Heat Pump COP and Efficiency Calculator
ANA›Life Services Authority›National Calculator Authority›Heat Pump COP and Efficiency Calculator
.calc-container { max-width: 640px; margin: 2rem 0; padding: 1.5rem; background: #fff; border: 1px solid #ddd; border-radius: 8px; box-shadow: 0 1px 3px rgba(0,0,0,0.06); font-family: system-ui, -apple-system, sans-serif; } .calc-container h3 { font-family: Georgia, serif; font-size: 1.15rem; color: #1a1a1a; margin-bottom: 1rem; padding-bottom: 0.5rem; border-bottom: 2px solid var(--ac, #3d5a80); } .calc-row { display: flex; align-items: center; gap: 0.75rem; margin-bottom: 0.75rem; flex-wrap: wrap; } .calc-row label { min-width: 160px; font-size: 0.9rem; color: #333; font-weight: 500; } .calc-row input[type="number"], .calc-row select { flex: 1; min-width: 120px; max-width: 200px; padding: 0.5rem 0.6rem; border: 1px solid #ccc; border-radius: 4px; font-size: 0.9rem; font-family: system-ui, sans-serif; color: #1a1a1a; background: #fafaf8; } .calc-row input:focus, .calc-row select:focus { outline: none; border-color: var(--ac, #3d5a80); box-shadow: 0 0 0 2px rgba(26,74,138,0.12); } .calc-row .unit { font-size: 0.82rem; color: #888; min-width: 30px; } .calc-btn { display: inline-block; margin-top: 0.5rem; padding: 0.55rem 1.5rem; background: var(--ac, #3d5a80); color: #fff; border: none; border-radius: 4px; font-size: 0.9rem; font-weight: 600; cursor: pointer; font-family: system-ui, sans-serif; } .calc-btn:hover { opacity: 0.9; } .calc-result { margin-top: 1.25rem; padding: 1rem 1.25rem; background: #f0f6fc; border-left: 3px solid var(--ac, #3d5a80); border-radius: 0 6px 6px 0; display: none; } .calc-result.visible { display: block; } .calc-result-label { font-size: 0.78rem; text-transform: uppercase; letter-spacing: 0.06em; color: #666; margin-bottom: 0.25rem; } .calc-result-value { font-size: 1.6rem; font-weight: 700; color: var(--ac, #3d5a80); } .calc-result-detail { font-size: 0.85rem; color: #555; margin-top: 0.5rem; line-height: 1.5; } .calc-note { margin-top: 1rem; font-size: 0.8rem; color: #888; font-style: italic; } .calc-grid { display: grid; grid-template-columns: 1fr 1fr; gap: 0.75rem; margin-top: 0.75rem; } .calc-grid-item { padding: 0.6rem 0.8rem; background: #f8f9fa; border-radius: 4px; border: 1px solid #eee; } .calc-grid-item .label { font-size: 0.75rem; color: #888; text-transform: uppercase; letter-spacing: 0.04em; } .calc-grid-item .value { font-size: 1.1rem; font-weight: 600; color: #1a1a1a; } @media (max-width: 720px) { .calc-row { flex-direction: column; align-items: flex-start; gap: 0.3rem; } .calc-row label { min-width: auto; } .calc-row input[type="number"], .calc-row select { max-width: 100%; width: 100%; } .calc-grid { grid-template-columns: 1fr; } } .calc-chart { margin: 1rem 0; text-align: center; } .calc-chart svg { max-width: 100%; height: auto; } .calc-chart-legend { display: flex; flex-wrap: wrap; justify-content: center; gap: 0.6rem 1.2rem; margin-top: 0.6rem; font-size: 0.8rem; color: #555; } .calc-chart-legend span { display: inline-flex; align-items: center; gap: 0.3rem; } .calc-chart-legend i { display: inline-block; width: 10px; height: 10px; border-radius: 2px; font-style: normal; } .calc-related { max-width: 640px; margin: 2rem 0 1rem; padding: 1.25rem 1.5rem; background: #f8f9fa; border: 1px solid #e8e8e8; border-radius: 8px; } .calc-related h3 { font-family: Georgia, serif; font-size: 1rem; color: #1a1a1a; margin: 0 0 0.75rem; padding-bottom: 0.4rem; border-bottom: 2px solid var(--ac, #3d5a80); } .calc-related-list { list-style: none; padding: 0; margin: 0 0 0.75rem; display: grid; grid-template-columns: 1fr 1fr; gap: 0.4rem 1.5rem; } .calc-related-list li a { font-size: 0.88rem; color: var(--ac, #3d5a80); text-decoration: none; } .calc-related-list li a:hover { text-decoration: underline; } .calc-browse-all { margin: 0.5rem 0 0; font-size: 0.9rem; font-weight: 600; } .calc-browse-all a { color: var(--ac, #3d5a80); text-decoration: none; } .calc-browse-all a:hover { text-decoration: underline; } @media (max-width: 720px) { .calc-related-list { grid-template-columns: 1fr; } }
Heat Pump COP and Efficiency Calculator
Calculate the Coefficient of Performance (COP), Heating Seasonal Performance Factor (HSPF), and Energy Efficiency Ratio (EER) for heat pumps operating in heating and cooling modes.
