Humidity and Cooling Load Calculator

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Humidity and Cooling Load Calculator

Calculate sensible and latent cooling loads for HVAC systems based on indoor/outdoor conditions, airflow rate, and occupancy. Results are given in BTU/hr and tons of refrigeration.

### Outdoor Conditions

Outdoor Dry-Bulb Temperature (°F)

Outdoor Relative Humidity (%)

### Indoor Design Conditions

Indoor Dry-Bulb Temperature (°F)

Indoor Relative Humidity (%)

### Airflow & Space

Airflow Rate (CFM)

Number of Occupants

Occupant Activity Level

Seated at rest (250 BTU/hr sensible, 200 BTU/hr latent) Office work (275 BTU/hr sensible, 275 BTU/hr latent) Standing/light work (305 BTU/hr sensible, 395 BTU/hr latent) Walking/light assembly (345 BTU/hr sensible, 525 BTU/hr latent) Heavy work (580 BTU/hr sensible, 870 BTU/hr latent)

### Lighting & Equipment

Lighting Load (W/ft²)

Floor Area (ft²)

Miscellaneous Equipment Load (BTU/hr)

Calculate Cooling Load

Results will appear here.

function humSatPressure(tF) { // Antoine equation adapted for °F → °C → kPa, then converted to psia // Using ASHRAE approximation: ln(Pws) = C8/T + C9 + C10T + C11T^2 + C12T^3 + C13ln(T) // Simplified Magnus formula for saturation pressure in kPa given T in °C var tC = (tF - 32) * 5 / 9; // Magnus formula: Pws (kPa) = 0.6108 * exp(17.27 * T / (T + 237.3)) var pws_kPa = 0.6108 * Math.exp(17.27 * tC / (tC + 237.3)); // Convert kPa to psia (1 kPa = 0.145038 psia) return pws_kPa * 0.145038; }

function humHumidityRatio(tF, rh) { // W = 0.62198 * (Pws * RH/100) / (P_atm - Pws * RH/100) // P_atm = 14.696 psia (standard atmosphere) var pAtm = 14.696; var pws = humSatPressure(tF); var pw = pws * (rh / 100); if (pw >= pAtm) pw = pAtm * 0.9999; return 0.62198 * pw / (pAtm - pw); // lb water / lb dry air }

function humDewPoint(tF, rh) { // Magnus formula inversion for dew point in °F var tC = (tF - 32) * 5 / 9; var alpha = (17.27 * tC / (tC + 237.3)) + Math.log(rh / 100); var dpC = (237.3 * alpha) / (17.27 - alpha); return dpC * 9 / 5 + 32; }

function humEnthalpy(tF, W) { // h = 0.240T + W(1061 + 0.444*T) [BTU/lb dry air] return 0.240 * tF + W * (1061 + 0.444 * tF); }

function humCalc() { var resultDiv = document.getElementById("hum-result");

var tOutDB = parseFloat(document.getElementById("hum-outdoor-db").value); var rhOut = parseFloat(document.getElementById("hum-outdoor-rh").value); var tInDB = parseFloat(document.getElementById("hum-indoor-db").value); var rhIn = parseFloat(document.getElementById("hum-indoor-rh").value); var cfm = parseFloat(document.getElementById("hum-cfm").value); var occ = parseFloat(document.getElementById("hum-occupants").value); var lightW = parseFloat(document.getElementById("hum-lighting").value); var area = parseFloat(document.getElementById("hum-floor-area").value); var equip = parseFloat(document.getElementById("hum-equipment").value); var actVal = document.getElementById("hum-activity").value.split(","); var occSens = parseFloat(actVal[0]); var occLat = parseFloat(actVal[1]);

// --- Validation --- var errors = []; if (isNaN(tOutDB) || tOutDB 150) errors.push("Outdoor dry-bulb must be between -50°F and 150°F."); if (isNaN(rhOut) || rhOut 100) errors.push("Outdoor RH must be between 0% and 100%."); if (isNaN(tInDB) || tInDB 120) errors.push("Indoor dry-bulb must be between 32°F and 120°F."); if (isNaN(rhIn) || rhIn 100) errors.push("Indoor RH must be between 0% and 100%."); if (isNaN(cfm) || cfm 0) { resultDiv.innerHTML = "Input Errors:" + errors.map(function(e){ return ""; }).join("") + ""; return; }

