact?
It is a useful engineering estimate, not an exact result. It covers about 98 percent of the power of a frequency-modulated signal when the modulation index is not small. Exact bandwidth depends on the modulation index, the pulse shaping and the allowed out-of-band emission, so a radio design has to be checked against the relevant standard.
Why do symbols get longer at lower baud rates?
The baud rate is symbols per second, so the duration of each symbol is its reciprocal. Halving the baud rate doubles the symbol duration. The bits carried per symbol do not change unless the modulation scheme changes.