### Operating Temperatures
Hot Reservoir Temperature (TH)
°C °F K
Indoor air temperature (heating) or outdoor condenser temperature (cooling)
Cold Reservoir Temperature (TC)
°C °F K
Outdoor source temperature (heating) or indoor evaporator temperature (cooling)
### Power & Heat Transfer (Optional)
Compressor Power Input (Win)
W
Electrical power consumed by the compressor
Heat Output / Cooling Capacity (Q)
W kW BTU/hr
Measured heat delivered (heating) or heat removed (cooling)
Operating Mode
Heating Mode Cooling Mode
Calculate
function heaToKelvin(val, unit) { if (unit === "C") return val + 273.15; if (unit === "F") return (val - 32) * 5/9 + 273.15; return val; // already Kelvin }
function heaCalc() { var resultDiv = document.getElementById("hea-result"); resultDiv.style.display = "block"; resultDiv.className = "calc-result";
// Read temperatures var tHotVal = parseFloat(document.getElementById("hea-t-hot").value); var tColdVal = parseFloat(document.getElementById("hea-t-cold").value); var tHotUnit = document.getElementById("hea-t-hot-unit").value; var tColdUnit = document.getElementById("hea-t-cold-unit").value;
// Validate temperatures if (isNaN(tHotVal) || isNaN(tColdVal)) { resultDiv.className = "calc-result calc-error"; resultDiv.innerHTML = "Error: Please enter both hot and cold reservoir temperatures."; return; }
var tHotK = heaToKelvin(tHotVal, tHotUnit); var tColdK = heaToKelvin(tColdVal, tColdUnit);
if (tHotK H) must be greater than cold reservoir temperature (TC) for a valid heat pump cycle."; return; }
var mode = document.getElementById("hea-mode").value;
// Carnot COP calculations // Heating COP (Carnot): COP_H = T_H / (T_H - T_C) // Cooling COP (Carnot): COP_C = T_C / (T_H - T_C) var deltaT = tHotK - tColdK; var copCarnotHeating = tHotK / deltaT; var copCarnotCooling = tColdK / deltaT;
// Actual COP from measured values (if provided) var powerInput = parseFloat(document.getElementById("hea-power-input").value); var heatOutput = parseFloat(document.getElementById("hea-heat-output").value); var heatUnit = document.getElementById("hea-heat-unit").value;
var hasActual = !isNaN(powerInput) && !isNaN(heatOutput) && powerInput > 0 && heatOutput > 0;
var copActual = null; var heatOutputW = null; var efficiency = null; var eer = null;
if (hasActual) { // Convert heat output to Watts if (heatUnit === "kW") heatOutputW = heatOutput * 1000; else if (heatUnit === "BTU") heatOutputW = heatOutput * 0.29307107; else heatOutputW = heatOutput;
// Actual COP = Q / W_in copActual = heatOutputW / powerInput;
// Efficiency relative to Carnot if (mode === "heating") { efficiency = (copActual / copCarnotHeating) * 100; } else { efficiency = (copActual / copCarnotCooling) * 100; }
if (efficiency > 100) { resultDiv.className = "calc-result calc-error"; resultDiv.innerHTML = "Error: Actual COP exceeds Carnot COP — please check your input values. No real heat pump can exceed Carnot efficiency."; return; }
// EER (Energy Efficiency Ratio) for cooling: BTU/hr per Watt if (mode === "cooling") { var heatOutputBTU = heatOutputW * 3.41214; eer = heatOutputBTU / powerInput; } }
