Ceiling Speaker Coverage and Spacing
The coverage diameter, spacing, and speaker count for a distributed ceiling system: diameter = 2 x (ceiling - ear height) x tan(coverage angle / 2); spacing = the diameter edge-to-edge, or 0.7 x diameter for even (minimum-overlap) coverage; count = ceil(area / spacing^2). A 10 ft ceiling over 4 ft ears at 90 deg covers a 12 ft circle, so a 1,200 ft^2 room needs 9 speakers edge-to-edge or 18 at minimum overlap -- smoother sound, more speakers. A layout aid; verify with the speaker's coverage angle at the design frequency and the target SPL.
Formula and source
diameter = 2 x (ceiling - ear) x tan(coverage_deg / 2); spacing = diameter (edge-to-edge) or 0.7 x diameter (minimum overlap); count = ceil(area / spacing^2).
Distributed ceiling-loudspeaker coverage geometry, standard commercial-audio design practice (manufacturer design guides, e.g. Bose / JBL / Atlas) by name; first-principles cone geometry.
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