Amp-hours vs watt-hours: how to convert and compare batteries

Two batteries, both "100 Ah"

Picture two batteries on a shelf, each labelled 100 Ah. One is a 12 V battery, the other a 51.2 V battery. They are not close to the same size, and the label does not tell you that. Amp-hours describe how much charge a battery holds; they say nothing about how much work that charge can do until you know the voltage.

Battery University gives the definition: a battery rated 1 Ah should provide 1 A for one hour. The same source notes that voltage multiplied by current equals watts. Put the two together and you get the conversion.

The Energy Information Administration defines the watt-hour as the energy of one watt used for one hour, and a kilowatt-hour as 1,000 watt-hours; its own example is a 40 W bulb running for five hours, which uses 200 Wh. If you want the full picture of power versus energy first, read watts vs watt-hours.

The same 100 Ah at four voltages

Run it the other way to see what the same energy looks like in amp-hours. To store 5,120 Wh you need 5,120 ÷ 12 = 427 Ah at 12 V, 213 Ah at 24 V, 107 Ah at 48 V and 100 Ah at 51.2 V (all our calculations, rounded). The amp-hour figure shrinks as voltage rises, so a bigger amp-hour number on a lower-voltage battery can still be the smaller battery: 200 Ah at 12 V is 2,400 Wh, less than half of a 100 Ah battery at 51.2 V.

Voltage is also what ties a battery to an inverter. Home systems use higher voltages because current falls as voltage rises; the reasoning is in 12 V, 24 V or 48 V: why battery voltage matters.

Why the voltage is "nominal"

A battery's voltage moves as it charges and discharges, so makers quote a nominal value. Battery University lists the conventions: lead acid is rated at 2 V per cell. A "12 V" lead-acid battery is therefore six cells in series (6 × 2 V), as our arithmetic shows. Lithium iron phosphate cells have a different nominal voltage, which is why EG4's lithium batteries say 51.2 V rather than 48 V; the EG4 LifePower4 sheet describes its 51.2 V pack as 16 prismatic 3.2 V cells in series. Our LiFePO4 explainer covers why. For energy maths, use the nominal voltage on the datasheet and keep to it throughout.

How EG4 states both numbers

EG4's battery sheets list capacity in amp-hours and energy in kilowatt-hours. Here is the check, using each sheet's own figures and our multiplication:

The numbers agree: the maker's kilowatt-hours are amp-hours times 51.2 V, rounded. Where the sheet gives conditions, keep them with the number. The 280Ah figure is quoted at 25 °C and 100% state of charge.

Nominal versus usable

Nominal energy is the full rated figure. Usable energy is what you are meant to take out. The 314Ah indoor sheet lists 16 kWh nominal and 12.86 kWh usable, with 80% depth of discharge recommended. The arithmetic checks: 16.077 kWh × 0.80 = 12.86 kWh. The 100Ah and 280Ah sheets list a state-of-charge cutoff recommendation of no lower than 20%, which keeps the battery at the recommended 80% depth of discharge. Applying the same 80% to the other two batteries gives, in our calculation, 4.10 kWh usable for the 100Ah (5.12 × 0.8) and 11.47 kWh for the 280Ah (14.336 × 0.8).

The rate you draw at matters too. Battery University notes that discharging at a faster rate than the rated one produces a lower capacity reading: a 1 Ah battery at 2C should ideally deliver its capacity in 30 minutes, but internal losses cut it to about 95% or less, while slow discharge can read above 100%. That is why datasheets state the rate, such as the 0.5C conditions on EG4's cycle-life figures.

Amps are not amp-hours: the current rating

A second use of "amps" causes confusion. Amp-hours are a quantity, how much charge is stored. Amps are a rate, how fast it is moving right now. Batteries list both. The 314Ah indoor sheet gives 157 A as the recommended charge and discharge current and 200 A as the maximum continuous discharge, with a recommended rate of 0.5C. The C-rate is simply the current as a fraction of the amp-hour rating, and the numbers fit: 0.5 × 314 Ah = 157 A (our calculation).

Multiply a current by the voltage to get power. At 51.2 V, 157 A is about 8.0 kW and 200 A is about 10.2 kW, which matches the 8 kW charge and 10.2 kW discharge power on the same sheet. So the sheet gives you all three families of number, and they connect:

Series and parallel: what adds and what stays

When identical batteries are wired in series the voltage adds and the amp-hours stay the same. When they are wired in parallel the amp-hours add and the voltage stays the same. Either way the watt-hours add, which is the reason to compare in watt-hours. Two 12 V, 100 Ah batteries make 24 V and 100 Ah in series (2,400 Wh) or 12 V and 200 Ah in parallel (also 2,400 Wh). EG4's 51.2 V batteries are built for paralleling: the 314Ah sheet lists up to 32 in parallel. Check the maker's limit and wiring rules before you buy a second battery, and have a licensed electrician do the connections under local code.

A quick conversion sheet

To go from the energy you want to the amp-hours you must buy, divide by the voltage. These rows are our arithmetic:

Read across any row: the same energy needs a quarter of the amp-hours at 48 V that it needs at 12 V. That is the whole reason a 100 Ah label cannot be compared across systems.

A worked sizing example

Suppose a house needs 10 kWh of usable energy overnight. These are planning numbers, not a design:

1. At 80% usable, the nominal energy needed is 10 ÷ 0.8 = 12.5 kWh.
2. At 51.2 V, that is 12,500 ÷ 51.2 = 244 Ah.
3. Two 100 Ah modules give 200 Ah, or 10.24 kWh nominal and 8.19 kWh usable. Short.
4. Three 100 Ah modules give 300 Ah: 15.36 kWh nominal, 12.29 kWh usable. Enough.
5. One 314 Ah battery gives 16.08 kWh nominal and about 12.86 kWh usable, according to the sheet.

Inverter losses come on top of this; see how much battery do you need and the runtime calculator. Batteries add up the same way: the newer IN-03 LifePower4 sheet says up to 32 in parallel give about 163.8 kWh (32 × 5.12 = 163.84), while the IN-02 sheet allows 64.

Where Ah still shows up

Inverter sheets also quote batteries in amp-hours. The 6000XP lists a recommended battery capacity of more than 200 Ah per inverter, and the 18kPV lists at least 300 Ah. At 51.2 V, 200 Ah is 10.24 kWh and 300 Ah is 15.36 kWh (our calculation). Those recommendations are in the maker's units; convert them with the voltage of the battery you are actually considering.

Common mistakes

• Comparing Ah across voltages. Always convert to Wh first.
• Comparing nominal with usable. A 16 kWh nominal battery gives 12.86 kWh at the recommended 80%.
• Using a 12 V formula for a 51.2 V battery. The voltage in the formula must be the battery's own.
• Ignoring the conditions. Temperature, state of charge and discharge rate come with the number.
• Stopping at the battery. The inverter's efficiency and idle draw come out of the same energy.