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Amp-hour ratings are how manufacturers rate a batterys electrical capacity, in the same way you might rate a buckets water capacity in gallons. Manufacturer amp-hour ratings are helpful when comparing different batteries and different brands, but be forewarned: all isnt necessarily what it appears to be on the label.
What is an Amp-Hour?
An amp-hour -- properly "ampere-hour" -- is a unit of measure describing electrical charge capacity. If a battery is said to have "20 amp-hours of capacity," it means that it can hypothetically discharge one amp of current for 20 hours, 20 amps for one hour, or any combination of amps and hours that equal 20 amp-hours. That might be five amps for four hours, 10 amps for two hours, or 6.66 amps for three hours.
Run-Time for Accessories
In theory, you can calculate the run-time for any of your batterys accessories by dividing the amp-hour rating of the battery by the amp draw of the accessory. You might have to convert from watts first. For instance, if you want to know how long you can bang a 1,000-watt stereo system on a heavy-duty 100-amp-hour battery, start by dividing the wattage by the voltage -- 12 volts, in this case -- to arrive at an 83.3-amp draw for the stereo system. Divide the batterys 100-amp-hour capacity by 83.3, and you get 1.2 hours, or about 1 hour and 12 minutes of tunes before the battery dies.
Caveat
Manufacturers test and rate batteries according to a certain discharge time -- in the automotive industry, usually 20 hours. In theory, that doesnt affect the actual amp-hour rating, but it does make a difference on how long your battery will last if you consistently discharge it outside of that 20-hour parameter. If youre using a standard battery rated for a 20-hour discharge, and you routinely kill it in an hour with a banging stereo, or 150 hours with a tiny trunk-light bulb that wont shut off, then the battery wont be long for this world.