Battery Runtime Calculation

How long will a battery power the system without alternator support?

t_hours = C_battery_Ah / I_average

When you know average electrical power instead of current:

I_average = P_average / V_system

For lead-acid batteries, high discharge current reduces usable capacity. A common correction is:

t_adjusted = C_rated * (I_rated / I_actual)^(k - 1) / I_actual

Where k is the Peukert exponent. Typical AGM values are around 1.1 to 1.3. Lithium systems are usually much closer to 1.0.

Worked example:

System: 2000 W RMS, 70% Class D efficiency -> 2857 W electrical draw at full output
Battery: 100 Ah AGM at 12 V
Average music use: 30% of peak -> 857 W average -> 71.4 A average

t = 100 / 71.4 = 1.40 hours (without Peukert)

Peukert correction using k = 1.2 and a 5 A reference discharge rate:

t = 100 * (5 / 71.4)^(1.2 - 1) / 71.4
t = 100 * (0.070)^(0.2) / 71.4
t = 100 * 0.588 / 71.4
t = 0.823 hours = 49 minutes

Bottom line: one 100 Ah AGM battery gives about 49 minutes at that 30% average-use assumption. Two matching batteries roughly double the runtime. Real results will be shorter if voltage sags early, the battery is aged, or you avoid deep discharge.