UART Baud Rate Calculator Formula
Understand the math behind the uart baud rate calculator. Each variable explained with a worked example.
Formulas Used
Baud Rate Divider
baud_divider = divider_intActual Baud Rate
actual_baud_rate = actual_baudBaud Rate Error
baud_error_pct = abs(actual_baud - desired_baud) / desired_baud * 100Bit Time
bit_time_us = 1e6 / actual_baudVariables
| Variable | Description | Default |
|---|---|---|
clock_hz | Peripheral Clock(Hz) | 16000000 |
desired_baud | Desired Baud Rate(baud) | 115200 |
oversampling | Oversampling Factor | 16 |
divider_exact | Derived value= clock_hz / (oversampling * desired_baud) | calculated |
divider_int | Derived value= floor(clock_hz / (oversampling * desired_baud) + 0.5) | calculated |
actual_baud | Derived value= clock_hz / (oversampling * divider_int) | calculated |
How It Works
UART Baud Rate Generation
UART baud rate is derived from the peripheral clock using an integer divider and oversampling.
Formula
Divider = round(Clock / (Oversampling x Baud Rate))
Actual Baud = Clock / (Oversampling x Divider)
Error = Actual - Desired
Baud rate error should stay below 2% for reliable communication. Errors above 3-5% cause framing errors, especially for multi-byte transfers.
Worked Example
16 MHz clock, 115200 baud, 16x oversampling.
- 01Exact divider: 16e6 / (16 x 115200) = 8.68
- 02Integer divider: round(8.68) = 9
- 03Actual baud: 16e6 / (16 x 9) = 111,111 baud
- 04Error: |111111 - 115200| / 115200 = 3.55%
- 05This is marginal; consider a different clock frequency
Frequently Asked Questions
What baud rate error is acceptable?
Below 2% is safe. At 3%+ errors accumulate over a byte (10 bits) and the last bits may be sampled incorrectly.
How do I reduce baud rate error?
Use a clock frequency that divides evenly into common baud rates. 14.7456 MHz and 11.0592 MHz give zero error at standard rates.
What is oversampling in UART?
The receiver samples each bit multiple times (typically 16x) and uses the middle samples for data recovery, improving noise immunity.
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Open UART Baud Rate Calculator