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| / Desired x 100%
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.
clock_hz = 16000000desired_baud = 115200oversampling = 16
- 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
Ready to run the numbers?
Open UART Baud Rate Calculator