Amp hour draw question for LED setups

Hi, I have an led setup that is drawing .39A  @12v. 
I am running it with a 4.5ah alarm panel battery.
My questions are:
Is there a way to calculate the how long this set up will run  knowing that leds stop working when the power dips under a certain amount? 
I have been running this set up for about 4 hours at a time, about once a week without issues for several years.  I always top off the battery at a 2amp setting on the charger.  It always takes less than an hour to top off after 4 hours of use.  This is probably good for the battery cause it shows that it isn't being drawn down much during it's 4 hours of use.  I then put it on a float charger for storage till the following week.   Could this be run on a smaller battery without affecting the battery life?    I would like to run the smallest and lightest set up possible while maintaining the health of the sealed battery that probably doesn't like heavy recharge cycles. What is the smallest I should go while keeping the battery healthy?  Thanks for the info. 

Magnus VII6 years ago
Typically you don't want to deplete a battery more than 60%. With this in mind, you can calculate your battery life with the following equation, 4.5Ah / .39A = ~11.5 hours. This means that with the loading you are applying to the battery, it will be completely depleted in 11.5 hours. However, since you want to keep it to only 60% of its full charge, then, 11.5 h * .6 = 6.92h. So running it 4 hours is OK. If you want to use an smaller battery then do the calculations with the equations I mention above to determine how much capacity you need (Ah).

Hope this helps.