// Format temperatures for display function fmtTemp(val, unit) { var k = heaToKelvin(val, unit); var c = k - 273.15; var f = c * 9/5 + 32; return val.toFixed(1) + " " + (unit === "K" ? "K" : (unit === "C" ? "°C" : "°F")) + " (" + c.toFixed(1) + " °C / " + f.toFixed(1) + " °F / " + k.toFixed(2) + " K)"; }
var html = "### Results "; html += "ParameterValue"; html += "Hot Reservoir (TH)" + fmtTemp(tHotVal, tHotUnit) + ""; html += "Cold Reservoir (TC)" + fmtTemp(tColdVal, tColdUnit) + ""; html += "Temperature Difference (ΔT)" + deltaT.toFixed(2) + " K"; html += "Carnot (Ideal) Performance"; html += "Max COP (Heating) — Carnot" + copCarnotHeating.toFixed(3) + ""; html += "Max COP (Cooling) — Carnot" + copCarnotCooling.toFixed(3) + "";
if (hasActual) { html += "Actual Performance"; html += "Power Input (Win)" + powerInput.toFixed(1) + " W"; html += "Heat Transfer (Q)" + heatOutputW.toFixed(1) + " W (" + (heatOutputW/1000).toFixed(3) + " kW)"; html += "Actual COP (" + (mode === "heating" ? "Heating" : "Cooling") + ")" + copActual.toFixed(3) + ""; html += "Carnot Efficiency (ηCarnot)" + efficiency.toFixed(1) + "%"; if (eer !== null) { html += "EER (Energy Efficiency Ratio)" + eer.toFixed(2) + " BTU/(hr·W)"; // SEER approximation note html += "Approximate SEER~" + (eer * 0.875).toFixed(1) + " (estimated seasonal)"; } // HSPF approximation for heating if (mode === "heating") { var hspf = copActual * 3.41214; html += "Approximate HSPF~" + hspf.toFixed(2) + " BTU/(hr·W)"; } }
html += "";
// Performance rating var copRef = (mode === "heating") ? copCarnotHeating : copCarnotCooling; var actualCopRef = hasActual ? copActual : null; html += "Performance Guide:"; html += "- Carnot COP (Heating): " + copCarnotHeating.toFixed(2) + " — theoretical maximum for these temperatures"; html += "- Carnot COP (Cooling): " + copCarnotCooling.toFixed(2) + " — theoretical maximum for these temperatures"; if (hasActual) { var rating = efficiency >= 80 ? "Excellent" : efficiency >= 60 ? "Good" : efficiency >= 40 ? "Average" : "Below Average"; html += "- Your system operates at " + efficiency.toFixed(1) + "% of Carnot efficiency — " + rating + ""; } html += ""; html += ""; html += "";
resultDiv.innerHTML = html; }
#### Formulas Used
Carnot COP (Heating Mode):
COPH,Carnot = TH / (TH − TC)
Carnot COP (Cooling Mode):
COPC,Carnot = TC / (TH − TC)
Actual COP (from measured values):
COPactual = Q / Win
Where Q = heat delivered or removed (W), Win = electrical power input (W)
Carnot Efficiency:
ηCarnot = COPactual / COPCarnot × 100%
Energy Efficiency Ratio (EER, cooling):
EER = QBTU/hr / Win,W [BTU/(hr·W)]
Heating Seasonal Performance Factor (HSPF):
HSPF ≈ COP × 3.41214 [BTU/(hr·W)] — steady-state approximation
All temperatures must be in Kelvin (absolute scale) for thermodynamic calculations.
#### Assumptions & References
- References: ASHRAE Handbook — Fundamentals (2021); Çengel & Boles, Thermodynamics: An Engineering Approach, 9th ed.; U.S. DOE ENERGY STAR Heat Pump Program.
More Calculators
- Irrigation Water Usage Estimator
- Sod & Lawn Installation Calculator
- Attorney Fee Estimator
- Case Timeline Estimator
- Court Filing Fee Estimator
- Humidity and Dew Point Calculator for Delaware Climate
Read Next
Study Time Planner Authority Network America › Life Services Authority › National Calculator Authority .calc-container { max-width: 640px;...