Enter any 3 values (angle, element spacing, number of elements, and distance to target) into the calculator to determine the missing variable for a geometric line-array setup.

Line Array Angle Calculator

Enter any 3 values to calculate the missing variable.

Geometry used: The array is a straight line of n equally spaced elements with total length L = d (n − 1). The “Distance to Target” (D) is the perpendicular distance from the first element (the near end) to the target point. The angle (θ) is the angle at the target between the line to the first element and the line to the last element. This is not an acoustic/RF beamwidth or directivity model.

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Line Array Angle Formula

The following formula calculates a geometric angle subtended by a straight line of equally spaced elements. It assumes the target point is a perpendicular distance D away from the first element (the near end of the array), and that the total array length is L = d (n − 1). This is not a loudspeaker/antenna beamwidth formula.

θ = atan((d * (n - 1)) / D) * (180 / π)

Variables:

  • θ is the angle at the target (in degrees) between the line to element 1 and the line to element n, under the right-triangle assumption described above
  • d is the element spacing (center-to-center distance between adjacent elements)
  • n is the number of elements in the line (an integer count)
  • D is the perpendicular distance from element 1 (the near end of the array) to the target point

To calculate the angle, take the arctangent of the total array length d(n−1) divided by the distance D. Multiply the result by 180 divided by π to convert from radians to degrees.

What is a Line Array?

A line array is a set of sources (for example, loudspeakers in sound reinforcement or antenna elements in RF) arranged approximately along a straight line. In real acoustic/RF systems, the radiated pattern (directivity, beamwidth, sidelobes, steering, etc.) depends on wavelength (frequency), element size, amplitude shading, and phase/steering—not just geometry. The calculator above only computes a simple geometric angle based on spacing, count, and a perpendicular distance.

How to Calculate Line Array Angle?

The following steps outline how to calculate the Line Array Angle (geometric).

  1. Determine the element spacing (d).
  2. Determine the number of elements (n).
  3. Determine the perpendicular distance to the target from the first element (D).
  4. Calculate the angle using the formula θ = atan((d * (n – 1)) / D) * (180 / π).
  5. After inserting the values and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Element spacing (d) = 0.5 meters

Element number (n) = 10

Distance to target (D) = 20 meters

Angle θ = atan((0.5 × (10 − 1)) / 20) × (180 / π) ≈ 12.68°