Insulation Thickness Calculator

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.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; } }

Insulation Thickness Calculator

Calculate the required insulation thickness for a flat wall or cylindrical pipe to meet a target heat flux or surface temperature limit.

Geometry

Flat Wall / Slab Cylindrical Pipe

Calculate For

Required Insulation Thickness Heat Loss per Unit Area / Length

Inner (Hot) Surface Temperature T₁ (°C)

Outer (Ambient) Temperature T₂ (°C)

Thermal Conductivity of Insulation k (W/m·K)

Target Heat Flux q (W/m²) — for flat wall thickness mode

Inner Pipe Radius r₁ (m)

Target Heat Loss per Unit Length Q/L (W/m) — for cylinder thickness mode

Known Insulation Thickness d (m) — for heat loss mode

Outer Surface Heat Transfer Coefficient h (W/m²·K) — set 0 to ignore

Calculate Results will appear here.

function insToggleGeometry() { var geo = document.getElementById('ins-geometry').value; document.getElementById('ins-cylinder-inputs').style.display = (geo === 'cylinder') ? 'block' : 'none'; }

function insToggleMode() { var mode = document.getElementById('ins-mode').value; // thickness mode: show target q or ql; heat loss mode: show known thickness document.getElementById('ins-group-q').style.display = (mode === 'thickness') ? 'flex' : 'none'; document.getElementById('ins-group-thick').style.display = (mode === 'heatloss') ? 'flex' : 'none'; // cylinder ql label visibility handled by geometry toggle }

function insCalc() { var resultDiv = document.getElementById('ins-result'); resultDiv.className = 'calc-result';

var geo = document.getElementById('ins-geometry').value; var mode = document.getElementById('ins-mode').value; var Ti = parseFloat(document.getElementById('ins-ti').value); var To = parseFloat(document.getElementById('ins-to').value); var k = parseFloat(document.getElementById('ins-k').value); var ho = parseFloat(document.getElementById('ins-ho').value);

// Validation if (isNaN(Ti) || isNaN(To) || isNaN(k)) { resultDiv.className = 'calc-result calc-error'; resultDiv.innerHTML = '⚠ Please enter valid numbers for all required fields.'; return; } if (k 0) { resultDiv.className = 'calc-result calc-error'; resultDiv.innerHTML = '⚠ Heat flows from hot to cold. Check temperature values.'; return; } // Total thermal resistance needed: R_total = ΔT / q // R_total = R_ins + R_surface = d/k + 1/h // d = k * (ΔT/q - 1/h) var R_total = Math.abs(deltaT) / q; var R_surf = (ho > 0) ? (1.0 / ho) : 0; var R_ins = R_total - R_surf; if (R_ins '; html += 'Temperature Difference ΔT' + Math.abs(deltaT).toFixed(2) + ' °C'; html += 'Target Heat Flux q' + q.toFixed(2) + ' W/m²'; html += 'Total Thermal Resistance R_total' + R_total.toFixed(4) + ' m²·K/W'; html += 'Surface Resistance R_surf (1/h)' + R_surf.toFixed(4) + ' m²·K/W'; html += 'Required Insulation Resistance R_ins' + R_ins.toFixed(4) + ' m²·K/W'; html += 'Required Insulation Thickness d' + (d * 1000).toFixed(1) + ' mm (' + d.toFixed(4) + ' m)'; html += 'Outer Insulation Surface Temperature' + T_surf_outer.toFixed(2) + ' °C'; html += '';

} else { // heat loss mode var d2 = parseFloat(document.getElementById('ins-thick').value); if (isNaN(d2) || d2 0) ? (1.0 / ho) : 0; var R_tot2 = R_ins2 + R_surf2; var q2 = Math.abs(deltaT) / R_tot2; var T_outer2 = (deltaT > 0 ? To : Ti) + q2 * R_surf2; html = '### ✓ Flat Wall — Heat Loss Result '; html += ''; html += 'Insulation Thickness d' + (d2 * 1000).toFixed(1) + ' mm'; html += 'Insulation Resistance R_ins = d/k' + R_ins2.toFixed(4) + ' m²·K/W'; html += 'Surface Resistance R_surf = 1/h' + R_surf2.toFixed(4) + ' m²·K/W'; html += 'Total Resistance R_total' + R_tot2.toFixed(4) + ' m²·K/W'; html += 'Heat Flux q' + q2.toFixed(2) + ' W/m²'; html += 'Outer Insulation Surface Temperature' + T_outer2.toFixed(2) + ' °C'; html += ''; }

// ── CYLINDRICAL PIPE ─────────────────────────────────────────────────────── } else { var ri = parseFloat(document.getElementById('ins-ri').value); if (isNaN(ri) || ri r1 var dT = Math.abs(deltaT); var TWO_PI = 2 * Math.PI;

function heatLossCyl(r2) { var R_cond = Math.log(r2 / ri) / k; var R_conv = (ho > 0) ? 1.0 / (ho * r2) : 0; return TWO_PI * dT / (R_cond + R_conv); }

