There are actually several questions.
The formula for calculating the "beam angle" of light (emitted from lights bulbs, flashlights etc) is -
α = 2 arcCos ( 1 - Lm ÷ ( 2 π Cd ))
Where, α = beam angle in degrees
Lm = luminous flux (Lumens)
Cd = luminous intensity (Candela)
The above formula...