# Calculating energy in battery

Let's imagine a regular deep cycle gel lead-acid battery from the building market.

• Capacity: 100Ah
• Nominal voltage: 12V

Is it really correct to say that the energy in the battery is 100Ah*12V = 1200Wh? Or should I rather consider that the voltage when fully charged is more like 13.5V and when fully discharged much less?

• It's all down to what you define as usable energy. A battery's capacity may be quoted as 100 ampere-hours but there will still be energy remaining and with the right sort of circuit you can maximize this to maybe get 150 Ah. Commented Sep 5, 2014 at 10:02

As a first very rough approximation, yes you can multiply the capacity and nominal voltage to get energy.

However, batteries are quite complicated with lots of variables. The output voltage will certainly vary over the discharge life. What does the 100 Ah spec actually mean? What is the output voltage at the end of those 100 Ah? To truly get delivered energy, you have to integrate the instantaneous product of the voltage and current over one full discharge.

But wait, it's not that simple either. That was one cycle at one temperature. Batteries can generally deliver less energy when cold, sometimes significantly so. Overall capacity generally decreases as a battery ages or as it is cycled. How deeply the battery has been cycled in the past can matter. The output voltage and capacity are a function of the current. 100 Ah doesn't necessarily mean that you can draw 100 A for one hour. It might be specified to deliver that charge at 10 A for 10 h, and if you draw 100 A you only get 80 Ah, for example.

How does your load actually use this energy? If you have a switching power supply, then maybe you can actually use the integral of voltage times current. If you have a linear regulator, then you really only care about the delivered current as long as the voltage stays above some mininum. Any extra energy the battery delivers in the form of higher voltage will just be dissipated as heat by the regulator. In that case, the Ah capacity figure is more relevant that a energy figure.

Due to all these variables, just multiply the capacity by the nominal voltage to get a rough idea of the energy, and realize a rough idea is all you're going to get. Good design will derate from there to a figure you can rely on over the range of temperature, age, and cycle lifetime you want the battery to work over.

Is it really correct to say that the energy in the battery is 100Ah*12V = 1200Wh?

It depends on how accurate you want to be. That is a mathematically sound assumption, but it assumes that the battery is a constant voltage for the entire cycle. For many needs, that is close enough.

However, battery voltage decreases as it is discharged. What you really need to do is measure the current and voltage at every instant during discharge to calculate power, then integrate power to get energy.

Of course, both the voltage and current will depend on many variables, among them temperature, age of the battery, how fully charged it was initially, how far discharged you are willing to run it, the rate at which you discharge it, and so on.

The nominal capacity and nominal voltage aren't really enough to calculate total energy capacity, they are just a quick way of comparing two batteries with the same chemistry.

Full battery specifications usually include a discharge curve which you can use to calculate usable energy for your application. For a quick example, see http://www.power-sonic.com/images/powersonic/technical/1277751263_20100627-TechManual-Lo.pdf

If you can only use the battery down to 11.5V, the useful energy will be lower than if you can use it when it has discharged further, and the rate that you take power from the battery will affect its usable capacity.

Some specification sheets have a more useful 'Wh vs voltage' graph, so you can quickly see that the battery capacity is 1200Wh when the terminal voltage is 11.2V, but that is not widespread. It also doesn't take account of the battery capacity being reduced at higher discharge rates