How is usable capacity found?

Usable energy equals total amp-hours times the system voltage times the depth-of-discharge fraction. A 200 Ah, 24 V bank at 50 percent DoD holds 200 times 24 times 0.5, which is 2400 usable watt-hours, even though its nominal energy is 4800 Wh.

Why does depth of discharge matter so much?

You cannot drain a battery fully without damaging it, so only the usable fraction counts toward autonomy. A lithium bank at 90 percent DoD delivers nearly twice the autonomy of a lead-acid bank at 50 percent for the same nameplate size.

Does this account for solar input?

No. Days of autonomy is deliberately the worst case of zero recharge, used to survive cloudy-day sequences. With partial solar your real endurance is longer, but autonomy sizing ensures you do not run out before the sun returns.

Should I round days down?

Yes, for planning treat the whole-day figure as your safe endurance and the fractional part as a buffer. Running a bank to total depletion shortens its life, so design so the worst expected outage ends before autonomy is exhausted.

What daily load should I enter?

Use the total daily watt-hours from a load audit, including the energy lost in the inverter for AC appliances. Underestimating the load is the most common cause of an off-grid system running flat sooner than expected.

Days of Autonomy Calculator

When the sun does not shine, your battery bank alone carries the load. This calculator divides usable battery energy by daily consumption to tell you how many days the system lasts, and shows the state of charge falling day by day.

How it works

Usable energy is the bank’s nameplate energy scaled by the depth of discharge. Days of autonomy is that usable energy divided by the daily load:

Usable Wh = total Ah × system V × DoD fraction
Days of autonomy = Usable Wh ÷ daily load Wh

The remaining state of charge after n full days is the usable energy minus n days of load, expressed as a percentage of usable capacity.

Example

A 300 Ah, 48 V bank at 80 percent DoD holds 300 × 48 × 0.8 = 11,520 usable Wh. Against a 3000 Wh/day load that is 11,520 ÷ 3000 = 3.84 days of autonomy.

Tips

Treat the whole-day figure as your safe endurance, the fraction as buffer.
Include inverter losses in the daily load for AC appliances.
Lithium’s deeper usable range stretches autonomy far past lead-acid.