HVAC Load and Duct Sizing Calculator

ANA›Life Services Authority›National Calculator Authority›HVAC Load and Duct Sizing Calculator

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HVAC Load and Duct Sizing Calculator

Calculate the heating/cooling load for a room and determine the required duct diameter or rectangular duct dimensions based on airflow requirements.

### Room Load Inputs

Room Length (ft)

Room Width (ft)

Ceiling Height (ft)

Insulation Quality

Poor (older home, minimal insulation) Average (standard insulation) Good (well-insulated, modern home) Excellent (energy-efficient/passive)

Number of Windows

Avg Window Area (sq ft each)

Outdoor Design Temp (°F)

Indoor Design Temp (°F)

Number of Occupants

Mode

Cooling Heating

### Duct Sizing Inputs

Duct Air Velocity (FPM)

Duct Shape

Round Duct Rectangular Duct

Duct Height (in) — for rectangular

Calculate

document.getElementById('hva-duct-type').addEventListener('change', function() { document.getElementById('hva-rect-row').style.display = this.value === 'rectangular' ? '' : 'none'; });

function hvaCalc() { var length = parseFloat(document.getElementById('hva-length').value); var width = parseFloat(document.getElementById('hva-width').value); var height = parseFloat(document.getElementById('hva-height').value); var insulation = document.getElementById('hva-insulation').value; var windows = parseFloat(document.getElementById('hva-windows').value); var winSize = parseFloat(document.getElementById('hva-window-size').value); var outdoorTemp = parseFloat(document.getElementById('hva-outdoor-temp').value); var indoorTemp = parseFloat(document.getElementById('hva-indoor-temp').value); var occupants = parseFloat(document.getElementById('hva-occupants').value); var mode = document.getElementById('hva-mode').value; var velocity = parseFloat(document.getElementById('hva-duct-velocity').value); var ductType = document.getElementById('hva-duct-type').value; var ductH = parseFloat(document.getElementById('hva-duct-height').value); var res = document.getElementById('hva-result');

// --- Validation --- if (isNaN(length) || length Please enter a valid room length.'; return; } if (isNaN(width) || width Please enter a valid room width.'; return; } if (isNaN(height) || height Please enter a valid ceiling height.'; return; } if (isNaN(windows)|| windows Number of windows must be 0 or more.'; return; } if (isNaN(winSize)|| winSize Window area must be 0 or more.'; return; } if (isNaN(outdoorTemp)) { res.innerHTML = 'Please enter a valid outdoor design temperature.'; return; } if (isNaN(indoorTemp)) { res.innerHTML = 'Please enter a valid indoor design temperature.'; return; } if (isNaN(occupants)|| occupants Occupants must be 0 or more.'; return; } if (isNaN(velocity) || velocity Please enter a valid duct velocity.'; return; } if (ductType === 'rectangular' && (isNaN(ductH) || ductH Please enter a valid duct height for rectangular duct.'; return; }

var deltaT = Math.abs(outdoorTemp - indoorTemp); if (deltaT === 0) { res.innerHTML = 'Outdoor and indoor temperatures cannot be equal.'; return; }

// --- U-values (BTU/hr·ft²·°F) by insulation quality --- // Wall, Ceiling, Window U-values var uWall, uCeil, uWin; if (insulation === 'poor') { uWall = 0.20; uCeil = 0.15; uWin = 1.10; } else if (insulation === 'average') { uWall = 0.10; uCeil = 0.07; uWin = 0.65; } else if (insulation === 'good') { uWall = 0.06; uCeil = 0.04; uWin = 0.35; } else { // excellent uWall = 0.03; uCeil = 0.02; uWin = 0.20; }

// --- Areas --- var floorArea = length * width; // ft² var ceilArea = floorArea; // ft² var wallArea = 2 * (length + width) * height; // ft² gross var windowArea = windows * winSize; // ft² var netWallArea = wallArea - windowArea; // ft²

// --- Conduction Loads (BTU/hr) --- var qWall = uWall * netWallArea * deltaT; var qCeil = uCeil * ceilArea * deltaT; var qWindow = uWin * windowArea * deltaT;

// --- Infiltration Load --- // ACH (air changes per hour) by insulation quality var ach; if (insulation === 'poor') ach = 1.5; else if (insulation === 'average') ach = 0.8; else if (insulation === 'good') ach = 0.5; else ach = 0.25;

var roomVolume = floorArea * height; // ft³ var cfmInfil = (ach * roomVolume) / 60; // CFM // Q_infiltration = 1.1 × CFM × ΔT (sensible, standard air) var qInfil = 1.1 * cfmInfil * deltaT;

// --- Internal Gains (cooling only) --- // Occupants: ~250 BTU/hr sensible each; Lighting: 3.4 BTU/hr per ft² (avg) var qOccupants = occupants * 250; var qLighting = 3.4 * floorArea; // BTU/hr

