Standby Battery Runtime from Capacity
The inverse of the standby-battery-sizing tile: the standby (supervisory) hours an installed fire-alarm or security battery supports before the alarm load, Hs = (battery_Ah/derate - alarm_Ah) / standby_current (NFPA 72 §10.6). A 14.6 Ah battery at 0.5 A standby, 2 A / 5 min alarm, and 1.2 derate holds 24 h; an 18 Ah battery holds about 30 h. Answers 'how long will this battery last' instead of the size for a required time. The derate divides the usable capacity; a battery too small for even the alarm reserve is flagged. The AHJ and the panel worksheet govern.
Formula and source
Hs = (battery_Ah / derate - I_alarm * alarm_min/60) / I_standby; the inverse of required_Ah = [(I_standby * Hs) + (I_alarm * alarm_h)] * derate.
Secondary (standby) battery runtime for a fire-alarm or security control unit - the sizing worksheet solved for the standby period - per NFPA 72 National Fire Alarm and Signaling Code §10.6 (secondary power supply), by name.
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