74 IoT Formula Calculator
Interactive Calculator for Common IoT Calculations
74.1 IoT Formula Calculator
NoteQuick Calculations
Select a formula category and enter values to get instant results. All calculations include explanations and typical values.
74.2 Select Calculation Type
74.3 Calculator
Show code
linkBudgetCalc = {
if (calculationType !== "Link Budget") return null;
return html`
<div style="background: linear-gradient(135deg, #E8F6F3 0%, #D5F4E6 100%); padding: 25px; border-radius: 12px;">
<h3 style="margin-top: 0; color: #16A085;">Link Budget Calculator</h3>
<p style="color: #666;">Calculate received signal strength and determine if a link is viable.</p>
</div>
`;
}
linkBudgetCalcShow code
viewof txPowerDbm = calculationType === "Link Budget" ? Inputs.range([-10, 30], {
label: "TX Power (dBm):",
value: 14,
step: 1
}) : null
viewof txAntennaGain = calculationType === "Link Budget" ? Inputs.range([0, 15], {
label: "TX Antenna Gain (dBi):",
value: 2,
step: 0.5
}) : null
viewof rxAntennaGain = calculationType === "Link Budget" ? Inputs.range([0, 15], {
label: "RX Antenna Gain (dBi):",
value: 2,
step: 0.5
}) : null
viewof distanceM = calculationType === "Link Budget" ? Inputs.range([1, 50000], {
label: "Distance (meters):",
value: 1000,
step: 10
}) : null
viewof frequencyMhz = calculationType === "Link Budget" ? Inputs.range([100, 6000], {
label: "Frequency (MHz):",
value: 868,
step: 1
}) : null
viewof rxSensitivity = calculationType === "Link Budget" ? Inputs.range([-150, -70], {
label: "RX Sensitivity (dBm):",
value: -120,
step: 1
}) : nullShow code
linkBudgetResult = {
if (calculationType !== "Link Budget") return null;
const fspl = 20 * Math.log10(distanceM) + 20 * Math.log10(frequencyMhz * 1e6) - 147.55;
const eirp = txPowerDbm + txAntennaGain;
const rxPower = eirp - fspl + rxAntennaGain;
const margin = rxPower - rxSensitivity;
const linkWorks = margin > 0;
return html`
<div style="background: ${linkWorks ? '#D5F4E6' : '#FADBD8'}; padding: 20px; border-radius: 12px; margin: 20px 0;">
<h4 style="margin-top: 0; color: ${linkWorks ? '#27AE60' : '#E74C3C'};">
${linkWorks ? 'Link is Viable' : 'Link Will Fail'}
</h4>
<div style="display: grid; grid-template-columns: repeat(auto-fit, minmax(150px, 1fr)); gap: 15px;">
<div style="background: white; padding: 12px; border-radius: 8px; text-align: center;">
<div style="font-size: 11px; color: #666;">EIRP</div>
<div style="font-size: 20px; font-weight: bold; color: #2C3E50;">${eirp.toFixed(1)} dBm</div>
</div>
<div style="background: white; padding: 12px; border-radius: 8px; text-align: center;">
<div style="font-size: 11px; color: #666;">Path Loss</div>
<div style="font-size: 20px; font-weight: bold; color: #E74C3C;">${fspl.toFixed(1)} dB</div>
</div>
<div style="background: white; padding: 12px; border-radius: 8px; text-align: center;">
<div style="font-size: 11px; color: #666;">RX Power</div>
<div style="font-size: 20px; font-weight: bold; color: #3498DB;">${rxPower.toFixed(1)} dBm</div>
</div>
<div style="background: white; padding: 12px; border-radius: 8px; text-align: center;">
<div style="font-size: 11px; color: #666;">Link Margin</div>
<div style="font-size: 20px; font-weight: bold; color: ${margin > 10 ? '#27AE60' : margin > 0 ? '#F39C12' : '#E74C3C'};">
${margin.toFixed(1)} dB
</div>
</div>
</div>
