Convert bits per second to symbol frequency in hertz, or solve for bit rate or bits per symbol, with bps, Kbps, Mbps, Gbps, Hz, kHz, MHz, and GHz.
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bps To Hz Formula
The following formula is used to calculate the conversion from bps to Hz.
Variables:
- Hz is the frequency in hertz (Hz)
- Bps is the data transmission rate in bits per second (bps)
- N is the number of bits per symbol (unitless)
Divide transmitted bit rate by bits per symbol to obtain symbol rate in symbols per second (baud). This page uses Hz only as the equivalent symbol repetition frequency; it does not calculate RF carrier frequency or occupied bandwidth. For an uncoded M-ary modulation, bits per symbol = log₂(M). BPSK uses 1 bit per symbol, QPSK 2, 8-PSK 3, 16-QAM 4, 64-QAM 6 and 256-QAM 8. Coding, framing, parallel streams and protocol overhead must be accounted for when relating payload bit rate to a per-stream symbol rate.
| Data Rate (bps) | Hz (N = 1) | Hz (N = 2) | Hz (N = 4) | Hz (N = 6) | Hz (N = 8) |
|---|---|---|---|---|---|
| 1000 | 1000.000 | 500.000 | 250.000 | 166.667 | 125.000 |
| 2000 | 2000.000 | 1000.000 | 500.000 | 333.333 | 250.000 |
| 4000 | 4000.000 | 2000.000 | 1000.000 | 666.667 | 500.000 |
| 8000 | 8000.000 | 4000.000 | 2000.000 | 1333.333 | 1000.000 |
| 16000 | 16000.000 | 8000.000 | 4000.000 | 2666.667 | 2000.000 |
| 32000 | 32000.000 | 16000.000 | 8000.000 | 5333.333 | 4000.000 |
| 64000 | 64000.000 | 32000.000 | 16000.000 | 10666.667 | 8000.000 |
| 128000 | 128000.000 | 64000.000 | 32000.000 | 21333.333 | 16000.000 |
| 256000 | 256000.000 | 128000.000 | 64000.000 | 42666.667 | 32000.000 |
| 512000 | 512000.000 | 256000.000 | 128000.000 | 85333.333 | 64000.000 |
| 1000000 | 1000000.000 | 500000.000 | 250000.000 | 166666.667 | 125000.000 |
| 2000000 | 2000000.000 | 1000000.000 | 500000.000 | 333333.333 | 250000.000 |
| 5000000 | 5000000.000 | 2500000.000 | 1250000.000 | 833333.333 | 625000.000 |
| 10000000 | 10000000.000 | 5000000.000 | 2500000.000 | 1666666.667 | 1250000.000 |
| 20000000 | 20000000.000 | 10000000.000 | 5000000.000 | 3333333.333 | 2500000.000 |
| 50000000 | 50000000.000 | 25000000.000 | 12500000.000 | 8333333.333 | 6250000.000 |
| 100000000 | 100000000.000 | 50000000.000 | 25000000.000 | 16666666.667 | 12500000.000 |
| 250000000 | 250000000.000 | 125000000.000 | 62500000.000 | 41666666.667 | 31250000.000 |
| 500000000 | 500000000.000 | 250000000.000 | 125000000.000 | 83333333.333 | 62500000.000 |
| 1000000000 | 1000000000.000 | 500000000.000 | 250000000.000 | 166666666.667 | 125000000.000 |
| * Rounded to 3 decimals. Formula: Hz = Bps ÷ Number of Bits per Symbol (N). Data rates shown in bits per second (bps). | |||||
What is bps To Hz?
This calculator relates bit rate to symbol rate using a specified number of bits per symbol. The numerical symbol repetition frequency in Hz equals the symbol rate in baud. Bit rate alone does not determine RF carrier frequency or occupied signal bandwidth. A fractional custom ratio represents an effective relationship and does not imply a whole-bit uncoded modulation alphabet.
How to Calculate bps To Hz?
The following steps outline how to calculate the bps To Hz using the formula: Hz = Bps / N.
- First, determine the data transmission rate in bits per second (Bps).
- Next, determine the number of bits per symbol (N).
- Next, gather the formula from above: Hz = Bps / N.
- Finally, calculate the frequency in hertz (Hz).
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
frequency in hertz (Hz) = 500
data transmission rate in bits per second (Bps) = 1000
number of bits per symbol (N) = 2
