Sprinkler Head Count and Spacing (NFPA 13)
How many sprinkler heads a room needs, how far apart, and how far off the walls: the governing spacing is the smaller of the linear cap and sqrt(protection area per head), then heads per line, lines, the total head count, the achieved area per head, and the maximum wall distance (spacing / 2). For ordinary hazard the 130 ft^2 area cap forces a spacing near 11.4 ft, tighter than the 15 ft linear cap, so a 40 x 30 ft room takes 12 heads rather than a naive 15-ft-grid's 6. A rectangular-bay standard-spray estimate; obstructions, the beam rule, and minimum head spacing are separate checks. A takeoff aid, not a stamped sprinkler layout; a qualified fire-protection designer and the AHJ govern.
Formula and source
spacing = min(max_spacing, sqrt(area_per_head)); heads_per_line = ceil(length / spacing); lines = ceil(width / spacing); total = heads_per_line x lines; achieved = room_area / total; wall_max = spacing / 2.
NFPA 13 (Standard for the Installation of Sprinkler Systems), 2022, by name; the protection-area and linear-spacing caps by hazard class for standard-spray upright / pendent heads.
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