// --- Psychrometric calculations --- var W_out = humHumidityRatio(tOutDB, rhOut); // lb/lb var W_in = humHumidityRatio(tInDB, rhIn); // lb/lb var h_out = humEnthalpy(tOutDB, W_out); // BTU/lb var h_in = humEnthalpy(tInDB, W_in); // BTU/lb var dpOut = humDewPoint(tOutDB, rhOut); var dpIn = humDewPoint(tInDB, rhIn);

// Air density at indoor conditions (approx): ρ = 0.075 lb/ft³ at standard conditions // More accurate: ρ = 1 / (0.3704 * (tInDB + 459.67) / 14.696) using ideal gas var rho = 14.696 / (0.3704 * (tInDB + 459.67)); // lb/ft³ dry air

// Mass flow rate of dry air var massFlow = cfm * rho; // lb/min dry air var massFlowHr = massFlow * 60; // lb/hr

// --- Sensible Cooling Load --- // Q_sensible = 1.1 * CFM * ΔT (standard ASHRAE approximation, BTU/hr) // Exact: Q_s = massFlowHr * Cp_air * ΔT, Cp_air = 0.240 BTU/(lb·°F) var deltaT = tOutDB - tInDB; var sensibleVentilation = massFlowHr * 0.240 * deltaT; // BTU/hr

// Lighting sensible load: 1 W = 3.412 BTU/hr var sensibleLighting = lightW * area * 3.412; // BTU/hr

// Occupant sensible load var sensibleOccupants = occ * occSens; // BTU/hr

// Equipment sensible load (already in BTU/hr) var sensibleEquipment = equip;

var totalSensible = sensibleVentilation + sensibleLighting + sensibleOccupants + sensibleEquipment;

// --- Latent Cooling Load --- // Q_latent = 0.68 * CFM * ΔW (ASHRAE approximation, BTU/hr, ΔW in grains/lb) // Exact: Q_l = massFlowHr * h_fg * ΔW, h_fg ≈ 1061 BTU/lb at 60°F var deltaW = W_out - W_in; // lb/lb var latentVentilation = massFlowHr * 1061 * deltaW; // BTU/hr

// Occupant latent load var latentOccupants = occ * occLat; // BTU/hr

var totalLatent = latentVentilation + latentOccupants;

// --- Total Cooling Load --- var totalLoad = totalSensible + totalLatent; // BTU/hr var totalTons = totalLoad / 12000; // 1 ton = 12,000 BTU/hr var totalKW = totalLoad / 3412.14; // BTU/hr to kW

// Sensible Heat Ratio var shr = (totalSensible > 0 && totalLoad > 0) ? totalSensible / totalLoad : 0;

// Humidity ratio in grains (1 lb = 7000 grains) var W_out_gr = W_out * 7000; var W_in_gr = W_in * 7000;

// --- Format output --- function fmt(v, d) { return isNaN(v) ? "N/A" : v.toFixed(d !== undefined ? d : 1); } function fmtSign(v, d) { return (v >= 0 ? "+" : "") + fmt(v, d); }

var warn = (totalLoad ⚠️ Total cooling load is negative — outdoor conditions are cooler/drier than indoors. No mechanical cooling required under these conditions."
"";

resultDiv.innerHTML = warn + "" +

"### 🌡️ Psychrometric Summary " + "ParameterOutdoorIndoorDifference" + "Dry-Bulb Temp (°F)" + fmt(tOutDB,1) + "" + fmt(tInDB,1) + "" + fmtSign(deltaT,1) + "" + "Relative Humidity (%)" + fmt(rhOut,1) + "" + fmt(rhIn,1) + "" + fmtSign(rhOut-rhIn,1) + "" + "Dew Point (°F)" + fmt(dpOut,1) + "" + fmt(dpIn,1) + "" + fmtSign(dpOut-dpIn,1) + "" + "Humidity Ratio (gr/lb)" + fmt(W_out_gr,2) + "" + fmt(W_in_gr,2) + "" + fmtSign(W_out_gr-W_in_gr,2) + "" + "Humidity Ratio (lb/lb)" + fmt(W_out,5) + "" + fmt(W_in,5) + "" + fmtSign(W_out-W_in,5) + "" + "Enthalpy (BTU/lb)" + fmt(h_out,2) + "" + fmt(h_in,2) + "" + fmtSign(h_out-h_in,2) + "" + "" +

