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Calcrivo

Beamforming Gain Calculator

Work out array gain, total antenna gain, directivity from beamwidth and the range multiplier a phased array delivers.

Inputs

elements
dBi
degrees
degrees
%

Total Array Gain

13.06dBi

Coherent Combining Gain

9.03dB

Directivity from Beamwidth

16.61dBi

Range Multiplier vs One Element

2.53×

Loss from Array Inefficiency

0.97dB

Step by step

  1. Values used

    Antenna elements in the array = 8 elements; Gain of a single element = 5 dBi; Azimuth beamwidth (3 dB) = 30 degrees; Elevation beamwidth (3 dB) = 30 degrees; Array efficiency = 80 %

  2. Beamforming Gain

    array gain = 10·log10(N elements); total gain = element gain + array gain − efficiency loss; directivity ≈ 10·log10(41253 ÷ (azimuth × elevation beamwidth)).

  3. Total Array Gain

    = 13.06 dBi

  4. Coherent Combining Gain

    = 9.03 dB

  5. Directivity from Beamwidth

    = 16.61 dBi

  6. Range Multiplier vs One Element

    = 2.53 ×

  7. Loss from Array Inefficiency

    = 0.97 dB

How it works

Signals from N elements combine coherently in the steered direction, giving 10·log10(N) of gain — 3 dB per doubling of elements. The same energy concentrated into a narrower beam can be cross-checked from the 3 dB beamwidths, and because free-space loss goes as distance squared, gain in dB translates to range through 10^(G/20). Beamforming gain is what lets a small 6 GHz cell reach across an open floor, but it applies only along the steered beam — the coverage hole is off-axis, where the same array is 20 dB down.

Formula

Beamforming Gain

array gain = 10·log10(N elements); total gain = element gain + array gain − efficiency loss; directivity ≈ 10·log10(41253 ÷ (azimuth × elevation beamwidth)).

41253
Square degrees in a sphere, used to convert beamwidth to directivity
N
Number of coherently driven antenna elements

Frequently Asked Questions

How is Beamforming Gain calculated?

array gain = 10·log10(N elements); total gain = element gain + array gain − efficiency loss; directivity ≈ 10·log10(41253 ÷ (azimuth × elevation beamwidth)). Signals from N elements combine coherently in the steered direction, giving 10·log10(N) of gain — 3 dB per doubling of elements. The same energy concentrated into a narrower beam can be cross-checked from the 3 dB beamwidths, and because free-space loss goes as distance squared, gain in dB translates to range through 10^(G/20).

Why does Beamforming Gain matter?

Beamforming gain is what lets a small 6 GHz cell reach across an open floor, but it applies only along the steered beam — the coverage hole is off-axis, where the same array is 20 dB down.

What values do I need to enter?

This calculator takes 5 inputs: Antenna elements in the array, Gain of a single element, Azimuth beamwidth (3 dB), Elevation beamwidth (3 dB), Array efficiency. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.

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