Calculate the angle seen at a target, element spacing, implied element count, or perpendicular target distance for a straight, equally spaced array. Choose a solve mode and supply the three known values with independent metric or imperial length units.
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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.
- 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. The element-count mode solves for an algebraic n, which may be fractional, and also reports the minimum whole count and the resulting geometric angle. Supplied physical element counts must be whole numbers. 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, directivity, cabinet splay, or rigging limits. Mechanical array splay and acoustic prediction require the applicable manufacturer model.
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 |
|---|---|---|
| 5ยฐ | 0.087 | Array length is small compared with distance |
| 10ยฐ | 0.176 | Narrow geometric angle |
| 20ยฐ | 0.364 | Moderate geometric angle |
| 30ยฐ | 0.577 | Array length is over half the target distance |
| 45ยฐ | 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:
Then calculate the angle:
The geometric angle is about 19.29ยฐ.
Example 2: Calculate element spacing
You want a 15ยฐ angle with 6 elements and a target distance of 12 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 0ยฐ and 90ยฐ?
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. For at least two elements with positive spacing and distance, the angle is greater than 0ยฐ and less than 90ยฐ. A single element has zero first-to-last length and a 0ยฐ angle; that angle cannot determine its spacing or target distance. Element-count mode can return one at 0ยฐ. At 90ยฐ, the finite-distance inverse geometry is invalid.
