Also known as: bit rate vs baud, baud rate, symbol rate vs bit rate
Bit rate versus baud is the distinction between how many symbols a link sends each second (the baud rate, or symbol rate) and how many bits it carries each second (the bit rate).1 They are equal only when each symbol conveys exactly one bit; whenever a modulation packs several bits into each symbol, the bit rate is a multiple of the baud rate — a distinction people routinely blur by calling everything “baud.”
How it works
A symbol is one signalling state held for one symbol period; the baud rate R_s is how many of those states are sent per second, and it — with the roll-off — sets the occupied bandwidth. The bit rate depends additionally on how many distinct symbols the alphabet has. With M possible symbols, each one selects among M choices and therefore carries log₂(M) bits, giving the core relation R_b = R_s · log₂(M). Binary schemes (M = 2, e.g. BPSK, 2-FSK) send one bit per symbol, so bit rate equals baud. A four-level scheme (M = 4, e.g. QPSK or 4-FSK) sends 2 bits/symbol; 16-QAM sends 4; 256-QAM sends
- So a modem running 4800 baud with a four-level alphabet moves 9600 bit/s — same symbol rate, same bandwidth, double the data.
The appeal of higher-order modulation is exactly this: pack more bits into each symbol and raise the bit rate (and spectral efficiency) without widening the channel. The cost is that the constellation points sit closer together, so a denser alphabet needs more signal-to-noise ratio to keep the error rate down. Choosing M is therefore a bandwidth-versus-robustness trade, and bandwidth is tied to baud, not to bit rate.
Relevance to SDR
Keeping the two rates straight is essential when reasoning about any digital signal an SDR decodes. GopherTrunk’s timing recovery locks to the symbol (baud) rate, because that is what determines where to sample; the bit rate then follows from the modulation order. P25 Phase 1 C4FM runs 4800 symbols/s with four levels for a 9600 bit/s gross channel rate, while P25 Phase 2 uses a two-slot TDMA π/4-DQPSK scheme at 6000 symbols/s carrying more bits per symbol — different baud and bit rates for the same family. When someone reports a “9600 baud” system that is really 4800 baud, four-level, the confusion is precisely this bit-rate-versus-baud mix-up, and it changes what symbol clock a decoder should hunt for.
The confusion has deep roots. The unit “baud” honors Émile Baudot, whose 1870s telegraph code sent one symbol per signalling interval, so in that binary world baud and bits per second genuinely were the same number — and the habit of using the words interchangeably stuck long after multi-level modems made them diverge. Early voiceband modems made the split concrete and public: a “2400 baud” telephone modem running four-level or higher modulation carried 4800, 9600, or more bits per second over the same 2400 symbols, and later modems held the symbol rate near the channel’s Nyquist limit while stacking ever denser constellations to push the bit rate up. The channel bandwidth never changed; only the bits per symbol did.
In practice
Because bandwidth scales with baud and not bit rate, engineers size filters and channelizers from the symbol rate, then report throughput as a bit rate. A quick sanity check on any modulation is R_b / R_s = log₂(M): if that ratio is not a clean power-of-two count of bits, either the order or one of the rates has been misquoted.
The distinction also reframes what “faster” means. Raising the baud rate widens the signal and needs more spectrum; raising the bits per symbol raises throughput within the same spectrum but demands more signal-to-noise ratio. Modern systems push both levers at once and adapt them to conditions — cellular and Wi-Fi links switch to a denser constellation (more bits/symbol) when the channel is clean and fall back to a sparser, more robust one when it degrades, all while holding the symbol rate fixed. Understanding which quantity a spec is quoting is therefore the difference between predicting a signal’s bandwidth (a baud question) and predicting its data throughput or its noise margin (a bits-per-symbol question).