If you are asking for a calculation based upon the characteristics of the beam, then trigonometry can be used. Let's say you measured the diameter of the beam to be 4 feet at a distance of 100 feet. You draw out a right triangle having a long side of 100 and a short side of the radius of the beam (2 feet). The tangent of the angle of interest of the triangle is equal to the ratio of the radius over the length. So, tan(angle)=2/100. The angle=arctan(2/100)=1.146 degrees. But, this angle is only 1/2 the total beam divergence since the triangle 'drawn' used the radius. So, the total beam angle from one side of the beam to the other is twice this, or 2.29 degrees.
Short and sweet version: Total angle=2*arctan[(beam diameter/(2*distance)]
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