# Calculating a battery's useful life

#### cmartinez

Joined Jan 17, 2007
7,082
Say I have a device that consumes around 20uA working with four Li-FeS2 AAA 1.5V batteries in series, delivering a total of 6V between them. According to Wikipedia, those batteries can deliver an average of 1,200 mAh. And according to Newark's website, a battery's life can be calculated with the simple formula:

estimated hours = 0.7*mAh/mA​

The above calculation is done for a single battery with a capacity of mAh. And I would understand that if I were to connect several batteries in parallel, they would deliver the same voltage but their mAh capacity would add up. Is that right?

But if I were to arrange them in series, their voltages add up, but the mAh capacity remains the same as if it were a single battery. Is that right?

So, for my arrangement, my batteries expected lifetime would be 0.7 * 1,200 / 0.020 = 42,000 hours = 4.8 years. Are my calculations correct?

And my last question would be: My intuition tells me that connecting batteries in parallel might discharge them prematurely due to small differences in voltages between them, but this is a problem that would not be present when connecting them in series, right?

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#### dl324

Joined Mar 30, 2015
11,490
So, for my arrangement, my batteries expected lifetime would be 0.7 * 1,200 / 0.020 = 42,000 hours = 4.8 years. Are my calculations correct?
You're neglecting self discharge.
And my last question would be: My intuition tells me that connecting batteries in parallel might discharge them prematurely due to small differences in voltages between them, but this is a problem that would not be present when connecting them in series, right?
That and self discharge.

In series things get bad when the weakest cell is completely discharged. I don't know about the battery chemistry you're using, but a half volt of reverse voltage is enough to kill NiCd and NiMH batteries.

#### cmartinez

Joined Jan 17, 2007
7,082
You're neglecting self discharge.
Yeah, I considered self discharge. But according to the info I've so far gathered, a lithium's battery shelf life is about 15 years. I'm guessing that's directly related to self discharge. On the other hand, I'm assuming that the 0.7 factor in the traditional formula is already taking that into account.... although, as they say, "Assumption is the mother of all f**k ups" ...

In series things get bad when the weakest cell is completely discharged. I don't know about the battery chemistry you're using, but a half volt of reverse voltage is enough to kill NiCd and NiMH batteries.
So what are my options to test my setup? Connect the circuit and wait 5 years to see what happens?

#### dl324

Joined Mar 30, 2015
11,490
So what are my options to test my setup? Connect the circuit and wait 5 years to see what happens?
What do the manufacturer datasheets say? Your load is so small that self discharge is more significant. My recollection of shelf life specs is that the battery still has "useful" capacity remaining.

#### KeithWalker

Joined Jul 10, 2017
1,216
You're neglecting self discharge.
That and self discharge.

In series things get bad when the weakest cell is completely discharged. I don't know about the battery chemistry you're using, but a half volt of reverse voltage is enough to kill NiCd and NiMH batteries.
Li-FeS2 batteries are primary cells and are not rechargeable. They have a self discharge rate of <1%/year. The "0.7" in the battery life calculation is to allow for that. Your assumptions, C. Martinez are all correct.

#### Tonyr1084

Joined Sep 24, 2015
5,039
What are you doing that you're drawing twenty micro-amps?

#### BobaMosfet

Joined Jul 1, 2009
1,207
Say I have a device that consumes around 20uA working with four Li-FeS2 AAA 1.5V batteries in series, delivering a total of 6V between them. According to Wikipedia, those batteries can deliver an average of 1,200 mAh. And according to Newark's website, a battery's life can be calculated with the simple formula:

estimated hours = 0.7*mAh/mA​

The above calculation is done for a single battery with a capacity of mAh. And I would understand that if I were to connect several batteries in parallel, they would deliver the same voltage but their mAh capacity would add up. Is that right?

But if I were to arrange them in series, their voltages add up, but the mAh capacity remains the same as it were a single battery. Is that right?

