Baud Rate Error Calculator
In embedded development, UART baud rate is derived from the system clock via division. When the crystal frequency doesn't evenly divide the target baud rate, error is introduced — exceeding ±2% can cause frame drops.
Core Formula
KATEX_0
Actual baud rate $BR_{actual} = f_{osc} / (16 \times N)$, where $N = \text{round}(f_{osc} / (16 \times BR_{target}))$ is the integer divisor register value.
slex: "0.1",
namespace: "example_baud_rate_calculator",
g: {
freq: 8,
freqUnit: "MHz",
baud: 115200,
freqHz: function () { var m = { MHz: 1e6, kHz: 1e3, Hz: 1 }; return this.freq * (m[this.freqUnit] || 1e6); },
divisor: function () { return this.freqHz() / (16 * this.baud); },
regValue: function () { return Math.round(this.divisor()); },
actualBaud: function () { return this.freqHz() / (16 * this.regValue()); },
error: function () { return Math.abs((this.actualBaud() - this.baud) / this.baud * 100); },
reliability: function () { var e = this.error(); return e < 0.5 ? "Excellent" : e < 2 ? "Acceptable" : e < 5 ? "Risky" : "Unusable"; },
tone: function () { var e = this.error(); return e < 0.5 ? "success" : e < 2 ? "info" : e < 5 ? "warning" : "danger"; }
},
layout: {
"section:baud": {
eyebrow: "Calculator",
title: "Baud Rate Error Calculator",
subtitle: "Enter crystal frequency and target baud rate to calculate error.",
"card:baud": {
title: "Baud Rate Error Calculator",
"grid:params": {
columns: 1, mdColumns: 2,
"column:freqField": {
"input:freq": { label: "Crystal frequency", "$value": "g.freq", type: "number", unit: "MHz", onchange: "g.freq = Number($event || 0)" }
},
"column:baudField": {
"select:baud": { label: "Target baud rate", "$value": "g.baud", options: [{ label: "9600", value: 9600 }, { label: "19200", value: 19200 }, { label: "38400", value: 38400 }, { label: "57600", value: 57600 }, { label: "115200", value: 115200 }, { label: "230400", value: 230400 }, { label: "460800", value: 460800 }], onchange: "g.baud = Number($event)" }
},
"column:unitField": {
"select:unit": { label: "Frequency unit", "$value": "g.freqUnit", options: [{ label: "MHz", value: "MHz" }, { label: "kHz", value: "kHz" }, { label: "Hz", value: "Hz" }], onchange: "g.freqUnit = String($event)" }
},
"column:divField": {
"stat:divisor": { label: "Division ratio", "$value": "g.divisor().toFixed(3)" }
}
},
"formula:equation": { "$tex": "'\\\\text{Error} = \\\\frac{|' + g.actualBaud().toFixed(0) + ' - ' + g.baud + '|}{' + g.baud + '} \\\\times 100\\\\% = ' + g.error().toFixed(2) + '\\\\%'" },
"grid:results": {
columns: 1, mdColumns: 4,
"stat:actualBaud": { label: "Actual baud rate", "$value": "g.actualBaud().toFixed(0)", unit: "bps" },
"stat:error": { label: "Error", "$value": "g.error().toFixed(2)", unit: "%" },
"stat:reliability": { label: "Reliability", "$value": "g.reliability()", "$tone": "g.tone()" },
"stat:regValue": { label: "Register value", "$value": "g.regValue()" }
},
"callout:advice": { "$tone": "g.tone()", "$text": "g.error() < 0.5 ? 'Minimal error — communication is reliable.' : g.error() < 2 ? 'Error is within acceptable range (<2%). Works in most scenarios.' : g.error() < 5 ? 'Error is high — long-frame communication may fail. Consider changing crystal or lowering baud rate.' : 'Error too high — communication is unreliable. Choose a crystal frequency that divides evenly.'" }
}
}
}
}
Common Crystal Frequencies vs Baud Rate Error
| Crystal | 9600 | 19200 | 38400 | 57600 | 115200 |
|---|---|---|---|---|---|
| 1.8432 MHz | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| 3.6864 MHz | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| 4.0000 MHz | 8.51 | 8.51 | 8.51 | 8.51 | 8.51 |
| 7.3728 MHz | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| 8.0000 MHz | 8.51 | 8.51 | 8.51 | 8.51 | 8.51 |
| 11.0592 MHz | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| 14.7456 MHz | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| 16.0000 MHz | 8.51 | 8.51 | 8.51 | 8.51 | 8.51 |
Engineering notes:
- The key to zero error: crystal frequency must be evenly divisible by $16 \times BR$
- 11.0592 MHz is the classic UART choice — zero error for all standard baud rates
- 7.3728 MHz and 14.7456 MHz are also zero-error
- Error < 2% usually works in practice, but high-speed long-frame scenarios should target < 1%