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How To Calculate Battery Capacity

By The Calcumatix Team Reviewed by Calcumatix Editorial Review 3 min read

Quick Answer

To calculate the required battery capacity in amp-hours (Ah), calculate your total energy needs in watt-hours (Wh) first, then divide by the nominal battery voltage (V) and the maximum safe depth of discharge (DoD). If you need to run a 100W load for 12 hours (1,200Wh) on a 12V system using a lead-acid battery limited to 50% DoD (0.50), the calculation is 1,200 divided by (12 times 0.50), which equals 200Ah required capacity.

Buying a battery without calculating your capacity needs first is a recipe for a dead system. If the battery is too small, your devices will shut off early. If it is too large, you spent money on weight and capacity you do not need. Battery capacity sizing is a backward calculation: you must start with the total power your devices consume and the time you need them to run, then work backward to find the exact amp-hour rating required on the battery label. This guide walks through a real sizing scenario to show how load, voltage, and depth of discharge determine the final capacity required.

The Battery Sizing Scenario: Calculating Required Capacity

Imagine you are building a small off-grid power setup. You need to run a 50W portable refrigerator and two 10W LED lights. You want them to run for exactly 10 hours overnight. You have decided to use a 12V lead-acid battery bank.

How do you calculate the exact battery capacity you need to buy off the shelf? You cannot just divide the total watts by the voltage. You must account for the time they run and the limits of the battery chemistry.

The battery capacity formula: Capacity (Ah) = Total Watt-Hours divided by (Nominal Voltage times Max Depth of Discharge)

Step by step:

  1. Calculate the total load watts by adding the wattage of every device.
  2. Multiply the total load watts by the number of hours they need to run. This gives you total watt-hours (Wh).
  3. Identify the nominal voltage of the battery system.
  4. Identify the maximum safe depth of discharge (DoD) for the battery type (typically 0.50 for lead-acid or 0.80 for lithium).
  5. Multiply the voltage by the DoD.
  6. Divide the total watt-hours by the result from Step 5 to find the required amp-hours (Ah).

Worked example: Inputs: 50W fridge plus two 10W lights equals 70W total load. Run time 10 hours. System voltage 12V. Lead-acid DoD 50% (0.50). Step 1 (total watt-hours): 70 × 10 = 700 Step 2 (usable voltage): 12 × 0.50 = 6 Step 3 (required capacity): 700 / 6 = 116.6

Required capacity: 117Ah minimum (rounded up to the nearest whole number)

In actual practice, you would round up to the next standard battery size available, such as a 120Ah or 150Ah battery. Use the Battery Capacity Calculator to adjust these inputs for your own scenario instantly.

Why Is Depth Of Discharge Required In Sizing?

The biggest mistake beginners make in battery sizing is ignoring depth of discharge. If you need 700 watt-hours of energy on a 12V system, straight division (700 / 12) says you only need a 58Ah battery.

If you buy a 58Ah lead-acid battery and pull 700 watt-hours out of it, you will drain it to 0%. Draining a lead-acid battery flat causes permanent sulfation on the lead plates, destroying its ability to hold a charge in the future. To get 700 watt-hours out safely without going below 50% capacity, the battery must hold 1,400 watt-hours total. That is why the DoD factor is mathematically required to size a system that survives more than a few cycles.

What Does The Formula Leave Out?

The formula provides a solid baseline for consumer and hobbyist systems, but it leaves out factors that industrial systems account for. According to IEEE 485 sizing standards, an actual system requires additional margins.

Inverter losses. If your 70W load consists of AC devices plugged into an inverter, the inverter loses about 15% of the power as heat. The battery must supply the 70W for the devices plus the 10W lost by the inverter. The load in the formula should be increased to account for this inefficiency.

Temperature derating. Battery capacity drops as temperatures fall. A 120Ah battery at 77°F might only deliver 90Ah at freezing. If the system operates outdoors in winter, the required capacity calculation must be multiplied by a temperature correction factor to ensure it still works in the cold.

Peukert effect. Lead-acid batteries deliver fewer total amp-hours if discharged rapidly. The sizing scenario above features a slow, steady drain overnight. If you attempted to pull all the power in one hour, the battery’s effective capacity would shrink significantly due to internal resistance. Explore the Calcumatix engineering calculators for related tools.

Sources and References

Frequently asked questions

Should I buy lead-acid or lithium batteries?

Lithium iron phosphate (LiFePO4) batteries cost more upfront but offer a much higher depth of discharge (up to 90% or 100% depending on the brand) and last for thousands of cycles. Lead-acid batteries cost less initially but are limited to 50% DoD and last fewer cycles. Because lithium batteries allow a deeper discharge, you can buy a smaller amp-hour capacity to get the same usable energy as a larger lead-acid bank.

How do I calculate capacity if I have multiple batteries?

It depends on how they are wired. If you wire two 12V 100Ah batteries in parallel (positive to positive), the voltage stays at 12V but the capacity doubles to 200Ah. If you wire them in series (positive to negative), the voltage doubles to 24V but the capacity stays at 100Ah. In both cases, the total watt-hour energy is exactly the same (2,400Wh).

What is the difference between starting and deep-cycle capacity?

Starting batteries (like standard car batteries) are designed to deliver a massive surge of amps for a few seconds to start an engine, then immediately recharge. They are not rated in amp-hours and cannot be deeply discharged. Deep-cycle batteries are designed to deliver a lower, steady amount of power over many hours and can be deeply discharged repeatedly. You must use deep-cycle batteries for off-grid or backup power systems.

Can I run the battery completely flat in an emergency?

You can, but it will severely degrade the battery's lifespan. Draining a lead-acid battery to 0% can permanently damage it in a single occurrence. Lithium batteries have built-in Battery Management Systems (BMS) that automatically shut off the power before the cells reach an unsafe low voltage, so a "0%" reading on a lithium battery usually means it has safely disconnected itself.

How do I account for solar panel charging during the day?

If solar panels are charging the battery while the load is running, the battery only needs to supply the net deficit. This is common in RV setups. You only use the battery capacity formula to cover the hours when the load exceeds the solar input, such as overnight or during heavy cloud cover.