So, for my arrangement, my batteries expected lifetime would be 0.7 * 1,200 / 0.020 = 42,000 hours = 4.8 years. Are my calculations correct?

And my last question would be: My intuition tells me that connecting batteries in parallel might discharge them prematurely due to small differences in voltages between them, but this is a problem that would not be present when connecting them in series, right?
Their calculator is nice, but not in any way accurate. Batteries vary greatly by brand. The only way you can do any sort of estimate is by finding the datasheet for the battery from the OEM, and looking at what they say for your load- and that will be _best case_. Battery interaction between batteries, including thermal atmosphere aspects, etc make this a non-trivial calculation.

#### cmartinez

Joined Jan 17, 2007
7,082
What are you doing that you're drawing twenty micro-amps?
Running a PIC10LF322 mcu along with tiny SMT hall sensor... neat, eh?

#### cmartinez

Joined Jan 17, 2007
7,082
Their calculator is nice, but not in any way accurate. Batteries vary greatly by brand. The only way you can do any sort of estimate is by finding the datasheet for the battery from the OEM, and looking at what they say for your load- and that will be _best case_. Battery interaction between batteries, including thermal atmosphere aspects, etc make this a non-trivial calculation.
Yeah ... I've noticed that the available public knowledge regarding batteries is very empirical ... And I knew that variance between brands was to be expected. I just didn't know by how much until I did some searching.

#### Tonyr1084

Joined Sep 24, 2015
5,039
Interesting. Care to share the purpose? Solving what problem? Performing what kind of task or service?

#### cmartinez

Joined Jan 17, 2007
7,082
Interesting. Care to share the purpose? Solving what problem? Performing what kind of task or service?
Sorry... but it's yet another of my professional secrets ... but let's just say that if things work the way I expect them to, I'll be more than happy to buy a round of beers to all the active members of this forum...

#### Tonyr1084

Joined Sep 24, 2015
5,039
I want beer goggles. Better yet, I want a bottle of UpDaug.

#### Tonyr1084

Joined Sep 24, 2015
5,039
Awe geez. Couldn't wait and see if someone would ask?

#### Ioannis66

Joined Nov 7, 2012
36
Does your device constantly draw 20 microamps or does it mostly do that and sometimes draws more like a short pulse?

For example, it has a duty cycle of 95% on 20 uA and 5% on 1mA. Then you need to recalculate the battery life.

#### MIS42N

Joined Jan 25, 2013
4
"My intuition tells me that connecting batteries in parallel might discharge them prematurely due to small differences in voltages between them, but this is a problem that would not be present when connecting them in series, right?"

It's the other way round. If batteries are in parallel then current is drawn mainly from the one with most charge, bringing the voltage of all batteries down to the point of being discharged. But if they are in series, if there is a difference in capacity the same charge is drawn from each battery and the one with the least charge determines how much charge can be drawn.

This is a problem both charging and discharging cells in series. Series Li-ion batteries have protection on every cell to stop charging when one cell reaches the maximum required charge, because overcharging any cell is dangerous. Series Lead Acid can take a small overcharge, so smart chargers provide a topping charge so all cells reach full charge. Most multi cell batteries with use cells made on the same production line on the same day, so differences between cells are small and they all behave the same way.

#### Audioguru

Joined Dec 20, 2007
11,249
People are talking about self discharge and rechargeable lithium batteries.
But your Li-FeS2 AAA 1.5V batteries are NOT rechargeable and Energizer guarantees a 20 years shelf life.

#### KeepItSimpleStupid

Joined Mar 4, 2014
4,197

batteries in series should be matched. If they are not rechargeable, capacities should be the same and then probably ESR.

if Lithium, they would need a balance charger. Again matched batteries make sense.

#### Duane P Wetick

Joined Apr 23, 2009
432
My laser computer mouse draws 0.020 amp. (avg.) from 1 AA cell and the average life is about 2 months... A fair represntation of AA life.

Cheers, DPW [ Everything has limitations, and I hate limitations.]