Gain from Beamwidths
Approximate directive gain from the two −3 dB beamwidths.
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The engineering
Gain is concentration: 41,253 square degrees on the sphere, divided by however many your beam occupies. A 10°×10° beam is ~26 dBi before losses.
It works in reverse on datasheets — a claimed 30 dBi with 8° beams doesn't add up, and now you can tell.
Where this math comes from
The approximation is John Kraus's — radio astronomer, W8JK, and author of the *Antennas* textbook (1950) that trained fifty years of practitioners. Counting the sphere in square degrees and dividing was exactly his kind of pedagogy: rough, physical, and memorable.
Precision antenna ranges exist because this estimate is where every design conversation starts, not ends.
- 1946John D. KrausHelical antenna; the practical-antenna era.
- 1950John D. Kraus*Antennas* — the beamwidth-gain approximation canonized.
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