Amp-Hour battery rating: Amp-hour rating of battery capacity is calculated by multiplying the current (in amperes) by discharge time (in hours). Amp-hour battery rating is commonly when describing sealed lead acid batteries used in alarm systems or access control systems.
For example: a battery which delivers 2 amperes for 20 hours would have a 40 amp-hour battery rating (2 * 20= 40).
A typical 12V alarm system will need from 4AH-8AH, depending on the number of powered devices like keypads and motion detectors. A lower or higher AH rating will not adversly affect your system, it is just a length of time to deliver power. It is still 12 Volts.
Example: You have an average sized alarm system drawing 375mA (0.375A). With a 8AH battery, you will have about 20 hours of back-up power.