OK I 'think' I might have it... lumens is the power of the light, how much comes out of it, lux is basically what the flashlight does with that light, throw (high cd) or flood (low cd)?
You're on the right track.
I'll add that they are measuring different things though.
Lumens are, as you did get, a measurement of the TOTAL light the LED is making/sending out. You can't SEE lumens.
Lux is actually a measure of the light that is reflected BACK at your eyes. This is what you CAN see.
The next part is how we USE the numbers. Strictly speaking, there would be lux measurements that could be taken at any part of what the light is shined onto...and all would represent ITS PART of the total LUMEN out put that reflected back to your eye.
To STANDARDIZE how to express the ability of the light to throw...we use the lux at one meter, taken at the BRIGHTEST/highest lux reading of the beam.
Lux at one meter = cd
That makes a comparison easier.
In real life....the ACTUAL lux at one meter might not BE the brightest part of the beam...as there is a a FOCUS involved. So, for a light that throws far, the real bright POINT might be at 10 meters, or 15 meters, etc....further out where the PARTS of the beam made by the reflector, converge. So, we (If doing this correctly) find where the beam converges, and measure the lux THERE.
We then take the lux at whatever THAT distance was, and back calculate to a EQUIVALENT lux at one meter. This means the lux at one meter number USED is NOT the REAL lux at one meter. Its the lux at one meter that would work if we wanted to CALCULATE the lux at OTHER distances, say to 1,000 meters, etc....and the number that converts to the cd.
Take all THAT, and then absorb that that beam might be a foot across, or 10' across....and have the same cd.
As described further above, think of the lux on the target as the DEPTH of the water pooled there by the light hose.
If ALL your total lumens were marched out the hose to that target, it could glow very brightly (Have a high lux number)...in a very small, but deep pool.
If you wanted to spread the lumens out more, to light up a larger AREA, you can't make them as DEEP.
If you imagine an ordinary coke bottle, 1 liter....full of coke...and pour it into a glass, it might be a few inches across (The diameter of the glass) but 10" deep, etc.
Take the same coke and pour it on the kitchen floor, and you might have a puddle several feet in diameter, maybe the entire floor, but only a millimeter deep, etc.
So, "flooding" the kitchen floor to a depth of 10" might take thousands of liters, but making it wet might only take ONE liter.
As you know things further away are dimmer...just add that if its twice as far away, it will be one QUARTER as bright (lux).
The ANSI standard uses 0.25 lux as the range definition...so the light's throw is how many meters to get down to 0.25 lux.
So, that's how they CALCULATE the throw.
The inverse square law is used to DO that math.
As we use the RANGE that the lux falls to 0.25 lux...to solve for...we are using the 0.25 lux to divide by.
If we want to simplify the equation, you take the square root of the cd (the lux at 1 meter), multiply it by 2, and THAT's the range in meters. (To hit 0.25 lux)
If the light's cd is 100k, the square root of 100k = 316
Multiply that by 2, and we get 632 meters as the throw for that light to 0.25 lux.
