Formula
Here, you can find some formula regarding cinematography or camera processing.
Lux, unit of illumination (see luminous intensity) in the International System of Units (SI). One lux (Latin for “light”) is the amount of illumination provided when one lumen is evenly distributed over an area of one square metre. This is also equivalent to the illumination that would exist on a surface all points of which are one metre from a point source of one international candle (candela). One lux is equal to 0.0929 foot-candle. (Britannica)
Foot-candle, unit of illuminance or illumination, equivalent to the illumination produced by a source of one candle at a distance of one foot and equal to one lumen incident per square foot. Abbreviation : FC (Dictionary.com)
To be simple:
1 foot-candle = 10.764 lux
There are three elements in the exposure triangle: shutter speed, aperture, and ISO. To make everything simpler, I can show you a chart:
I think there are so many ways to calculate for an exposure, but I find that this way is easier for me:
aperture = ( (1 / (2 * fps)) * foot-candle * Constant ) / ISO
where each Constant for each FPS is different (I'll develop a new one later on)
24 fps-based (valid for 24, 48, 72, and 96 fps): 0.009696
25 fps-based (valid for 25, 50, 75, and 100 fps): 0.0099
30 fps-based (valid for 30, 60, 90, and 120 fps): 0.01086
This is just a reverse formula with finding the aperture:
foot-candle = ( aperture / ( ( 1 / (2 * fps) ) * ISO * Constant
There might be more possibilities rather than just calculating how much ISO you'll need, something like how much is the lux or foot-candle with X lighting from Y distance, using inverse square law. I am currently developing a photo-metric database, and I will shortly learn on implementing somewhat huge database to be executed by JavaScript.
Here's the Newton's Inverse Square Law formula, if you're curious about it:
You can use feet or meters for distance (it depends whether you're using imperial or metrics system) and you can use both foot-candle and lux.