How to find capacity of a battery in terms of mAh or Ah?

I know that this question has been asked a number of times and even received negative feedback but I want to find a shortcut method of determining capacity of a battery in terms of mAh instead of using that Q = It method which may take upto several hours.

Example: The initial reading of my 3.7v battery was 3.93 volts. I connected a load to it which started draining a current of 660 mA. After 15 minutes, the current being drained was 570 mA while the reading on my voltmeter was 3.65 volts (when disconnected from the load). How can I use this data to find the capacity of the battery?

• Why do you think the behavior of your battery is different than all of those other batteries in all of those other questions? You should explain why your situation is unlike the others. Sep 18 at 16:17
• No, all the batteries have the same behavior. The difference is in the question. I just want to know that shortcut method which would take just a few minutes rather than several hours - or otherwise being told that it is just not possible without that Q = It method. Sep 18 at 16:20
• Does this answer your question? Conventional way to measure Li-Ion cell capacity? Sep 18 at 16:32
• You may have an easier way to solve the task of integration: Use constant current circuit to load the battery. Then all you need is to know the time needed to reach the terminal voltage. When reaching terminal voltage you also want to stop the discharge as (lithium based) batteries can be damaged by discharging under recommended voltage. Sep 18 at 16:49
• No that answer doesn't help but TimWescott's Answer to this question is really helpful to have an understanding of this problem. Sep 18 at 21:19

Here's your problem, in a nice graphic from Battery University. Most battery chemistries in use today (Li-whatever, NiCd, NiMH, lead-acid) have a discharge curve that features a short downward drop in voltage, a long nearly-level voltage vs. charge section, then a "knee" leading to a quick drop-off.

To complicate things:

• the cell voltage is often more sensitive to the current draw than to state of charge
• the cell voltage is sensitive to temperature
• the cell voltage, and it's drop-off is sensitive to construction and chemistry details of the cell
• the cell voltage is sensitive to aging in hard-to-predict ways (basically, as it ages its "chemistry and construction" change).

This means that any attempt to determine the battery's capacity before it hits that knee in the discharge curve is just guesswork, and probably bad guesswork.

There have been attempts made to determine state of charge by drawing a pulsed current from a battery, because a cell's internal resistance also depends on the state of charge (this is more or less the reason that you have different discharge curves in the graph corresponding to different discharge currents). But a cell's behavior in this regard is also dependent on temperature, construction, chemistry, aging, etc. So that doesn't work well, either, except perhaps as a route to a PhD for someone who wants to get a job designing batteries.

Bottom line: you'd be better off determining its general chemistry, weighing it, and multiplying that by some constant that matches its chemistry -- you'd still be wildly wrong, but you'd be less wrong than trying to do it by discharging and watching the voltage, and it'll take less time.

• The 3.7V battery used has a voltage that is too high for the LiFePO4 and A123 batteries in the attachment. Instead it is an older and normal Lithium battery that is fully charged at 4.2V and is almost dead at 3.2V, half-charged voltage at 3.7V. Some ebay 18650 batteries are marked 9700mAh (!) which is a lie. Some ebay batteries weight is too low because they are full of rice flour instead of battery chemicals. Sep 18 at 17:17
• That does not matter. Pay no attention to the absolute voltages. It is the shape of the curve that is common between different batteries, and what leads to the difficulty in determining state of charge from voltage. Sep 18 at 17:23
• Well explained. Thanks. Sep 18 at 19:42
• So what would be the "Guesswork" based on the data I provided? Sep 18 at 21:21
• What is the exact chemistry? How old is the battery? How did it age? What's the temperature? Was there any noise in the measurement? Who made the battery? Was the battery made on a Monday or a Thursday? Were the line workers unhappy or happy? Did the lithium come from supplier A or supplier B? It's all guesswork. That's the point -- all of the totally unpredictable things that you have no control over cause more voltage variation than the voltage variation caused by discharge. [Edited by a moderator.] Sep 18 at 21:26

Example: The initial reading of my 3.7v battery was 3.93 volts. I connected a load to it which started draining a current of 660 mA. After 15 minutes, the current being drained was 570 mA while the reading on my voltmeter was 3.65 volts (when disconnected from the load). How can I use this data to find the capacity of the battery?

You can use the resting voltage vs state of charge for your battery type. Luckily this is fairly well defined in Li-ion batteries, however suitable data may not be easy to find because it is not often published. Here is an example:-

measured resting cell voltage for a range of 3S 2200 mAh packs

In this case we see that 3.93 V corresponds to ~65% capacity, and 3.65 V corresponds to ~5%. This is ~60% of the battery's capacity.

Your average discharge current was ~(660+570)/2 = 615 mA, which over a period of 15 minutes is 615*(15/60) = 154 mAh. 154/60% = 257 mAh estimated (fully charged) capacity.

For more accurate State of Charge estimation you could test your battery by fully charging it, then removing various amounts of charge and measuring the resting voltages.

• Of course, this would be different between different li-ion chemistries. I'm sure it wouldn't work for LiFePO₄ for instance. Sep 19 at 2:49
• @Hearth no it wouldn't work so well for LIFePO4, that's why I said 'luckily this is fairly well defined in Li-ion batteries' - which the OP is talking about. As a practical matter, I have been able to accurately determine the SoC of the Lipos we used in the drone aircraft I was piloting, which was important because we had to do several flights on a single battery. I have been using Lipos in model aircraft since they were first introduced in 2003, and have become quite adept at estimating remaining capacity from voltage alone. Sep 19 at 8:51