Sprinkler Head Flow Rate & Pressure Calculator
ANA›Life Services Authority›National Calculator Authority›Sprinkler Head Flow Rate & Pressure 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; } }
Sprinkler Head Flow Rate & Pressure Calculator
Calculate sprinkler head flow rate from pressure and K-factor, or determine the required pressure for a desired flow rate using the standard sprinkler discharge formula.
Calculation Mode
Calculate Flow Rate (Q) from Pressure (P) Calculate Pressure (P) from Flow Rate (Q)
K-Factor (K)
US (gpm / psi^0.5) Metric (L/min / bar^0.5)
Common K-factors: 2.8, 4.2, 5.6, 8.0, 11.2, 14.0, 16.8, 19.6, 22.4, 25.2 (US units)
Pressure at Sprinkler Head (P)
psi bar kPa
Desired Flow Rate (Q)
gpm L/min
Calculate
function sprToggleMode() { var mode = document.getElementById('spr-calc-mode').value; document.getElementById('spr-pressure-group').style.display = (mode === 'flow') ? '' : 'none'; document.getElementById('spr-flow-group').style.display = (mode === 'pressure') ? '' : 'none'; document.getElementById('spr-result').style.display = 'none'; }
function sprCalc() { var resultDiv = document.getElementById('spr-result'); resultDiv.style.display = 'none';
var mode = document.getElementById('spr-calc-mode').value; var K_raw = parseFloat(document.getElementById('spr-kfactor').value); var kUnit = document.getElementById('spr-kfactor-unit').value;
// --- Validate K-factor --- if (isNaN(K_raw) || K_raw ⚠ Please enter a valid positive K-factor.'; resultDiv.style.display = 'block'; return; }
// Convert K to US units (gpm / psi^0.5) for internal calculation // 1 US K = 14.4 metric K => metric K = US K / 14.4 var K_us; if (kUnit === 'us') { K_us = K_raw; } else { // metric: L/min per bar^0.5 -> gpm per psi^0.5 // 1 L/min = 0.264172 gpm; 1 bar = 14.5038 psi => bar^0.5 = 3.80838 psi^0.5 // K_us = K_metric * (0.264172 / 3.80838) K_us = K_raw * (0.264172 / 3.80838); }
var html = '';
if (mode === 'flow') { // Q = K * sqrt(P) var P_raw = parseFloat(document.getElementById('spr-pressure').value); var pUnit = document.getElementById('spr-pressure-unit').value;
if (isNaN(P_raw) || P_raw ⚠ Please enter a valid positive pressure value.'; resultDiv.style.display = 'block'; return; }
// Convert pressure to psi var P_psi; if (pUnit === 'psi') { P_psi = P_raw; } else if (pUnit === 'bar') { P_psi = P_raw * 14.5038; } else { P_psi = P_raw * 0.145038; } // kPa
var Q_gpm = K_us * Math.sqrt(P_psi); var Q_lpm = Q_gpm * 3.78541; var Q_m3h = Q_lpm / 1000 * 60;
// Also express pressure in other units var P_bar = P_psi / 14.5038; var P_kpa = P_psi / 0.145038;
// Velocity pressure check (NFPA 13 minimum 7 psi) var nfpaWarn = P_psi ⚠ NFPA 13 requires a minimum operating pressure of 7 psi (0.48 bar) for most sprinkler heads.' : '';
html = '### ✓ Flow Rate Results ' + nfpaWarn + '' + 'ParameterValue' + 'K-Factor (K)' + K_raw.toFixed(2) + ' ' + (kUnit === 'us' ? 'gpm/psi½' : 'L/min/bar½') + '' + 'Pressure (P)' + P_psi.toFixed(3) + ' psi | ' + P_bar.toFixed(3) + ' bar | ' + P_kpa.toFixed(2) + ' kPa' + 'Flow Rate (Q)' + Q_gpm.toFixed(2) + ' gpm' + 'Flow Rate (Q)' + Q_lpm.toFixed(2) + ' L/min' + 'Flow Rate (Q)' + Q_m3h.toFixed(4) + ' m³/h' + '';
} else { // P = (Q / K)^2 var Q_raw = parseFloat(document.getElementById('spr-flow').value); var qUnit = document.getElementById('spr-flow-unit').value;
if (isNaN(Q_raw) || Q_raw ⚠ Please enter a valid positive flow rate.'; resultDiv.style.display = 'block'; return; }
// Convert flow to gpm var Q_gpm; if (qUnit === 'gpm') { Q_gpm = Q_raw; } else { Q_gpm = Q_raw * 0.264172; } // L/min to gpm
var P_psi = Math.pow(Q_gpm / K_us, 2); var P_bar = P_psi / 14.5038; var P_kpa = P_psi / 0.145038; var Q_lpm = Q_gpm * 3.78541;
var nfpaWarn = P_psi ⚠ Resulting pressure (' + P_psi.toFixed(2) + ' psi) is below the NFPA 13 minimum of 7 psi. Increase flow rate or select a smaller K-factor.' : '';
html = '### ✓ Required Pressure Results ' + nfpaWarn + '' + 'ParameterValue' + 'K-Factor (K)' + K_raw.toFixed(2) + ' ' + (kUnit === 'us' ? 'gpm/psi½' : 'L/min/bar½') + '' + 'Flow Rate (Q)' + Q_gpm.toFixed(2) + ' gpm | ' + Q_lpm.toFixed(2) + ' L/min' + 'Required Pressure (P)' + P_psi.toFixed(3) + ' psi' + 'Required Pressure (P)' + P_bar.toFixed(4) + ' bar' + 'Required Pressure (P)' + P_kpa.toFixed(2) + ' kPa' + ''; }
resultDiv.innerHTML = html; resultDiv.style.display = 'block'; }
#### Formulas Used
Sprinkler Discharge Formula (NFPA 13 / FM Global):
Q = K × √P
Where:
- Q = Flow rate (gpm or L/min)
- K = K-factor, the discharge coefficient of the sprinkler orifice (gpm/psi½ or L/min/bar½)
- P = Pressure at the sprinkler head (psi or bar)
Rearranged to find pressure:
P = (Q / K)²
Unit Conversion (K-factor): KUS (gpm/psi½) = Kmetric (L/min/bar½) × (0.264172 / 3.80838) ≈ Kmetric / 14.4
#### Assumptions & References
- The formula Q = K√P is derived from Torricelli's theorem and the orifice flow equation, standardized in NFPA 13 (Standard for the Installation of Sprinkler Systems) and FM Global Data Sheet 2-0.
- NFPA 13 specifies a minimum operating pressure of 7 psi (0.48 bar) for standard spray sprinklers and varies for ESFR and other special types.
- Maximum operating pressure is typically 175 psi (12.1 bar) unless otherwise listed by the manufacturer.
- This calculator assumes steady-state, incompressible flow with no pipe friction losses at the sprinkler head itself.
- Pressure used is the residual pressure at the sprinkler head, not the static supply pressure. Pipe friction losses must be calculated separately (Hazen-Williams equation).
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