// --- Total Load --- var qSensible, totalLoad; if (mode === 'cooling') { qSensible = qWall + qCeil + qWindow + qInfil + qOccupants + qLighting; totalLoad = qSensible * 1.15; // 15% safety factor } else { qSensible = qWall + qCeil + qWindow + qInfil; // no internal gains for heating totalLoad = qSensible * 1.10; // 10% safety factor }

var loadTons = totalLoad / 12000; // 1 ton = 12,000 BTU/hr

// --- Required CFM --- // Cooling: CFM = BTU/hr / (1.1 × ΔT_supply) — supply air typically 20°F below room // Heating: CFM = BTU/hr / (1.1 × ΔT_supply) — supply air typically 30°F above room var supplyDeltaT = (mode === 'cooling') ? 20 : 30; var cfmRequired = totalLoad / (1.1 * supplyDeltaT);

// --- Duct Sizing --- // CFM = Area (ft²) × Velocity (FPM) // Area (ft²) = CFM / Velocity var ductAreaFt2 = cfmRequired / velocity; var ductAreaIn2 = ductAreaFt2 * 144; // convert to in²

var roundDiamIn, rectWidthIn, deqIn; // Round duct: A = π/4 × D² → D = sqrt(4A/π) roundDiamIn = Math.sqrt((4 * ductAreaIn2) / Math.PI);

// Rectangular duct: A = W × H → W = A / H rectWidthIn = ductAreaIn2 / ductH;

// Equivalent diameter for rectangular duct (ASHRAE formula): // D_eq = 1.30 × (a×b)^0.625 / (a+b)^0.25 deqIn = 1.30 * Math.pow(rectWidthIn * ductH, 0.625) / Math.pow(rectWidthIn + ductH, 0.25);

// --- Friction Loss (Darcy-Weisbach approximation for sheet metal duct) --- // ΔP/100ft ≈ 0.109 × (V/1000)^1.82 / D^1.22 (in. w.g. per 100 ft, D in inches) var dForFriction = (ductType === 'round') ? roundDiamIn : deqIn; var frictionPer100 = 0.109 * Math.pow(velocity / 1000, 1.82) / Math.pow(dForFriction, 1.22);

// --- Format helpers --- function fmt(v, d) { return isNaN(v) ? 'N/A' : v.toFixed(d !== undefined ? d : 1); }

var modeLabel = mode === 'cooling' ? 'Cooling' : 'Heating';

var ductResult = ''; if (ductType === 'round') { ductResult = 'Required Round Duct Diameter' + fmt(roundDiamIn, 2) + ' in' + 'Nearest Standard Size (round up to even inch)' + Math.ceil(roundDiamIn / 2) * 2 + ' in'; } else { ductResult = 'Rectangular Duct Height (given)' + fmt(ductH, 1) + ' in' + 'Required Rectangular Duct Width' + fmt(rectWidthIn, 2) + ' in' + 'Equivalent Round Diameter (Deq)' + fmt(deqIn, 2) + ' in'; }

res.innerHTML = '### ' + modeLabel + ' Load & Duct Sizing Results ' + '' + 'ParameterValue' + 'Floor Area' + fmt(floorArea, 1) + ' ft²' + 'Room Volume' + fmt(roomVolume, 1) + ' ft³' + 'Temperature Difference (ΔT)' + fmt(deltaT, 1) + ' °F' + '— Conduction Loads —' + 'Wall Conduction Load' + fmt(qWall, 0) + ' BTU/hr' + 'Ceiling Conduction Load' + fmt(qCeil, 0) + ' BTU/hr' + 'Window Conduction Load' + fmt(qWindow, 0) + ' BTU/hr' + 'Infiltration Load' + fmt(qInfil, 0) + ' BTU/hr' + (mode === 'cooling' ? 'Occupant Sensible Gain' + fmt(qOccupants, 0) + ' BTU/hr' + 'Lighting Gain' + fmt(qLighting, 0) + ' BTU/hr' : '') + 'Subtotal Sensible Load' + fmt(qSensible, 0) + ' BTU/hr' + 'Total Design Load (w/ safety factor)' + fmt(totalLoad, 0) + ' BTU/hr' + 'Equivalent Tonnage' + fmt(loadTons, 2) + ' tons' + '— Airflow & Duct Sizing —' + 'Required Airflow (CFM)' + fmt(cfmRequired, 1) + ' CFM' + 'Design Duct Velocity' + fmt(velocity, 0) + ' FPM' + 'Required Duct Cross-Section Area' + fmt(ductAreaIn2, 2) + ' in²' + ductResult + 'Friction Loss (approx.)' + fmt(frictionPer100, 4) + ' in w.g. / 100 ft' + ''; }

#### Formulas Used

Conduction Load: Q = U × A × ΔT  (BTU/hr)

Infiltration Load: Qinfil = 1.1 × CFMinfil × ΔT  |  CFMinfil = (ACH × Volume) / 60

Total Load: Qtotal = (Qwall + Qceil + Qwin + Qinfil + Qint) × SF  (SF = 1.15 cooling, 1.10 heating)

Required CFM: CFM = Qtotal / (1.1 × ΔTsupply)  (ΔTsupply = 20°F cooling, 30°F heating)

Round Duct Diameter: D = √(4A / π)  where A = CFM / Velocity (ft²)

Rectangular Duct Width: W = A / H  (given duct height H)

Equivalent Diameter (ASHRAE): Deq = 1.30 × (a·b)0.625 / (a+b)0.25

Friction Loss (Darcy-Weisbach approx.): ΔP/100ft = 0.109 × (V/1000)1.82 / D1.22  (in. w.g.)

#### Assumptions & References

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