<div style="margin-top: 15px; padding: 10px; background: white; border-radius: 6px; font-size: 13px;">
<strong>Calculation:</strong><br>
FSPL = 20×log(${distanceM}) + 20×log(${frequencyMhz}×10⁶) - 147.55 = ${fspl.toFixed(1)} dB<br>
RX Power = ${txPowerDbm} + ${txAntennaGain} - ${fspl.toFixed(1)} + ${rxAntennaGain} = ${rxPower.toFixed(1)} dBm<br>
Margin = ${rxPower.toFixed(1)} - (${rxSensitivity}) = ${margin.toFixed(1)} dB
</div>
</div>
`;
}
linkBudgetResultShow code
batteryLifeCalc = {
if (calculationType !== "Battery Life") return null;
return html`
<div style="background: linear-gradient(135deg, #FEF5E7 0%, #FCF3CF 100%); padding: 25px; border-radius: 12px;">
<h3 style="margin-top: 0; color: #E67E22;">Battery Life Calculator</h3>
<p style="color: #666;">Estimate how long your IoT device will run on battery power.</p>
</div>
`;
}
batteryLifeCalcShow code
viewof batteryCapacity = calculationType === "Battery Life" ? Inputs.range([50, 10000], {
label: "Battery Capacity (mAh):",
value: 2000,
step: 50
}) : null
viewof activeCurrent = calculationType === "Battery Life" ? Inputs.range([0.1, 500], {
label: "Active Current (mA):",
value: 80,
step: 0.1
}) : null
viewof sleepCurrent = calculationType === "Battery Life" ? Inputs.range([0.001, 10], {
label: "Sleep Current (mA):",
value: 0.01,
step: 0.001
}) : null
viewof activeTimePercent = calculationType === "Battery Life" ? Inputs.range([0.01, 100], {
label: "Active Time (%):",
value: 1,
step: 0.01
}) : null
viewof batteryEfficiency = calculationType === "Battery Life" ? Inputs.range([50, 100], {
label: "Usable Capacity (%):",
value: 80,
step: 5
}) : nullShow code
batteryResult = {
if (calculationType !== "Battery Life") return null;
const avgCurrent = (activeCurrent * activeTimePercent / 100) + (sleepCurrent * (100 - activeTimePercent) / 100);
const effectiveCapacity = batteryCapacity * batteryEfficiency / 100;
const lifeHours = effectiveCapacity / avgCurrent;
const lifeDays = lifeHours / 24;
const lifeMonths = lifeDays / 30;
const lifeYears = lifeDays / 365;
let lifeDisplay, lifeUnit;
if (lifeYears >= 1) {
lifeDisplay = lifeYears.toFixed(1);
lifeUnit = "years";
} else if (lifeMonths >= 1) {
lifeDisplay = lifeMonths.toFixed(1);
lifeUnit = "months";
} else if (lifeDays >= 1) {
lifeDisplay = lifeDays.toFixed(1);
lifeUnit = "days";
} else {
lifeDisplay = lifeHours.toFixed(1);
lifeUnit = "hours";
}
return html`
<div style="background: #D5F4E6; padding: 20px; border-radius: 12px; margin: 20px 0;">
<h4 style="margin-top: 0; color: #27AE60;">Estimated Battery Life</h4>
<div style="display: grid; grid-template-columns: repeat(auto-fit, minmax(150px, 1fr)); gap: 15px;">
<div style="background: white; padding: 12px; border-radius: 8px; text-align: center;">
<div style="font-size: 11px; color: #666;">Average Current</div>
<div style="font-size: 20px; font-weight: bold; color: #2C3E50;">
${avgCurrent < 1 ? (avgCurrent * 1000).toFixed(1) + ' uA' : avgCurrent.toFixed(2) + ' mA'}
</div>
</div>
<div style="background: white; padding: 12px; border-radius: 8px; text-align: center;">
<div style="font-size: 11px; color: #666;">Usable Capacity</div>
<div style="font-size: 20px; font-weight: bold; color: #E67E22;">${effectiveCapacity.toFixed(0)} mAh</div>
</div>
<div style="background: white; padding: 12px; border-radius: 8px; text-align: center;">
<div style="font-size: 11px; color: #666;">Battery Life</div>
