Comments noted.

Actually I am aware how beam angle is *measured* to 50% of initial intensity.

My questions are more related to LED driven flashlights. And yes, I am aware that flashlight reflectors and lens will affect type of light (flood, narrow/spot).

Manufacturers do not usually provide beam angle data, this is where the formula I mentioned previously becomes useful in that beam angle (to 50%) can be calculated from lumen and candela or beam throw (until 0.25 lux). This latter data is usually provided by manufacturers. But the supplied data usually consists of total lumen output and maximum candela, and does not provide the 50% candela data.

This formula can then calculate "beam angle" based on total lumen and maximum candela. However, as mentioned previously, on first inspection of the formula, it suggests this formula calculates the total (maximum) "beam angle" down to where the candela intensity has dropped to zero or near to it. But in reality, this formula calculates only to 50% of maximum candela!?

So how is it that this formula only calculates beam angle down to 50% of maximum candela, when no 50% candela data is provided by manufacturers to begin with? As far as I can tell, even from the derivation of this formula, the calculated "beam angle" appears to be for the entire beam!?

The "beam angle" is important as it gives an indication of how much light is available for certain specific tasks. Some tasks require a spot type beam, where other tasks require a more flood type beam. Also important (to a slightly lesser extent) is the "field angle" where this data gives an indication of how much "spill" light is also available. So a formula that calculates this field angle when candela intensity drops to 10% is also very useful.

So my two initial questions still remain to be answered.