Peukert’s Law  A Nerd’s Attempt to Explain Battery Capacity
Normal People be Wary
In lieu of an Introduction, I have a confession: I am a nerd. Not the nerd of the recent past, with large framed glassed and #2 pencils in my shirt pocket, no, I come from a different generation of nerds who wear contacts and prefer the keys (readkeyboard NOT typewriter). The nerd of past decades has been replaced by my fellow undercover nerds (ninja nerds?) whose love for detail and number crunching can still lead to squinty eyed headaches over 3 generation spreadsheets. If any part of this attempt at an explanation seems archaic or confusing, don’t despair, you are normal. On the other hand, if when you are done reading this you have a grin on your face and a light feeling in your step, you have left the earthlings and entered nerdom. Welcome to the family.
When I first entered the arena of lead acid batteries and their neurotic tendencies, it was presented to me that the easiest way to rate and understand how long a leadacid battery (be it flooded, AGM, VRLA, or Gel) would last, would be to use the AH (Amp Hour) rating that is so often designated to them. I was told that if a battery was rated at 100AH, then that was more or less indicative that it would last either 100 hours under a 1 amp load, or 1 hour under a 100 amp load. But in like manner to my calculus teacher, who explained that all my previous notions of the logic of numbers were about to be shot to threads, it soon became apparent that this notion of order was false; everything previously understood had been a lie. I know it’s dramatic but it makes the point.
When a battery is given an AH (Amp Hour) rating, it is always accompanied by the number of hours that rate is taken at. The most often listed rate is 20 hours. So, if you were to see a battery rated at 100AH, it would have been tested at a 20 hour rate, unless otherwise noted. This means that the manufacturer slapped the 100AH rating on the battery after testing that battery for 20 hours with an actual amperage drain of 5 amps. What this also means is that your load of 15 amps will not actually last 6.6 hours, as one may think, but a much smaller number. Luckily for us, there is a very handydandy formula to figure out exactly how long a lead acid battery will last, under any load. It is called Peukert’s Law. Peukert’s law expresses mathematically that as the rate of discharge increases, the available capacity of that battery decreases.
The formula that states the Law in a usable format is as follows:
H is the rated discharge time, in (hours).
C is the rated capacity at that discharge rate, in (Amperehours).
I is the actual discharge current, in (Amps).
k is the Peukert constant, (dimensionless).
t is the actual time to discharge the battery, in (hours).
The formula, as we use it, is then rewritten to:
It is the discharge rate at the time to discharge eg. the new AH rating.
If you’ve gotten this far, you may see that in our supposed situation we have the H=20 hours, we have the C=100AH, and we have the I=15 amps (being the new discharge current), but we do not have the k. At this stage it gets fairly complicated if we do not have kthe Peukert constant. Unlike the name suggests, it is not constant at least not across the board. Each battery will have a different Peukert constant. The value of k is normally between 1.1 and 1.3. It can range from 1.05  1.15 for AGM batteries, 1.11.25 for Gel, and 1.21.6 for Flooded Batteries. Our options at this point are to guess (gasp in horror) at the number, and risk being wrong, or b. to actually go through the work of finding the Peukert constant for your battery. Fortunately for you we have a calculator to figure out your Peukert constant, and you can use that to find the exact number*. The only caveat is that the Peukert constant has no way to account for age of the battery, or the temperature at which it is being discharged inboth of which will have a negative effect on the battery capacity.
Getting back to our example here, we have figured out that this particular battery has a Peukert constant of 1.3, so if we plug that in to the equation we end up with an effective capacity of 71.9AH at an amperage drain of 15 amps, for 4.79 hours. So, if you apply a 15 amp load to this battery which is rated at 100AH at a 20 hour rate, you end up with a 71.9AH battery at a 4.79 hour rate. The advantage of being able to do this, other than massive bragging rights  ( come on, who isn’t impressed that you can still do advanced math? just don’t mention the calculator)  is that you will not be surprised when your battery lasts almost 2 hours less than a person would have figured by using the 100AH rating as their guide. The greater the load on the battery, the less realized capacity you will have.
As stated before, using Peukert’s law, you will not be figuring for temperature or age of the batteries. When I do calculations for extreme temperature or age greater than 6 months, I add between .05 and .1 to Peukert’s constant. There is actually no proven method, that I know of, to figure out the difference in the projected Peukert’s constant from the actual, other than retesting the batteries in the manner that they were tested when they had the original AH rating stamped on them. Since that would be a massive pain, I just add .1 to Peukert’s constant.
Ok, so if you have made it this far, and your still conscious, good job. Hopefully you know just a little bit more about the nature of the LeadAcid battery and why it can be tricky sometimes to put a finger on just how long it's going to last. (If you have a grin plastered on your face you’re sick, and incidentally  just as crazy as I am.)
* If you really want to know how we get the Peukert constant, then see our Math behind the Magic explanation of that calculator. For all but the extreme nerds, it works so just accept it.
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Kathy
I have set 2  12 volt batteries up in series to equal 24 volts. This required to 24 volt system to run a 80 lb thrust trolling motor. It seems I am loosing power before batteries are drained half down why?
BatteryStuff Tech
Kathy If the battery pack is fully charged and is no longer holding under load it could be the batteries are sulfated. The typical lifespan of a lead acid AGM, Flooded, or Gel battery is approximately 35 years, assuming the battery isn't discharged below 50%. If the battery is being discharged below 50% the cyclelife drastically decreases. If you are unsure of the age of the batteries or if you have been excessively discharging the battery pack, I suggest testing the batteries. You can use a load tester or take them to a local battery shop, but before testing them, I would fully charge the battery pack, then wait at least 12 hrs after charge to test them.