<div style="font-size: 24px; font-weight: bold; color: #27AE60;">${lifeDisplay} ${lifeUnit}</div>
</div>
</div>
<div style="margin-top: 15px; padding: 10px; background: white; border-radius: 6px; font-size: 13px;">
<strong>Calculation:</strong><br>
Avg Current = (${activeCurrent} × ${activeTimePercent}%) + (${sleepCurrent} × ${100-activeTimePercent}%) = ${avgCurrent.toFixed(4)} mA<br>
Life = ${effectiveCapacity} mAh ÷ ${avgCurrent.toFixed(4)} mA = ${lifeHours.toFixed(0)} hours = ${lifeDays.toFixed(1)} days
</div>
</div>
`;
}
batteryResultShow code
adcCalc = {
if (calculationType !== "ADC/Signal") return null;
return html`
<div style="background: linear-gradient(135deg, #E8F4FD 0%, #D4E6F1 100%); padding: 25px; border-radius: 12px;">
<h3 style="margin-top: 0; color: #3498DB;">ADC & Signal Calculator</h3>
<p style="color: #666;">Calculate ADC resolution, quantization error, and sampling requirements.</p>
</div>
`;
}
adcCalcShow code
viewof adcBitsCalc = calculationType === "ADC/Signal" ? Inputs.range([8, 24], {
label: "ADC Resolution (bits):",
value: 12,
step: 1
}) : null
viewof vrefCalc = calculationType === "ADC/Signal" ? Inputs.range([1.0, 5.0], {
label: "Reference Voltage (V):",
value: 3.3,
step: 0.1
}) : null
viewof signalFreqCalc = calculationType === "ADC/Signal" ? Inputs.range([1, 100000], {
label: "Max Signal Frequency (Hz):",
value: 1000,
step: 1
}) : nullShow code
adcResult = {
if (calculationType !== "ADC/Signal") return null;
const levels = Math.pow(2, adcBitsCalc);
const stepSize = vrefCalc / levels;
const stepSizeMv = stepSize * 1000;
const quantError = stepSize / 2;
const snrDb = 6.02 * adcBitsCalc + 1.76;
const nyquistRate = signalFreqCalc * 2;
const recommendedRate = signalFreqCalc * 5;
return html`
<div style="background: #D4E6F1; padding: 20px; border-radius: 12px; margin: 20px 0;">
<h4 style="margin-top: 0; color: #3498DB;">ADC Specifications</h4>
<div style="display: grid; grid-template-columns: repeat(auto-fit, minmax(150px, 1fr)); gap: 15px;">
<div style="background: white; padding: 12px; border-radius: 8px; text-align: center;">
<div style="font-size: 11px; color: #666;">Quantization Levels</div>
<div style="font-size: 20px; font-weight: bold; color: #2C3E50;">${levels.toLocaleString()}</div>
</div>
<div style="background: white; padding: 12px; border-radius: 8px; text-align: center;">
<div style="font-size: 11px; color: #666;">Step Size (LSB)</div>
<div style="font-size: 20px; font-weight: bold; color: #E67E22;">
${stepSizeMv < 1 ? (stepSizeMv * 1000).toFixed(1) + ' uV' : stepSizeMv.toFixed(2) + ' mV'}
</div>
</div>
<div style="background: white; padding: 12px; border-radius: 8px; text-align: center;">
<div style="font-size: 11px; color: #666;">Max Quant Error</div>
<div style="font-size: 20px; font-weight: bold; color: #E74C3C;">
+/-${(quantError * 1000).toFixed(2)} mV
</div>
</div>
<div style="background: white; padding: 12px; border-radius: 8px; text-align: center;">
<div style="font-size: 11px; color: #666;">Theoretical SNR</div>
<div style="font-size: 20px; font-weight: bold; color: #9B59B6;">${snrDb.toFixed(1)} dB</div>
</div>
</div>
<div style="margin-top: 15px; padding: 10px; background: white; border-radius: 6px; font-size: 13px;">
<strong>Sampling Requirements for ${signalFreqCalc} Hz signal:</strong><br>
