Fire Sprinkler Density, K-Factor & Design Area Calculator

How it works

Q_head = K × √P; required Q = density × area per head; P_min = (Q ÷ K)² (≥ 7 psi); heads = design area ÷ spacing; demand = heads × Q × overage + hose allowance; volume = demand × duration

NFPA 13 sizes a sprinkler system by requiring a minimum water density over a hydraulically remote design area — the assumption being that only the sprinklers over the fire open, and the system must still deliver enough water to each of them even in the worst-located corner. Each head's discharge follows Q = K√P, so the density at the chosen spacing fixes the minimum pressure at the most remote sprinkler, and the pressure and flow grow as the calculation works back toward the riser through pipe friction, which is why closer heads flow more than the minimum and a 10–20% "overage" appears in every calc. Adding the hose allowance for firefighters and multiplying by the required duration gives the water-supply volume that a city main, fire pump or tank must guarantee.

Worked example

An ordinary hazard group 1 warehouse office designed at 0.15 gpm/ft² over 1,500 ft² with K 5.6 heads at 130 ft² spacing: each remote head needs 19.5 gpm, which K 5.6 delivers at 12.1 psi; 12 heads with 15% overage demand 269 gpm, plus 250 gpm hose allowance — 519 gpm for 60 minutes, about 31,000 gallons of supply.

Frequently asked questions