Beamforming Gain Calculator
Work out array gain, total antenna gain, directivity from beamwidth and the range multiplier a phased array delivers.
Inputs
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
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 %
Beamforming Gain
array gain = 10·log10(N elements); total gain = element gain + array gain − efficiency loss; directivity ≈ 10·log10(41253 ÷ (azimuth × elevation beamwidth)).
Total Array Gain
= 13.06 dBi
Coherent Combining Gain
= 9.03 dB
Directivity from Beamwidth
= 16.61 dBi
Range Multiplier vs One Element
= 2.53 ×
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.