Nyquist minimum: ${nyquistRate.toLocaleString()} Hz<br>
Recommended (5x): ${recommendedRate.toLocaleString()} Hz
</div>
</div>
`;
}
adcResultShow code
dataRateCalc = {
if (calculationType !== "Data Rate") return null;
return html`
<div style="background: linear-gradient(135deg, #F5EEF8 0%, #E8DAEF 100%); padding: 25px; border-radius: 12px;">
<h3 style="margin-top: 0; color: #9B59B6;">Data Rate Calculator</h3>
<p style="color: #666;">Calculate bandwidth requirements for your IoT data stream.</p>
</div>
`;
}
dataRateCalcShow code
viewof sensorCount = calculationType === "Data Rate" ? Inputs.range([1, 100], {
label: "Number of Sensors:",
value: 10,
step: 1
}) : null
viewof bytesPerReading = calculationType === "Data Rate" ? Inputs.range([1, 100], {
label: "Bytes per Reading:",
value: 4,
step: 1
}) : null
viewof readingsPerSecond = calculationType === "Data Rate" ? Inputs.range([0.001, 1000], {
label: "Readings per Second:",
value: 1,
step: 0.001
}) : null
viewof overheadPercent = calculationType === "Data Rate" ? Inputs.range([0, 100], {
label: "Protocol Overhead (%):",
value: 20,
step: 5
}) : nullShow code
dataRateResult = {
if (calculationType !== "Data Rate") return null;
const rawBytesPerSec = sensorCount * bytesPerReading * readingsPerSecond;
const withOverhead = rawBytesPerSec * (1 + overheadPercent / 100);
const bitsPerSec = withOverhead * 8;
const mbPerDay = (withOverhead * 86400) / (1024 * 1024);
const gbPerMonth = (mbPerDay * 30) / 1024;
return html`
<div style="background: #E8DAEF; padding: 20px; border-radius: 12px; margin: 20px 0;">
<h4 style="margin-top: 0; color: #9B59B6;">Data Rate Requirements</h4>
<div style="display: grid; grid-template-columns: repeat(auto-fit, minmax(150px, 1fr)); gap: 15px;">
<div style="background: white; padding: 12px; border-radius: 8px; text-align: center;">
<div style="font-size: 11px; color: #666;">Raw Data Rate</div>
<div style="font-size: 20px; font-weight: bold; color: #2C3E50;">
${rawBytesPerSec < 1024 ? rawBytesPerSec.toFixed(1) + ' B/s' : (rawBytesPerSec / 1024).toFixed(2) + ' KB/s'}
</div>
</div>
<div style="background: white; padding: 12px; border-radius: 8px; text-align: center;">
<div style="font-size: 11px; color: #666;">With Overhead</div>
<div style="font-size: 20px; font-weight: bold; color: #E67E22;">
${bitsPerSec < 1000 ? bitsPerSec.toFixed(0) + ' bps' : (bitsPerSec / 1000).toFixed(2) + ' kbps'}
</div>
</div>
<div style="background: white; padding: 12px; border-radius: 8px; text-align: center;">
<div style="font-size: 11px; color: #666;">Per Day</div>
<div style="font-size: 20px; font-weight: bold; color: #3498DB;">
${mbPerDay < 1 ? (mbPerDay * 1024).toFixed(1) + ' KB' : mbPerDay.toFixed(1) + ' MB'}
</div>
</div>
<div style="background: white; padding: 12px; border-radius: 8px; text-align: center;">
<div style="font-size: 11px; color: #666;">Per Month</div>
<div style="font-size: 20px; font-weight: bold; color: #27AE60;">
${gbPerMonth < 1 ? (gbPerMonth * 1024).toFixed(1) + ' MB' : gbPerMonth.toFixed(2) + ' GB'}
</div>
</div>
</div>
</div>
`;
}
dataRateResultShow code
unitConvertCalc = {
if (calculationType !== "Unit Converter") return null;
return html`
<div style="background: linear-gradient(135deg, #FADBD8 0%, #F5B7B1 100%); padding: 25px; border-radius: 12px;">
<h3 style="margin-top: 0; color: #E74C3C;">Unit Converter</h3>
