Spot Smoke / Heat Detector Count (Smooth Ceiling)
Spot smoke or heat detectors on a smooth ceiling per NFPA 72: rows = ceil(length / listed spacing); columns = ceil(width / spacing); detectors = rows x columns; the first detector sits within spacing/2 of each wall. A 60 x 40 ft room at a 30 ft listed spacing takes 4 detectors (a 2 x 2 grid, 15 ft off each wall); a 100 x 80 ft open area takes 12. The 0.7-times-spacing rule confirms every point is covered; beams, high ceilings, and HVAC tighten it. Like sprinkler-head-layout, an install estimate the stamped fire-alarm plan and AHJ govern.
Formula and source
rows = ceil(room_length_ft / listed_spacing_ft); cols = ceil(room_width_ft / listed_spacing_ft); detectors = rows x cols; wall_max_ft = listed_spacing_ft / 2.
NFPA 72 spot-detector grid identity by name (grid count over the listed spacing; wall maximum at half the spacing); first-principles grid arithmetic.
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