How to Size a Lithium Battery Bank: Ah, kWh and Depth of Discharge, Explained

Why Battery Sizing Matters

A battery bank that is too small may shut down before the backup period ends. Repeatedly operating near the battery’s limits can also increase stress on the cells, inverter, cables, and battery management system. For an off-grid system, this may mean losing power overnight or during several cloudy days.

A battery bank that is too large creates a different problem: unnecessary purchase cost, more installation space, higher shipping weight, and a longer return on investment. The goal is not simply to buy the largest battery available. The goal is to match usable energy, voltage, discharge limits, and expected operating conditions to the application.

Step 1: Start from the Load

First, list the equipment that the battery must power. For each load, record its rated power in watts and the number of hours it will operate during the required backup period.

The basic calculation is:

Energy consumption (Wh) = Power (W) × Operating time (h)

For example, a 100 W device running for 6 hours uses:

100 W × 6 h = 600 Wh = 0.6 kWh

Repeat this calculation for every load and add the results. Avoid sizing from the inverter’s maximum output alone. A 5 kW inverter may deliver 5 kW for a short period, but the battery capacity depends mainly on the actual energy consumed over time. You should still check the maximum simultaneous load separately to confirm that the battery, inverter, fuse, and cables can handle the required power.

Step 2: Convert to Ah at Your System Voltage

Battery manufacturers often specify capacity in amp-hours, while the load is usually calculated in watt-hours or kilowatt-hours. Convert between these units with the following formula:

Capacity (Ah) = Energy (Wh) ÷ System voltage (V)

For a 2,400 Wh requirement on a 48 V battery system:

2,400 Wh ÷ 48 V = 50 Ah

This is the theoretical capacity before considering inverter losses, DoD, temperature, aging, or a safety margin. The same energy requires a different Ah rating at another voltage. At 24 V, 2,400 Wh requires 100 Ah. At 12 V, it requires 200 Ah. This is why Ah should never be compared without also checking the battery voltage.

For a complete system, decide whether your energy figure is measured on the AC load side or the DC battery side. If the battery powers AC loads through an inverter, include inverter efficiency in the calculation. With 2,400 Wh of AC demand and a 90% efficient inverter:

Battery energy required = 2,400 Wh ÷ 0.90 = 2,667 Wh

At 48 V, that is approximately:

2,667 Wh ÷ 48 V = 55.6 Ah

Step 3: Account for Depth of Discharge

DoD describes the percentage of nominal battery capacity that has been used. If a battery is operated at 80% DoD, 80% of its rated energy is available for normal use, while 20% remains as a reserve.

The relationship is:

Usable energy = Nominal energy × DoD

For a 48 V, 100 Ah battery:

Nominal energy = 48 V × 100 Ah = 4,800 Wh

At 80% DoD:

Usable energy = 4,800 Wh × 0.80 = 3,840 Wh

If you need 2,400 Wh of usable battery energy and want to limit normal operation to 80% DoD:

Required nominal energy = 2,400 Wh ÷ 0.80 = 3,000 Wh

At 48 V, the required nominal capacity is:

3,000 Wh ÷ 48 V = 62.5 Ah

Using a moderate DoD can help preserve long-term performance. The appropriate limit depends on the battery chemistry, BMS settings, operating temperature, discharge current, and the manufacturer’s specifications. LiFePO4 batteries are commonly selected for stationary storage because they offer stable operation and long service life. Quality systems such as LINEX Power LiFePO4 batteries are designed for 6,000+ cycles under specified operating conditions.

Step 4: Add a Safety Margin

Real installations rarely operate under perfect laboratory conditions. Load estimates may be low, the inverter may consume standby power, temperatures may fall, and battery capacity gradually declines with age. A practical margin of 10% to 25% is common, depending on the application.

Use this simplified formula:

Required nominal capacity (Ah) = Load energy (Wh) ÷ inverter efficiency ÷ DoD ÷ system voltage × (1 + margin)

For critical backup systems, a 20% margin is often a reasonable starting point. An engineer may select a higher margin where replacement access is difficult, the load is uncertain, or several days of autonomy are required.

A Worked Example: Home Backup

Consider a home that needs evening backup power from a 48 V LiFePO4 battery bank. The estimated loads are:

The total AC energy requirement is:

960 + 300 + 150 + 400 + 300 = 2,110 Wh

Assume inverter efficiency of 90%. The battery must provide:

2,110 Wh ÷ 0.90 = 2,344 Wh

Using an 80% DoD limit:

2,344 Wh ÷ 0.80 = 2,930 Wh of nominal battery energy

Convert this to Ah at 48 V:

2,930 Wh ÷ 48 V = 61.0 Ah

Add a 20% safety margin:

61.0 Ah × 1.20 = 73.2 Ah

The calculated minimum is therefore about 73 Ah at 48 V. A practical selection would be a 48 V 100 Ah LiFePO4 battery, providing 4.8 kWh of nominal energy. At 80% DoD and 90% inverter efficiency, the estimated AC energy available is:

4.8 kWh × 0.80 × 0.90 = 3.456 kWh

This exceeds the estimated 2.11 kWh requirement and leaves room for load variation, battery aging, and short-term demand changes. The inverter must still be checked against refrigerator startup current and the home’s peak simultaneous load.

When the Numbers Are Close

If the calculated requirement falls just above a standard battery size, choose the next suitable capacity rather than operating with no reserve. For example, if the calculation requires 96 Ah, a 48 V 100 Ah battery may be adequate for a non-critical application, while a 48 V 200 Ah bank may be more appropriate for long backup hours or future load growth.

Parallel expansion is another option, provided the battery model, voltage, BMS communication, cables, fusing, and installation method support it. Two 48 V 100 Ah batteries provide approximately 9.6 kWh nominal energy, but they also require correct current sharing and protection. Confirm the manufacturer’s parallel limits before installation.

For project procurement, also verify the battery’s cycle-life test conditions, operating temperature range, communication protocol, shipping documents, and certifications. LINEX Power LiFePO4 batteries are specified with 6,000+ cycles, and product documentation can include UN38.3, CE, and RoHS compliance, with a 5-year warranty for applicable models. Correct sizing remains the starting point: the best battery is the one whose voltage, usable energy, power rating, installation format, and service conditions match the project.