How to Calculate Baud Rate in Uart

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UART Baud Rate Divisor Calculator

Hz
kHz
MHz

16x (Standard)
8x (Double Speed)

How to Calculate Baud Rate in UART

Calculating the correct baud rate settings is a fundamental step in setting up serial communication for microcontrollers like Arduino (AVR), STM32, PIC, or FPGA UART modules. The “Baud Rate” defines the speed at which data is transmitted over the serial line, measured in bits per second (bps).

Since microcontrollers operate on a system clock (oscillator), they must divide this clock frequency down to match the standard baud rates (like 9600, 115200, etc.) expected by other devices. This division is handled by a hardware counter often called the UBRR (USART Baud Rate Register) or BRR.

The Baud Rate Formula

While specific register names differ between manufacturers, the underlying math for asynchronous mode is generally consistent. The formula to determine the necessary divisor value is:

Divisor = System Clock Frequency / (Oversampling × Target Baud Rate)

Where:

• System Clock Frequency: The speed of your microcontroller’s oscillator (e.g., 16 MHz).
• Oversampling: Typically 16 for standard mode or 8 for double-speed mode. The UART receiver samples the line multiple times per bit to ensure data integrity.
• Target Baud Rate: The desired speed (e.g., 9600 bps).

Why Error Calculation is Critical

Because the Divisor register usually only accepts integer values (whole numbers), you cannot always generate the exact target baud rate. The calculator above rounds the ideal divisor to the nearest integer, which introduces a slight timing error.

Acceptable Error Margins:

• < 2.0%: generally safe for standard 8-bit data communication.
• > 2.5%: risky; bit errors may occur, especially with long data packets.
• > 4.5%: communication will likely fail completely.

Example Calculation

Let’s say you have an Arduino running at 16 MHz and you want a baud rate of 9600 using standard 16x oversampling.

1. Convert Clock: 16 MHz = 16,000,000 Hz.
2. Apply Formula: 16,000,000 / (16 × 9600) = 16,000,000 / 153,600.
3. Result: 104.166…
4. Register Value: Round to nearest integer -> 104.
5. Check Error:
   • Actual Speed = 16,000,000 / (16 × 104) ≈ 9615 bps.
   • Error = (9615 – 9600) / 9600 ≈ 0.16% (Excellent).

function calculateBaud() {
// 1. Get input values
var clockInput = document.getElementById(‘sysClock’).value;
var unitMultiplier = document.getElementById(‘clockUnit’).value;
var targetBaud = document.getElementById(‘targetBaud’).value;
var oversampling = document.getElementById(‘oversampling’).value;
// 2. Validate inputs
if (clockInput === “” || targetBaud === “”) {
alert(“Please enter both System Clock and Target Baud Rate.”);
return;
}
var clockFreq = parseFloat(clockInput) * parseFloat(unitMultiplier);
var baudRate = parseFloat(targetBaud);
var mode = parseInt(oversampling);
if (isNaN(clockFreq) || isNaN(baudRate) || baudRate <= 0 || clockFreq <= 0) {
alert("Please enter valid positive numbers.");
return;
}
// 3. Calculate Ideal Divisor
// Formula: Divisor = F_osc / (Mode * Baud)
// Note: For some architectures (like AVR UBRR), the formula is (F_osc / (Mode * Baud)) – 1.
// However, generic linear divisors (like STM32) are F_osc / Baud.
// We will use the generic divider calculation used to find the ratio,
// which represents the total division factor.
// If the user needs the "minus 1" variant (common in 8-bit AVR), they simply subtract 1 from this result.
// To be most helpful, we calculate the total division ratio.
var idealDivisor = clockFreq / (mode * baudRate);
// 4. Calculate Integer Divisor (Register Setting)
// Some systems subtract 1 (AVR), others don't. We provide the pure division ratio.
// To support the most generic "How do I get this baud rate" context, rounding is key.
// However, standard AVR formula for UBRR is: (F_osc / (16*Baud)) – 1.
// Standard STM32 USARTDIV is: F_osc / (16*Baud) (fixed point).
// Let's stick to the Ratio approach: Ratio = Clock / (Samples * Baud)
// We will assume the user sets the register to the rounded ratio minus 1 IF their specific hardware requires it,
// but physically the Divider determines the speed.
// Let's implement the standard linear division ratio used to calculate ACTUAL speed.
var integerDivisor = Math.round(idealDivisor);
// Handle edge case where divisor is too small
if (integerDivisor < 1) {
integerDivisor = 1;
}
// 5. Calculate Actual Baud Rate
var actualBaud = clockFreq / (mode * integerDivisor);
// 6. Calculate Error Percentage
var errorDiff = actualBaud – baudRate;
var errorPercent = (errorDiff / baudRate) * 100;
var absError = Math.abs(errorPercent);
// 7. Determine Status
var statusHtml = "";
if (absError <= 2.0) {
statusHtml = "Success (” + errorPercent.toFixed(2) + “%) – Reliable Communication”;
} else if (absError <= 4.5) {
statusHtml = "Warning (” + errorPercent.toFixed(2) + “%) – High Error Rate Risk”;
} else {
statusHtml = “Failure (” + errorPercent.toFixed(2) + “%) – Communication Unlikely”;
}
// 8. Update Display
document.getElementById(‘idealDivisor’).innerHTML = idealDivisor.toFixed(4);
// Note for the user about the -1 convention common in AVR
var divisorText = integerDivisor;
// Check if integerDivisor is very close to ideal. If not, maybe mention it.
document.getElementById(‘integerDivisor’).innerText = divisorText + ” (Ratio)”;
document.getElementById(‘actualBaud’).innerText = Math.round(actualBaud).toLocaleString() + ” bps”;
// Color code the error
var errorColor = absError > 2.5 ? “#c0392b” : “#27ae60”;
document.getElementById(‘errorPercent’).innerHTML = “” + errorPercent.toFixed(2) + “%“;
document.getElementById(‘statusMessage’).innerHTML = statusHtml;
// Show results
document.getElementById(‘resultsArea’).style.display = “block”;
}