We use batteries to store electric energy. Batteries normally have two main attributes. One of them is voltage and the other one is capacity of a battery.
– Capacity (CA or CW)
Batteries provide electric voltage to circuits where they are installed, so they serve as voltage sources. As such, voltage can always be found clearly specified on battery labels or batteries themselves.
Now the capacity is a tricky one because sometimes it is expressed as an electric charge stored in a battery, while at other times it denotes the amount of electric energy contained in a battery. It is very important to distinguish between the two because those are really two different electrical quantities.
One of the good ways to distinguish between charge and energy capacity is to look at the unit. Electric charge that is stored in a battery is normally expressed in Amp-hours or Ah for short. On the other hand, electric energy stored in a battery is usually expressed in Watt-hours or Wh for short.
In electrical engineering, we normally use coulombs or C for short, as a unit for electric charge. However, for batteries, Amp-hour is actually a more appropriate unit because it tells us how much of a current battery can provide and for how long.
The product of battery’s current Ibatt and the time of discharge t amounts to battery’s electric charge capacity CA (of course, this is for an ideal case when we neglect losses and other efficiency factors). Thus if we have battery’s capacity expressed in Ah, we can drain that battery for 1h with as many Amps as the capacity of that battery is. Or we can drain that battery for 10h with 1/10th of a current in Amps as the capacity of the battery is, and so on.
It turns out that capacity of a battery expressed in Ah is actually industry norm and electric charge capacity is the value normally specified when we look at the label of a battery.
However capacity of a battery expressed as the amount of electric energy stored in it is more important. We are actually more interested in how much energy can be stored in a battery. Manufacturers sometimes put this capacity on the label and sometimes this value is omitted.
However that is not a problem as we can always calculate it on our own. In order to obtain the amount of electric energy stored in a battery, we need to multiply the amount of electric charge stored in a battery with battery’s voltage.
Since voltage V is always clearly specified, we know how much that is. And also charge capacity CA is the norm of being specified. So we can obtain the amount of energy CW simply by multiplying CA and V.
In this calculation example, we will consider rechargeable Nickel-Metal Hydride (NiMH) AAA size battery, AA size battery and one standard Lead-acid car battery. First we will look at what information is specified for each one of these batteries. We can read the following electrical specifications:
– Capacity CA = 1,000 mAh = 1 Ah
– Capacity CA = 2,600 mAh = 2.6 Ah
– Capacity CA = 60 Ah
– Cold Cranking Amps CCA = 356A
So the AAA size battery that we have in this example has voltage labeled as 1.2V. Also when fully charged, this battery can contain 1,000 mAh of charge. That is equivalent to 1 Ah. So knowing the voltage and the amount of charge stored in this battery, we can calculate the amount of energy that is stored in this little AAA battery as:
1.2 Wh is not some tremendous amount of energy, but at least we calculated how much energy we have in one AAA battery.
AA size batteries have the same voltage but their capacity is larger – so there we have 2.6 Ah. Thus when we calculate the amount of energy stored in a AA battery, we can see that we obtain roughly three times more or 3.12 Wh of energy:
Just note that the common AAA and AA batteries that we see in ordinary life, are usually non-chargeable batteries and they have voltage 1.5V. 1.5V is obviously different than the voltage of these rechargeable batteries and that is the consequence of a different chemistry of those non-chargeable batteries.
Finally, one standard SUV (Toyota Rav4 with 2.0L gasoline engine) battery label that is shown above says the voltage is 12V. That is quite a standard voltage for car installations. Also the capacity as the amount of charge stored in this car’s battery is 60 Ah. So we can calculate the amount of energy stored in this battery as:
In the video below, you can see couple more batteries and their labeled capacities. One thing you can observe is that for a bit more serious applications, manufacturers tend to specify both charge and energy capacities of batteries:
– Capacity CA = 2,100 mAh = 2.1 Ah
– Capacity CW = 7.98 Wh
– Capacity CA = 5,900 mAh = 5.9 Ah
– Capacity CW = 88 Wh
The mobile phone battery in the video is battery from my old Samsung Galaxy S3 cell phone. The laptop battery is from ASUS ROG G750 laptop. Both of those batteries are Lithium-ion batteries.
Let’s have a look at one exercise question, just as an example of some battery capacity comparisons:
As we have seen above, car battery had capacity expressed as 60 Ah, while capacity of a AAA battery was 1,000 mAh, which is the same as 1 Ah.
Obviously capacity of a car battery is 60 times larger than the capacity of a AAA battery. Does that mean we need 60 AAA batteries in order to replace one car battery?
Well the answer is no.
We cannot compare charge capacities if we talk about batteries that have different voltages. Because the voltages are different, we need to take them into consideration and we need to calculate the energy stored in each one of those batteries first. Only then we can perform a proper comparison.
So knowing that car battery’s voltage is 12V, we can calculate energy stored in a car battery as 720 Wh. AAA battery has 1.2V so that corresponds to 1.2 Wh of energy stored in a AAA battery. Dividing 720 Wh with 1.2 Wh, we obtain 600.
That means we need 600 AAA batteries in order to replace one car battery!
I hope this article helped you learn a thing or two about batteries and their capacities. Now you understand the basics of this concept better and you can do a little bit of battery capacity calculations on your own.
As always, if you prefer watching videos, here is the “Capacity of a Battery – Charge versus Energy Stored” video for you.
I am constantly developing new courses that go into much more depth in all of these topics. Thank you very much for stopping by and see you soon!
Below you can find the slides I used to develop this blog post and the video:
Can measuring the charging voltage, current and time to charge a NiMH battery be used to determine its capacity?
Or how can you use the charging parameters for a NiMH battery to find its capacity?
To measure NiMH battery capacity, the experts all seem to say that to get an accurate evaluation you have to measure the discharge parameters. I have yet to see anybody state that measuring charging parameters will also give you, if not accurate, but a good ballpark evaluation of the batteries capacity. Understandably, what goes in must come out. Of course neglecting intrinsic electric losses.
Hi Philip, thanks for your questions. I have written an article that may help you understand a bit better the process of charging and discharging of a battery and associated efficiencies. Have a look at the following blog post:
Efficiency of a Battery Cycle and its Capacity