How big a battery — and can it carry the load?
Energy and power are separate problems, so this checks them separately. No chemistry limit is ever applied without you choosing it.
How big a battery?
Energy and power are separate problems. A bank can hold plenty of kilowatt-hours and still refuse to start your pump.
1 · What it has to supply
2 · What your battery can actually give back
3 · The battery you are considering
4 · Putting it back
The two checks, made separately
Working
Runtime at different loads
How this is calculated
requiredUsable = dailyEnergy × daysOfAutonomy
requiredNominal = requiredUsable ÷ (1 − reserve) ÷ (depthOfDischarge × dischargeEfficiency × temperatureDerate)
Module count rounds up — you cannot buy two thirds of a battery.
The power checks are separate and neither substitutes for the other. Continuous output must cover the running load; surge rating must cover the largest start. A bank that fails either one will not do the job however many kilowatt-hours it holds, and when power rather than energy sets the module count the tool says so explicitly.
runtime = usableEnergy × inverterEfficiency ÷ averageLoad, shown as a band because temperature, age, the real load pattern and the inverter's cutoff all move it — nearly always downwards.
Why reserve costs more than it looks
Holding 20% back is not 20% more battery. The reserve comes off the usable share, which was already reduced by depth of discharge and efficiency, so the effects multiply. Working through a typical example: 5 kWh a day, 90% depth of discharge, 95% discharge efficiency and a 20% reserve needs roughly 7.3 kWh of nominal capacity, not 5.5 kWh. That is the honest number, and it is why banks always end up larger than the first estimate.
The recharge has to balance
A battery that supplies 5 kWh a day needs 5 kWh a day put back into it, and the charging window is shorter than people assume — good generating sun is a few hours either side of noon, not the whole of daylight. If the arithmetic does not close, the bank runs down a little further each day until it is flat, and no amount of extra storage fixes it. That check is run above and flagged as an error rather than a note, because it is the failure mode that actually strands people.
Limitations and safety
This sizes capacity. It says nothing about wiring, fusing, disconnects, ventilation, mounting, temperature management or interconnection, all of which are governed by regulations and manufacturer requirements that vary by location and by product. Lithium batteries in particular have specific installation and clearance requirements. Have the design reviewed by a qualified installer before buying, and treat the battery's own documentation as the authority over anything here.