Speaker Coverage & Aiming Calculator
Estimate where a loudspeaker’s nominal beam meets the listening plane, or start with audience boundaries and solve for an aiming angle and minimum dispersion. Use one distance unit throughout and measure from the loudspeaker acoustic center to representative listener ear height.
Acoustic-axis landing distance (ft)13.86
- Height above listening plane (ft)
- 8
- Near coverage boundary (ft)
- 6.71
- Far coverage boundary (ft)
- 45.37
- Coverage depth (ft)
- 38.66
- Width at near boundary (ft)
- 20.89
- Width at acoustic axis (ft)
- 32
- Width at far boundary (ft)
- 92.14
- Approximate listening-plane footprint (ft²)
- 2,184.67
- Required down-tilt (degrees)
- Fit mode only
- Required vertical coverage (degrees)
- Fit mode only
- Minimum horizontal coverage (degrees)
- Fit mode only
- Geometry status
- Two forward intersections
How to use this calculator
- Choose Predict coverage to check a known speaker specification, or Fit target area to solve an audience zone.
- Choose feet or meters and enter the speaker acoustic-center height and representative listener ear height.
- For prediction, enter the down-tilt and nominal horizontal and vertical coverage angles from the manufacturer.
- For target fitting, enter the near and far listener boundaries plus the full width needed at the near boundary.
- Review the geometry status before using the aim or coverage result as a starting point for a design.
How speaker coverage and aiming are calculated
The calculation begins with the height difference between the loudspeaker acoustic center and the listening plane: H = speaker height − listener height. It models the published horizontal and vertical coverage angles as sharp, symmetrical beam edges. That is useful for first-pass geometry, but it is not a prediction of sound pressure level or frequency response.
In Predict coverage mode, the acoustic axis lands at xAxis = H ÷ tan(a), where a is the speaker down-tilt below horizontal. The lower and upper vertical beam-edge depression angles are bNear = a + V ÷ 2 and bFar = a − V ÷ 2. Each edge reaches the listening plane at x = H ÷ tan(b). A positive lower edge produces the near boundary; a positive upper edge produces the far boundary.
For any horizontal distance x, the slant range is s = √(H² + x²). The estimated width is w = 2 × s × tan(Q ÷ 2), where Q is the horizontal coverage angle. When both vertical edges meet the plane ahead of the speaker, the footprint is treated as a trapezoid: area = (far − near) × (wNear + wFar) ÷ 2.
Solving a target audience area
Fit target area mode starts with the near distance N, far distance F, and required near-boundary width W. The depression angles to those boundaries are atan(H ÷ N) and atan(H ÷ F). Their average is the required down-tilt, and their difference is the required vertical coverage. The minimum horizontal coverage is 2 × atan(W ÷ (2 × √(H² + N²))). The near boundary is the narrowest part of a forward beam, so it controls the horizontal-angle requirement.
How to read the geometry status
Two forward intersections means both vertical edges cross the listening plane ahead of the speaker. An unbounded far edge means the upper edge is horizontal or points upward, so it does not have a finite intersection with a flat listening plane. An invalid lower edge means the lower edge is vertical or points behind the speaker; reduce down-tilt or vertical coverage before relying on the footprint.
What this calculation leaves out
Nominal coverage is normally a frequency-specific attenuation contour, often the −6 dB points, rather than a hard border. Real loudspeakers have gradual, frequency-dependent directivity, and a room adds reflections, absorption, obstructions, crossover effects, acoustic-center offsets, SPL loss, and interaction with other loudspeakers. Check manufacturer polar plots and verify the installed system with measurements; this tool does not specify mounting, suspension, structural, or rigging hardware.
Worked example
A speaker with an acoustic center 12 ft high serves listeners at a 4 ft ear height, so H = 8 ft. With 30° down-tilt and 40° vertical coverage, the near edge is 50° below horizontal and the far edge is 10° below horizontal. The boundaries are 8 ÷ tan(50°) = 6.71 ft and 8 ÷ tan(10°) = 45.37 ft.
With 90° horizontal coverage, the widths are 20.89 ft at the near boundary and 92.14 ft at the far boundary. The estimated trapezoidal footprint is (45.37 − 6.71) × (20.89 + 92.14) ÷ 2 = 2,184.7 ft². In Fit target area mode, the same 8 ft height, an 8 to 30 ft audience zone, and a 20 ft near width require about 29.97° down-tilt, 30.07° vertical coverage, and 82.95° horizontal coverage.
Common questions
How do I calculate speaker coverage from dispersion angle?
Find the vertical beam-edge angles by adding and subtracting half the vertical coverage from the down-tilt. Divide the height above the listener plane by the tangent of each positive edge angle to find the near and far floor intersections. At either intersection, use the slant distance and half the horizontal angle to estimate the full width.
Where should a wall-mounted PA speaker be aimed?
Aim the acoustic axis approximately halfway between the depression angles to the near and far audience boundaries. That gives equal angular margin above and below the axis. Then check that the needed vertical coverage spans the two boundary angles and that the near listeners are not outside the beam.
What does a 90° × 40° speaker coverage specification mean?
It usually means a nominal 90-degree horizontal pattern and a 40-degree vertical pattern, often stated at a particular attenuation contour and frequency range. It does not mean every frequency or every point in the rectangle has the same level. Read the manufacturer’s polar plots for the exact conditions.
Why is my far coverage boundary unbounded?
The upper vertical beam edge is horizontal or aimed above the listening plane, so it never crosses a flat floor ahead of the speaker. That is a geometric result, not an infinitely useful coverage area: level falls with distance and the real pattern changes with frequency. Add down-tilt or use a narrower vertical pattern if a finite far boundary is required.
Does speaker dispersion change with frequency?
Yes. A typical loudspeaker narrows at higher frequencies and can widen or become irregular near crossover regions and at lower frequencies. A single nominal angle is therefore a useful planning shorthand, not a complete acoustic model.