How to Calculate Baud Rate for Uart

UART Baud Rate & Register Calculator

Calculate divisor values and error percentages for microcontroller UART communication.

MHz kHz Hz

16x (Normal Mode) 8x (Double Speed)

Universal Asynchronous Receiver-Transmitter (UART) is one of the most common serial communication protocols in electronics. Unlike SPI or I2C, UART is asynchronous, meaning there is no shared clock signal between the sender and receiver. Instead, both devices must agree on a specific timing interval for each bit of data. This timing is defined by the Baud Rate.

When configuring a microcontroller (like an Arduino (AVR), STM32, or PIC) to communicate via UART, you typically cannot just type "9600" into a register. Instead, you must calculate a Divisor or Prescaler value based on your system's clock frequency.

The Baud Rate Formula

While specific register names (like UBRR in AVR or BRR in STM32) vary, the underlying math generally follows this structure based on the system clock frequency ($f_{osc}$) and the oversampling rate (usually 16 or 8):

Standard Formula (16x Oversampling):

Calculated Baud = f_osc / (16 * (Divisor + 1))

To find the value you need to write to the register (the Divisor), you rearrange the formula:

Divisor = (f_osc / (16 * Target Baud)) - 1

Why Error Calculation is Critical

The system clock and the target baud rate rarely divide perfectly into an integer. The "Divisor" must be an integer (in most basic implementations). This rounding causes a discrepancy between the Target Baud Rate and the Actual Baud Rate.

The error percentage is calculated as:

Error % = ((Actual Baud - Target Baud) / Target Baud) * 100

Reliability Thresholds:

• < 2% Error: Generally safe for standard communication.
• > 2% Error: Risk of frame errors increases.
• > 5% Error: Communication will likely fail, resulting in garbage data.

Example Calculation

Let's say you have an Arduino running at 16 MHz and you want a baud rate of 9600.

1. Convert Clock: 16 MHz = 16,000,000 Hz.
2. Calculate Ideal Divisor: 16,000,000 / (16 * 9600) = 104.166…
3. Subtract 1: 103.166…
4. Round to Integer: The register value is 103.
5. Calculate Actual Baud: 16,000,000 / (16 * (103 + 1)) = 9615.38 bps.
6. Calculate Error: (9615.38 – 9600) / 9600 = +0.16%.

Since 0.16% is well below the 2% threshold, this connection will be stable.

Clock too slow for target baud

Excellent (Stable)

Marginal (Risk of Errors)

Unstable (High Error)