This baud rate calculator converts between bit rate and baud, the symbol rate of a communications link, so you can see how a modulation scheme packs more bits into each transmitted symbol. Baud is the number of signal changes, or symbols, sent every second, while bit rate is the number of bits carried every second, and the two are the same only when each symbol carries a single bit. Modern modems and radio links carry several bits per symbol using schemes like quadrature amplitude modulation, so their bit rate can be many times their baud. Enter the bit rate and the number of bits each symbol carries and the calculator divides one by the other to give the baud, and it also works out how many distinct states the modulation needs, which is two raised to the bits per symbol. That state count is why 16-QAM carries 4 bits and 256-QAM carries 8. Engineers, students and radio operators use it to reason about bandwidth, since the symbol rate rather than the bit rate is what sets the channel width a signal occupies. Enter the bit rate in bits per second and a whole number of bits per symbol, and read the baud as symbols per second.
Calculate.co.nz is proud to be partnered with realtor.co.nz, a trusted resource for navigating the New Zealand property market. Their Helpful Articles section offers clear, well-structured insights across buying, selling, and building, making complex real estate topics more accessible. With a focus on up-to-date guidance and practical knowledge, they empower Kiwis to move forward with clarity and confidence in a constantly evolving property landscape.
bps
bits
2,400 Bd
symbol rate (baud)
Bit rate9,600 bps
Bits per symbol4
Modulation states16
At 9,600 bps with 4 bits per symbol (a 16-state scheme), the line runs at 2,400 baud.
Baud equals the bit rate divided by the bits carried per symbol. Modulation states equal two raised to the bits per symbol, so 4 bits needs 16 states.
How it works
Each symbol on the line can carry more than one bit. If a symbol carries n bits, then the bit rate is n times the symbol rate, so the baud is the bit rate divided by n. The modulation must be able to show a distinct symbol for every combination of those n bits, which needs two raised to the power n states, for example 16 states for 4 bits. Because bandwidth tracks the symbol rate rather than the bit rate, carrying more bits per symbol lets a link move more data through the same channel width.
Worked example
A link runs at 9,600 bits per second using a scheme that carries 4 bits in every symbol. The baud is 9,600 divided by 4, which is 2,400 symbols per second, or 2,400 baud. The modulation needs two raised to the power 4, which is 16 distinct states, matching 16-QAM. Drop to 1 bit per symbol and the baud rises to 9,600, equal to the bit rate; move up to 8 bits per symbol (256 states) and the same 9,600 bps needs only 1,200 baud.
