Speaker Coverage Calculator - Area, Angle & Count

Calculate speaker coverage diameter, area, overlap spacing, and room count from mounting height and dispersion, or reverse-solve the required angle.

Related Calculators

Speaker Coverage Formula

For a circularly symmetric loudspeaker cone aimed perpendicular to a flat listener plane, the footprint is a circle. Its radius follows a right triangle using the perpendicular speaker-to-plane throw and half the full conical angle. Here h_m is mounting height and h_e is listener ear height, measured from the same reference. A circular-sector formula does not describe this projection.

T = hₘ - hₑ; r = Ttan(θ / 2); D = 2r; A = π r²

Where:

Variable	Meaning	Calculator units
A	Circular footprint area πr²	m² or ft²
T	Perpendicular speaker-to-listener-plane throw; mounting height minus ear height in coverage mode	m or ft
θ	Full symmetric conical angle; 0° < θ < 180°	degrees

Important relationship: A = πT²tan²(θ/2). At a fixed angle, doubling perpendicular throw makes the ideal area four times as large. Angle dependence is nonlinear: it is not proportional to θ, and the projection has no finite 180° or 360° case.

Rearranged Forms

If the perpendicular throw T and required footprint diameter D are known, reverse mode finds the full angle. Coverage mode also uses a chosen overlap percentage o to form a geometric room grid:

θ deg = (360) / (π)arctan((D) / (2T))

S = D(1 - o / 100); N = ceil(L / S) \times ceil(W / S)

How to Use the Speaker Coverage Calculator

Choose footprint/grid mode and enter mounting height, listener ear height, nominal full conical angle, room length/width and overlap. Mounting height must exceed ear height.
For inverse mode, enter the perpendicular speaker-to-listener-plane throw and target footprint diameter; this is not a slanted distance to an outer listener.
Choose ft or m for each length input and choose the displayed length/area result unit independently.
Read the circle dimensions, 10/20/30% overlap spacing alternatives, and geometric planning count, or the inverse 80/100/120% target-diameter angles.

These are ideal geometric planning comparisons. They do not guarantee level uniformity, intelligibility or complete room coverage. Your last successful inputs are saved in this browser; other scripts on this site may access them, and Reset clears this calculator’s saved data.

Example

For a perpendicular throw of 10 m and a full conical angle of 120°, the radius is 10tan60° = 10√3 m and the diameter is 20√3 ≈ 34.6410 m. The circular footprint area is:

A = π[10tan(60^°)]² = 300π \approx 942.4778 m²

The ideal circular footprint is about 942.4778 m²; it is not a guaranteed uniform acoustic coverage area. Conversely, a 20 m target diameter at 10 m perpendicular throw requires 2atan(20/20) = 90°.

Quick Angle Reference

Full conical angle	Diameter / throw D/T	Area / throw² A/T²
60°	1.1547	1.0472
90°	2.0000	3.1416
120°	3.4641	9.4248
150°	7.4641	43.7567
170°	22.8601	410.4368

How to Interpret the Result

Angle dependence is nonlinear. Diameter scales with tan(θ/2), and area with tan²(θ/2). Very wide nominal angles can create very large geometric projections without useful uniform SPL.
Throw is perpendicular distance. At fixed angle, area scales with throw squared; mounting and ear heights determine that throw in coverage mode.
Grid count is a planning quantity. Spacing S > D/√2 can leave gaps between diagonal circular footprints even when they overlap along rows. Overlap below about 29.2893% has this property under the stated spacing convention.
No audience-capacity or sound-level conclusion follows. Grid positioning, room edges, seating layout, reflections and SPL targets require separate assessment.

Assumptions and Limitations

The listener surface is flat, and the speaker axis is perpendicular to it; the model assumes a circularly symmetric cone. Tilted axes or separate horizontal/vertical beamwidths require another projection.
Manufacturer dispersion is nominal and frequency/level dependent. HARMAN explains conical coverage and level boundaries; this is not a hard sound/no-sound edge.
Coverage mode accounts for mounting-minus-ear height, but it does not calculate aiming, acoustic interaction, reflections, obstructions, room response, SPL or intelligibility.
Check actual manufacturer polar/listening-plane data. For example, QSC’s nominal coverage specification states a frequency averaging band and −6 dB criterion; no product-specific pattern is simulated here.

Practical Planning Notes

Use this calculator for a first geometric layout, then verify placement and coverage with suitable manufacturer data or acoustic modeling.
The spacing percentage is a chosen geometric overlap convention, not an acoustic standard or a guarantee. Even 30% overlap passing the square-grid diagonal condition does not establish room-edge or SPL coverage.
For long rooms or high mounting positions, check whether listener positions meet the required sound level and intelligibility; those quantities are not calculated.
If a loudspeaker has different horizontal and vertical beamwidths, asymmetric coverage or electronic steering, do not interpret this circular footprint as its actual listening-plane pattern.