Beamforming Gain Calculator
Work out array gain, total antenna gain, directivity from beamwidth and the range multiplier a phased array delivers.
About Beamforming Gain Calculator
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
Worked example
With the default values below, Beamforming Gain Calculator returns Total Array Gain of 13.06. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Antenna elements in the arrayaccepts 1–1,024 elements
- 8 elements
- Gain of a single elementaccepts 0–30 dBi
- 5 dBi
- Azimuth beamwidth (3 dB)accepts 1–360 degrees
- 30 degrees
- Elevation beamwidth (3 dB)accepts 1–180 degrees
- 30 degrees
- Array efficiencyaccepts 10–100 %
- 80 %
Results
- 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
Step by step
- 1Values used
- 2Beamforming Gain
- 3Total Array Gain= 13.06 dBi
- 4Coherent Combining Gain= 9.03 dB
- 5Directivity from Beamwidth= 16.61 dBi
- 6Range Multiplier vs One Element= 2.53 ×
- 7Loss from Array Inefficiency= 0.97 dB
Assumptions and limits
- The result is derived only from the 5 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, fees or charges or compounding frequency into account.
- Figures are rounded for display to 2 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
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.