"### ❄️ Sensible Cooling Load " + "ComponentBTU/hr% of Sensible" + "Ventilation / Infiltration" + fmt(sensibleVentilation,0) + "" + fmt(totalSensible > 0 ? sensibleVentilation/totalSensible100 : 0,1) + "%" + "Lighting (" + fmt(lightW,1) + " W/ft² × " + fmt(area,0) + " ft²)" + fmt(sensibleLighting,0) + "" + fmt(totalSensible > 0 ? sensibleLighting/totalSensible100 : 0,1) + "%" + "Occupants (" + fmt(occ,0) + " × " + fmt(occSens,0) + " BTU/hr)" + fmt(sensibleOccupants,0) + "" + fmt(totalSensible > 0 ? sensibleOccupants/totalSensible100 : 0,1) + "%" + "Equipment / Miscellaneous" + fmt(sensibleEquipment,0) + "" + fmt(totalSensible > 0 ? sensibleEquipment/totalSensible100 : 0,1) + "%" + "Total Sensible" + fmt(totalSensible,0) + " BTU/hr100%" + "" +

"### 💧 Latent Cooling Load " + "ComponentBTU/hr% of Latent" + "Ventilation / Infiltration" + fmt(latentVentilation,0) + "" + fmt(totalLatent > 0 ? latentVentilation/totalLatent100 : 0,1) + "%" + "Occupants (" + fmt(occ,0) + " × " + fmt(occLat,0) + " BTU/hr)" + fmt(latentOccupants,0) + "" + fmt(totalLatent > 0 ? latentOccupants/totalLatent100 : 0,1) + "%" + "Total Latent" + fmt(totalLatent,0) + " BTU/hr100%" + "" +

"### 📊 Total Cooling Load Summary " + "MetricValue" + "Total Sensible Load" + fmt(totalSensible,0) + " BTU/hr" + "Total Latent Load" + fmt(totalLatent,0) + " BTU/hr" + "Total Cooling Load" + fmt(totalLoad,0) + " BTU/hr" + "Cooling Load (Tons)" + fmt(totalTons,2) + " tons" + "Cooling Load (kW)" + fmt(totalKW,2) + " kW" + "Sensible Heat Ratio (SHR)" + fmt(shr,3) + "" + "Air Mass Flow Rate" + fmt(massFlowHr,1) + " lb/hr dry air" + "Air Density (indoor)" + fmt(rho,4) + " lb/ft³" + "" +

""; }

#### Formulas Used

Saturation Pressure (Magnus Formula):

Pws = 0.6108 × exp(17.27 × TC / (TC + 237.3)) [kPa]

Humidity Ratio:

W = 0.62198 × (Pws × RH/100) / (Patm − Pws × RH/100) [lb water / lb dry air]

where Patm = 14.696 psia (standard atmosphere)

Enthalpy of Moist Air:

h = 0.240 × TDB + W × (1061 + 0.444 × TDB) [BTU/lb dry air]

Air Density (Ideal Gas):

ρ = Patm / (0.3704 × Tabs) [lb/ft³], where Tabs = T°F + 459.67 °R

Sensible Cooling Load — Ventilation:

Qs,vent = ṁair × Cp × ΔT = (CFM × ρ × 60) × 0.240 × (Tout − Tin) [BTU/hr]

Sensible Cooling Load — Lighting:

Qs,light = W/ft² × Area × 3.412 [BTU/hr] (1 W = 3.412 BTU/hr)

Latent Cooling Load — Ventilation:

Ql,vent = ṁair × hfg × ΔW = (CFM × ρ × 60) × 1061 × (Wout − Win) [BTU/hr]

where hfg ≈ 1061 BTU/lb is the latent heat of vaporization at ~60°F

Sensible Heat Ratio:

SHR = Qsensible / Qtotal

Tons of Refrigeration:

Tons = Qtotal / 12,000 [BTU/hr per ton]

#### Assumptions & References

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