I use the Binford 2000 which has 1 million amp hours! Seriously there is a formula
for actually finding the correct size battery you need. People will say their battery works great but their unit might only have a .25 amp draw and yours might have a 1.5 amp draw.
Look in your owners manual and it will tell you what amps the unit uses. Plug in that number with how long you want to use it.
If the current drawn is x amps, the time is T hours then the capacity C in amp-hours is
C = xT
For example, if your pump is drawing 120 mA and you want it to run for 24 hours
C = 0.12 Amps * 24 hours = 2.88 amp hours
Step 2. Cycle life considerations
It isn’t good to run a battery all the way down to zero during each charge cycle. For example, if you want to use a lead acid battery for many cycles you shouldn’t run it past 80% of its charge, leaving 20% left in the battery. This not only extends the number of cycles you get, but lets the battery degrade by 20% before you start getting less run time than the design calls for
C’ = C/0.8
For the example above
C’ = 2.88 AH / 0.8 = 3.6 AH
Step 3: Rate of discharge considerations
Some battery chemistries give much fewer amp hours if you discharge them fast. This is called the Peukart effect. This is a big effect in alkaline, carbon zinc, zinc-air and lead acid batteries. For example if you draw at 1C on a lead acid battery you will only get half of the capacity that you would have if you had drawn at 0.05C. It is a small effect in NiCad, Lithium Ion, Lithium Polymer, and NiMH batteries.
For lead acid batteries the rated capacity (i.e. the number of AH stamped on the side of the battery) is typically given for a 20 hour discharge rate. If you are discharging at a slow rate you will get the rated number of amp-hours out of them. However, at high discharge rates the capacity falls steeply. A rule of thumb is that for a 1 hour discharge rate (i.e. drawing 10 amps from a 10 amp hour battery, or 1C) you will only get half of the rated capacity (or 5 amp-hours from a 10 amp-hour battery). Charts that detail this effect for different discharge rate can be used for greater accuracy. For example the data sheets listed in /BB.htm
For example, if your portable guitar amplifier is drawing a steady 20 amps and you want it to last 1 hour you would start out with Step 1:
C=20 amps * 1 hour = 20 AH
Then proceed to Step 2
C’ = 20 AH / 0.8 = 25 AH
Then take the high rate into account
C’‘=25 /.5 = 50 AH
Thus you would need a 50 amp hour sealed lead acid battery to run the amplifier for 1 hour at 20 amps average draw.
Step 4. What if you don’t have a constant load? The obvious thing to do is the thing to do. Figure out an average power drawn. Consider a repetitive cycle where each cycle is 1 hour. It consists of 20 amps for 1 second followed by 0.1 amps for the rest of the hour. The average current would be calculated as follows.
20*1/3600 + 0.1(3599)/3600 = 0.1044 amps average current.
(3600 is the number of seconds in an hour).
In other words, figure out how many amps is drawn on average and use steps 1 and 2. Step 3 is very difficult to predict in the case where you have small periods of high current. The news is good, a steady draw of 1C will lower the capacity much more than short 1C pulses followed by a rest period. So if the average current drawn is about a 20 hour rate, then you will get closer to the capacity predicted by a 20 hour rate, even though you are drawing it in high current pulses. Actual test data is hard to come by without doing the test yourself.