Battery bank size and how long it should last

Converting daily demand and autonomy into stored energy, and why depth of discharge changes the answer so much.

The engineering question

How many ampere-hours of battery does an off-grid system need, and what does the autonomy figure really promise?

Worked example

The figures below were produced by running the Battery Bank Sizing Calculator with the same inputs — during the build, from its authoritative engine.

Results
Required bank energy	18500 Wh
Required bank capacity	385.4167 Ah
Series strings	4 no
Parallel strings	4 no
Assessment	18.5 kWh bank ≈ 385 Ah at 48 V → 4S × 4P of 100 Ah 12 V batteries. Size cables and OCPD for the bank current.

Stored energy is daily demand times autonomy, divided by usable depth of discharge.
Capacity in ampere-hours is that energy divided by the system voltage.
Series batteries set the voltage; parallel strings set the capacity.

Sanity check

Lead-acid at 50 % depth of discharge needs roughly twice the lithium bank for the same autonomy. If the two give the same answer, the depth of discharge was not applied.

Tools for this problem

These are the EngiMetric calculators that compute the numbers in this topic. Each one shows its formula, its units and its limits rather than returning a bare result.

Engineering review required

This topic supports professional engineering work; it does not replace a sealed design. The result depends on site data, the governing standard and engineering judgement, and should be confirmed by a competent engineer before it is built.

References & standards

IEC 62619 — industrial lithium cells and batteries
NREL — off-grid system sizing