<p style="color: #666;">Convert between common IoT units.</p>
</div>
`;
}
unitConvertCalcShow code
viewof conversionType = calculationType === "Unit Converter" ? Inputs.radio(
["dBm ↔ mW", "Frequency", "Data Size", "Time"],
{label: "Convert:", value: "dBm ↔ mW"}
) : null
viewof inputValue = calculationType === "Unit Converter" ? Inputs.range([-50, 50], {
label: conversionType === "dBm ↔ mW" ? "dBm value:" :
conversionType === "Frequency" ? "MHz value:" :
conversionType === "Data Size" ? "KB value:" : "ms value:",
value: 0,
step: 0.1
}) : nullShow code
unitResult = {
if (calculationType !== "Unit Converter") return null;
let results = [];
if (conversionType === "dBm ↔ mW") {
const mw = Math.pow(10, inputValue / 10);
const dbmFromMw = 10 * Math.log10(Math.abs(inputValue) || 0.001);
results = [
{label: "dBm → mW", value: inputValue + " dBm = " + (mw < 0.01 ? (mw * 1000).toFixed(3) + " uW" : mw.toFixed(4) + " mW")},
{label: "mW → dBm", value: Math.abs(inputValue) + " mW = " + dbmFromMw.toFixed(2) + " dBm"}
];
} else if (conversionType === "Frequency") {
results = [
{label: "MHz → Hz", value: inputValue + " MHz = " + (inputValue * 1e6).toLocaleString() + " Hz"},
{label: "MHz → GHz", value: inputValue + " MHz = " + (inputValue / 1000).toFixed(4) + " GHz"},
{label: "Wavelength", value: "λ = " + (299792458 / (inputValue * 1e6)).toFixed(2) + " m"}
];
} else if (conversionType === "Data Size") {
results = [
{label: "KB → Bytes", value: inputValue + " KB = " + (inputValue * 1024).toLocaleString() + " bytes"},
{label: "KB → MB", value: inputValue + " KB = " + (inputValue / 1024).toFixed(4) + " MB"},
{label: "KB → bits", value: inputValue + " KB = " + (inputValue * 8192).toLocaleString() + " bits"}
];
} else {
results = [
{label: "ms → seconds", value: inputValue + " ms = " + (inputValue / 1000).toFixed(4) + " s"},
{label: "ms → microseconds", value: inputValue + " ms = " + (inputValue * 1000).toLocaleString() + " us"},
{label: "Frequency", value: "1/" + inputValue + " ms = " + (1000 / inputValue).toFixed(2) + " Hz"}
];
}
return html`
<div style="background: #F5B7B1; padding: 20px; border-radius: 12px; margin: 20px 0;">
<h4 style="margin-top: 0; color: #E74C3C;">Conversion Results</h4>
${results.map(r => html`
<div style="background: white; padding: 12px; border-radius: 8px; margin: 10px 0;">
<strong>${r.label}:</strong> ${r.value}
</div>
`)}
</div>
`;
}
unitResult74.4 Export Results
Show code
exportData = {
const timestamp = new Date().toISOString();
const tool = "IoT Formula Calculator";
if (calculationType === "Link Budget") {
const fspl = 20 * Math.log10(distanceM) + 20 * Math.log10(frequencyMhz * 1e6) - 147.55;
const eirp = txPowerDbm + txAntennaGain;
const rxPower = eirp - fspl + rxAntennaGain;
const margin = rxPower - rxSensitivity;
return {
title: "Link Budget Calculation",
tool: tool,
timestamp: timestamp,
inputs: {
txPower: txPowerDbm + " dBm",
txAntennaGain: txAntennaGain + " dBi",
rxAntennaGain: rxAntennaGain + " dBi",
distance: distanceM + " m",
frequency: frequencyMhz + " MHz",
rxSensitivity: rxSensitivity + " dBm"
},
results: {
eirp: eirp.toFixed(1) + " dBm",
pathLoss: fspl.toFixed(1) + " dB",
rxPower: rxPower.toFixed(1) + " dBm",
linkMargin: margin.toFixed(1) + " dB",
linkViable: margin > 0 ? "Yes" : "No"
}
};
}
if (calculationType === "Battery Life") {
