How to calculate battery capacity: formula and examples

"How many amp-hours do I need?" is the most common question before buying a battery, and the answer takes a minute to work out. All you need is a list of appliances, the length of the outage and three corrections people often forget. Below: the formula, two complete examples and a table for converting amp-hours to kilowatt-hours.

The formula in one line

First, the energy your appliances will use during the outage:

E = sum of (appliance power × hours of use)

Then the battery capacity needed to supply it:

Capacity = E ÷ (depth of discharge × inverter efficiency) × margin

• Depth of discharge is the share of capacity you can use regularly without shortening battery life: 0.8–0.9 for LiFePO4, about 0.5 for lead-acid AGM and gel.
• Inverter efficiency is 0.85–0.92: some energy turns into heat during conversion.
• Margin is 1.15–1.2: for cold weather, battery ageing, and outages that run longer than scheduled.

Step 1. List the load

An apartment and a 6-hour outage.

Why is the fridge 60 W and not 150? The compressor runs in cycles: it switches on, cools and stops. A typical fridge uses 0.9–1.5 kWh a day, or 40–60 W on average. The inverter does have to handle its start-up surge — but that's a question of choosing the inverter, not capacity.

Step 2. Three corrections

For LiFePO4: 932 ÷ (0.9 × 0.9) × 1.2 ≈ 1.4 kWh.

For AGM: 932 ÷ (0.5 × 0.9) × 1.2 ≈ 2.5 kWh.

So a single 12.8 V 100–120 Ah LiFePO4 battery covers 6 hours in an apartment, while lead-acid would take two 12 V 100 Ah blocks — twice the weight and space. Why, and what else separates the two chemistries, is covered in LiFePO4 vs AGM.

Example for a house

An 8-hour outage, a gas boiler and a well.

3060 ÷ (0.9 × 0.9) × 1.2 ≈ 4.5 kWh — one 51.2 V 100 Ah LiFePO4 module (5.12 kWh). If outages sometimes last 12 hours, or the boiler works harder in winter, plan for two modules: in 48 V systems you simply add them in parallel.

Amp-hours and kilowatt-hours

Amp-hours mean nothing without voltage: 100 Ah at 12 V and at 48 V are four times different amounts of energy. Compare batteries only in kilowatt-hours: kWh = Ah × nominal voltage ÷ 1000.

Important: power banks and portable power stations often state capacity in mAh at single-cell voltage — 3.6–3.7 V. "30,000 mAh" is about 110 Wh, not 360 as you'd get by multiplying by 12 V. Look for the Wh figure — that's the honest one.

Discharge current matters too

Capacity answers "how long"; the battery's maximum current answers "how much power". Current is I = P ÷ U.

• A 3 kW inverter on 51.2 V draws about 60–65 A including losses — a normal load for most modules.
• The same inverter on 12.8 V would need over 250 A: thick cables, heat, BMS protection tripping. That's why powerful systems use 48 V.

Check the battery's maximum continuous discharge current against what the inverter draws at full power. If one module isn't enough, add modules in parallel — they share the load.

Cold and ageing

• In an unheated room in winter, usable capacity drops, and LiFePO4 must not be charged below 0 °C without heating — the BMS will block charging. Keep the battery somewhere warm.
• After a few years a battery loses some capacity. The 15–20 % margin in the formula covers exactly that, so the system doesn't "shrink" before you notice.

Quick reference

For more precise numbers, use the consumption table for specific appliances in how long will your appliances run on a battery.