// Check: at r2 = ri (zero thickness) heat loss is infinite (or very large) // To find r2 where heatLossCyl(r2) = QL // Heat loss decreases as r2 increases (for large r2, conduction dominates) // But for cylinders there's a critical radius r_crit = k/h // Beyond r_crit, adding insulation increases heat loss; below it decreases. // We search for r2 > ri where Q/L = QL

// Check feasibility: as r2 → ∞, Q/L → 0 (conduction term dominates) // So if QL ri var r2_lo = ri * 1.0001; var ql_lo = heatLossCyl(r2_lo); if (QL > ql_lo) { resultDiv.className = 'calc-result calc-error'; resultDiv.innerHTML = '⚠ Target Q/L (' + QL.toFixed(2) + ' W/m) exceeds the maximum possible (' + ql_lo.toFixed(2) + ' W/m at zero thickness). Increase target or reduce temperatures.'; return; }

// Bisection: find r2 in [ri, large_r2] var r2_hi = ri; // Expand upper bound until Q/L = QL) { resultDiv.className = 'calc-result calc-error'; resultDiv.innerHTML = '⚠ Could not find a solution. The target Q/L may be too low for these parameters.'; return; }

// Bisection loop var r2_mid; for (var iter = 0; iter QL) { r2_lo = r2_mid; } else { r2_hi = r2_mid; } } var r2_sol = (r2_lo + r2_hi) / 2; var thick_sol = r2_sol - ri; var R_cond_sol = Math.log(r2_sol / ri) / k; var R_conv_sol = (ho > 0) ? 1.0 / (ho * r2_sol) : 0; var R_tot_sol = R_cond_sol + R_conv_sol; var QL_check = TWO_PI * dT / R_tot_sol; var T_outer_sol = (deltaT > 0 ? To : Ti) + QL_check * R_conv_sol / TWO_PI;

html = '### ✓ Cylindrical Pipe — Thickness Result '; html += ''; html += 'Inner Radius r₁' + (ri * 1000).toFixed(1) + ' mm'; html += 'Target Q/L' + QL.toFixed(2) + ' W/m'; html += 'Required Outer Radius r₂' + (r2_sol * 1000).toFixed(2) + ' mm'; html += 'Required Insulation Thickness' + (thick_sol * 1000).toFixed(2) + ' mm'; html += 'Conduction Resistance ln(r₂/r₁)/(2πk)' + (R_cond_sol / TWO_PI).toFixed(5) + ' m·K/W'; html += 'Convection Resistance 1/(2π·h·r₂)' + (R_conv_sol / TWO_PI).toFixed(5) + ' m·K/W'; html += 'Verified Q/L' + QL_check.toFixed(3) + ' W/m'; html += 'Outer Surface Temperature' + T_outer_sol.toFixed(2) + ' °C'; if (ho > 0) { var r_crit = k / ho; html += 'Critical Radius r_crit = k/h' + (r_crit * 1000).toFixed(2) + ' mm ' + (r_crit > ri ? '(adding insulation up to this radius increases heat loss)' : '') + ''; } html += '';

} else { // heat loss mode — known thickness var d3 = parseFloat(document.getElementById('ins-thick').value); if (isNaN(d3) || d3 0) ? 1.0 / (ho * r2b) : 0; var R_tot_b = R_cond_b + R_conv_b; var QL_b = TWO_PI2 * Math.abs(deltaT) / R_tot_b; var T_outer_b = (deltaT > 0 ? To : Ti) + QL_b * R_conv_b / TWO_PI2;

html = '### ✓ Cylindrical Pipe — Heat Loss Result '; html += ''; html += 'Inner Radius r₁' + (ri * 1000).toFixed(1) + ' mm'; html += 'Insulation Thickness' + (d3 * 1000).toFixed(1) + ' mm'; html += 'Outer Radius r₂' + (r2b * 1000).toFixed(2) + ' mm'; html += 'Conduction Resistance ln(r₂/r₁)/(2πk)' + (R_cond_b / TWO_PI2).toFixed(5) + ' m·K/W'; html += 'Convection Resistance 1/(2π·h·r₂)' + (R_conv_b / TWO_PI2).toFixed(5) + ' m·K/W'; html += 'Heat Loss Q/L' + QL_b.toFixed(2) + ' W/m'; html += 'Outer Surface Temperature' + T_outer_b.toFixed(2) + ' °C'; if (ho > 0) { var r_crit2 = k / ho; html += 'Critical Radius r_crit = k/h' + (r_crit2 * 1000).toFixed(2) + ' mm'; } html += ''; } }

resultDiv.className = 'calc-result calc-success'; resultDiv.innerHTML = html; }

// Initialize visibility insToggleGeometry(); insToggleMode();

#### Formulas Used

Flat Wall — Thickness: Total resistance: Rtotal = ΔT / q Insulation resistance: Rins = Rtotal − 1/h Thickness: d = k · Rins

Flat Wall — Heat Flux: q = ΔT / (d/k + 1/h)

Cylindrical Pipe — Heat Loss per Unit Length: Q/L = 2π·ΔT / [ln(r₂/r₁)/k + 1/(h·r₂)] For thickness mode, r₂ is solved numerically (bisection) since the equation is implicit in r₂.

Critical Radius (cylinder): rcrit = k / h — adding insulation below this radius increases heat loss.

#### Assumptions & References

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References

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