Calculate symbol rate or bit rate from bits per symbol, converting between Hz, kHz, MHz, GHz, bps, kbps, Mbps, and Gbps units as needed.
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kHz to Bits Per Second Formula
There is no universal direct conversion from a radio/audio carrier frequency (kHz) to bits per second (bps). However, if kHz is being used to express a symbol rate (symbols per second) and you know the bits per symbol (based on modulation), then you can compute bit rate.
bps = (kHz \times 1000) \times (bits\ per\ symbol)
Variables:
- bps is the bit rate in bits per second
- kHz is the symbol rate expressed in kilohertz (1 kHz = 1000 symbols/s)
- bits per symbol depends on modulation (e.g., 1 for BPSK, 2 for QPSK, 4 for 16‑QAM, 6 for 64‑QAM)
To estimate bits per second from a symbol rate given in kHz, multiply the kHz value by 1000 to get symbols per second, then multiply by the assumed bits per symbol.
| Symbol Rate (kHz) | Bit Rate (bps) |
|---|---|
| 0.1 | 100 |
| 0.5 | 500 |
| 1 | 1,000 |
| 2 | 2,000 |
| 2.4 | 2,400 |
| 5 | 5,000 |
| 7.5 | 7,500 |
| 8 | 8,000 |
| 10 | 10,000 |
| 11.025 | 11,025 |
| 12 | 12,000 |
| 16 | 16,000 |
| 20 | 20,000 |
| 22.05 | 22,050 |
| 24 | 24,000 |
| 32 | 32,000 |
| 44.1 | 44,100 |
| 48 | 48,000 |
| 50 | 50,000 |
| 100 | 100,000 |
| Table assumes 1 bit per symbol. For other modulations, multiply by (bits per symbol). | |
What is Kilohertz?
Kilohertz (kHz) is a unit of frequency equivalent to 1,000 cycles per second. It is commonly used to measure the frequency of radio waves, audio signals, and other periodic phenomena. In digital communications, a value with the same unit (s−1) is also used to express symbol rate (baud); bit rate depends on how many bits are encoded per symbol and is not determined by carrier frequency alone.
How to Calculate Bits Per Second?
The following steps outline how to calculate bits per second from a symbol rate given in kHz.
- First, determine the symbol rate in kHz (and convert to Hz by multiplying by 1000).
- Next, determine the bits per symbol for the modulation being used.
- Use the formula bps = (kHz × 1000) × (bits per symbol) to calculate bits per second.
Example Problem :
Use the following variables as an example problem to test your knowledge.
Symbol Rate (kHz) = 5
Bits per Symbol = 1
Bit Rate (bps) = 5000
