The beamwidth distance of a simple directional antenna at distance d from the antenna of a beamwidth angle of α, can be calculated using the following formula:
2dtan(α/2)
d = distance and α = angle
There is no formula that fits all types of antennae for beamwidth angle calculation, however a formula that can be used for parabolic antennae is:
Beamwidth = 70 * lambda / d
where lamba = the wavelength, d = the antennae diameter

Several online beamwidth calculators are available:
- Parabolic beamwidth calculator by Eric Johnston
- NOAA's beam property calculator
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