const avgCurrent = (activeCurrent * activeTimePercent / 100) + (sleepCurrent * (100 - activeTimePercent) / 100);
const effectiveCapacity = batteryCapacity * batteryEfficiency / 100;
const lifeHours = effectiveCapacity / avgCurrent;
return {
title: "Battery Life Calculation",
tool: tool,
timestamp: timestamp,
inputs: {
batteryCapacity: batteryCapacity + " mAh",
activeCurrent: activeCurrent + " mA",
sleepCurrent: sleepCurrent + " mA",
activeTime: activeTimePercent + " %",
usableCapacity: batteryEfficiency + " %"
},
results: {
averageCurrent: avgCurrent.toFixed(3) + " mA",
effectiveCapacity: effectiveCapacity.toFixed(0) + " mAh",
batteryLifeHours: lifeHours.toFixed(1) + " hours",
batteryLifeDays: (lifeHours / 24).toFixed(1) + " days",
batteryLifeYears: (lifeHours / 8760).toFixed(2) + " years"
}
};
}
return {
title: calculationType + " Results",
tool: tool,
timestamp: timestamp,
inputs: {},
results: { message: "Select Link Budget or Battery Life for detailed export" }
};
}
// Export buttons
html`
<div style="background: #f8f9fa; padding: 15px; border-radius: 10px; margin: 15px 0;">
<strong style="display: block; margin-bottom: 10px;">Export Your Results:</strong>
<div style="display: flex; gap: 10px; flex-wrap: wrap;">
<button onclick="
const data = ${JSON.stringify(exportData)};
navigator.clipboard.writeText(JSON.stringify(data, null, 2));
this.textContent = 'Copied!';
setTimeout(() => this.textContent = 'Copy JSON', 1500);
" style="padding: 8px 16px; background: #2C3E50; color: white; border: none; border-radius: 6px; cursor: pointer;">
Copy JSON
</button>
<button onclick="
const data = ${JSON.stringify(exportData)};
let md = '## ' + data.title + '\\n\\n';
md += '**Generated:** ' + new Date(data.timestamp).toLocaleString() + '\\n\\n';
md += '### Inputs\\n';
for (const [k,v] of Object.entries(data.inputs)) md += '- **' + k + ':** ' + v + '\\n';
md += '\\n### Results\\n';
for (const [k,v] of Object.entries(data.results)) md += '- **' + k + ':** ' + v + '\\n';
navigator.clipboard.writeText(md);
this.textContent = 'Copied!';
setTimeout(() => this.textContent = 'Copy Markdown', 1500);
" style="padding: 8px 16px; background: #16A085; color: white; border: none; border-radius: 6px; cursor: pointer;">
Copy Markdown
</button>
<button onclick="
const data = ${JSON.stringify(exportData)};
const blob = new Blob([JSON.stringify(data, null, 2)], {type: 'application/json'});
const url = URL.createObjectURL(blob);
const a = document.createElement('a');
a.href = url;
a.download = 'iot-calculation-' + Date.now() + '.json';
a.click();
" style="padding: 8px 16px; background: #E67E22; color: white; border: none; border-radius: 6px; cursor: pointer;">
Download JSON
</button>
</div>
</div>
`74.5 Quick Reference
| Formula | Equation | Example |
|---|---|---|
| FSPL | 20log(d) + 20log(f) - 147.55 | 1km @ 868MHz = 91.3dB |
| Link Budget | Ptx + Gtx - PathLoss + Grx | 14 + 2 - 91 + 2 = -73dBm |
| Battery Life | Capacity / Avg_Current | 2000mAh / 0.1mA = 20000h |
| ADC Step | Vref / 2^bits | 3.3V / 4096 = 0.8mV |
| Nyquist | Fs > 2 × Fmax | 1kHz signal → > 2kHz sample |
| SNR (ADC) | 6.02 × bits + 1.76 | 12-bit = 74dB |
74.6 Related Resources
- Quick Reference Cards - Protocol cheat sheets
- Wireless Range Calculator - Detailed link budget tool
- ADC Resolution Visualizer - Visual ADC exploration
- Power Budget Calculator - Battery life estimation