Calculate line array angle, element spacing, number of elements, or target distance from any 3 values with metric or imperial units.

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

This calculator uses a right-triangle geometry model for a straight line array. The array has n equally spaced elements, and the total array length is measured from the first element to the last element.

L = d(n - 1)
theta = atan(L / D) * 180 / pi
d = D * tan(theta * pi / 180) / (n - 1)
n = D * tan(theta * pi / 180) / d + 1
D = d(n - 1) / tan(theta * pi / 180)
  • theta = angle at the target, in degrees
  • L = total array length from the first element to the last element
  • d = spacing between adjacent array elements
  • n = number of elements in the array
  • D = perpendicular distance from the first element to the target
  • pi = 3.14159265…

If the angle is missing, the calculator first finds the total array length, then uses the arctangent of L / D. If element spacing is missing, it rearranges the tangent relationship to solve for d. If the number of elements is missing, it solves for n, which may return a decimal result. If the distance is missing, it solves for D using the known angle and array length.

This is a geometric angle calculation. It does not calculate acoustic or RF beamwidth, steering angle, interference pattern, coverage, or directivity.

Angle and Length Reference Tables

The angle depends on the ratio between total array length and distance to the target:

Angle theta L / D ratio Meaning
5° 0.087 Array length is small compared with distance
10° 0.176 Narrow geometric angle
20° 0.364 Moderate geometric angle
30° 0.577 Array length is over half the target distance
45° 1.000 Array length equals target distance
Unit Meters equivalent Use in calculator
1 m 1 m Base unit
1 cm 0.01 m Small element spacing
1 ft 0.3048 m Imperial spacing or distance
1 in 0.0254 m Small imperial spacing

Line Array Angle Examples

Example 1: Calculate the angle

You have 8 elements spaced 0.5 m apart. The target is 10 m from the first element, measured perpendicular to the array.

First find the array length:

L = 0.5(8 - 1) = 3.5 m

Then calculate the angle:

theta = atan(3.5 / 10) * 180 / pi = 19.29 degrees

The geometric angle is about 19.29°.

Example 2: Calculate element spacing

You want a 15° angle with 6 elements and a target distance of 12 m.

d = 12 * tan(15 * pi / 180) / (6 - 1)
d = 0.643 m

The required element spacing is about 0.643 m.

Line Array Angle FAQ

Is this the same as line array beamwidth?

No. This calculator only finds a geometric angle between the first and last elements as seen from the target point. Beamwidth depends on wavelength, frequency, phase, element behavior, array shading, steering, and other acoustic or RF effects.

Why does the number of elements calculation return a decimal?

The formula can produce a decimal because it is solving the geometry exactly. A real array usually needs a whole number of elements. If you are designing an array and the result is 7.3 elements, you would normally choose 8 elements if you need at least that much array length.

Why must the angle be between 0° and 90°?

This calculator is based on a right triangle where the target distance is perpendicular to the first element and the array length is the opposite side. In that setup, a valid solved angle must be greater than 0° and less than 90°. At 0°, the array length would be zero. At 90°, the tangent value is undefined.