Gus J
For a battery/inverter set up running 120V AC is there an advantage to having a higher voltage system, ie 48V vs 12V?
BatteryStuff Tech
Higher voltage systems pull less amperage which in turn makes them more efficient. Pulling a small amp load out of a higher voltage battery pack will in most cases last longer than pulling a larger amp load in a lower voltage battery pack.


Louwrentius
Thanks for this article. I've been reading about lead acid batteries and trying to better understand them and this really helped a lot. Being able to predict how long a lead acid battery will last (neglecting age) given a particular load is quite useful. What is difficult though is to understand the voltage drop under load and determining SoC under that particular load. I wonder if there is any kind of formula for that. Normal SoC is always measured based on the voltage 'at rest' but I don't want to switch off the load and wait 10 minutes to get a somewhat okish reading on the SoC. 
Ross Williams
I think the easiest explanation is that AH tells you how long the battery can provide its power without regard to the battery voltage. Most often this is what people want to know, how long will this battery last in my device that uses this size battery. It ignores the voltage of the battery. A 9 volt battery and a 1.5 volt battery with the same ah will last the same amount of time, but the 9 volt will produce 6 times as many watts of power over that time. 
Michael
I’d like to rate your article, but is 1 the best or worst? Numero Uno says it’s best, but 1 often doesn’t. I enjoyed it, anyway.
I have an aging (bought it in 1993) rider mower. It runs well, but is getting hard to start. It uses a 12N143A. I’d like to use a higher current battery. I’m stuck with the X and Y dimensions, but I could go about 2” taller. Is such a thing available?
thanks, Michael
BatteryStuff Tech
I would suggest looking at our Motocross YTX14AH, which is a sealed version meant to replace the 12N143A battery. The battery measures:
Length 5 5/16
Width 3 1/2
Height 6 9/16If you have any further question on selecting a battery I would suggest contact hour TECH Department.


Gary Kirouac
I purchased 28 T105 trogan batteries for my whole house backup power supply in 1999 as of today I still have 12 batteries working. Used in a 24 volt system using a trace inverter which also has an battery equalization function which extends the overall battery life. You have to be on top of the maintenance and equalization too however this system was 150% larger than the minimum requirements needed so YES a larger system with a lower discharge rate also extends the battery life. I made one of these for my brother in law who survived Katrina in LA and was the only person with 24 hour power for 12 weeks. I also set up a 1000 gal propane pig with a trifuel 9000 watt generator to recharge. Recharge average rate was 6 hours and the equalization rate 9+ hours. He was supplying power even to the local policefire units as they set up a recharging system at his home to recharge all of there portable communication equipment. That system used 32 trogan 6v T105 set up in a 24 volt configuration. 
Fred
Great information, but none of the calculators seem to work.
BatteryStuff Tech
Sorry to hear about the technical issues. Which calculators are you having trouble with? Are all of the field boxes properly filled in? Each calculator has a walkthrough with examples to help you figure out what the fields are looking for. Try using the numbers in the examples provided and you should get the same results shown in the walkthrough. UN less, of course, the “calculate” button is not functioning at all. Can you confirm this?
Sailinglegend
The really interesting fact about Peukert is that if you take much less than the 20 hour rate, i.e only take 1 amp from your 100 Ah battery, then you actual battery capacity is much higher. This means if you have a larger battery bank than you need and you are always below the 20 hour rate then the bank will appear to be larger than you thought, and therefore last longer. Bigger is much better.
BatteryStuff Tech
That‘s right. If the rate if discharge is less, the actual capacity of the battery will be perceived as being more.


