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 (read-keyboard 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 The nerd of past decades has been replaced by my fellow undercover nerds (ninja nerds?)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 lead-acid 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 handy-dandy 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 (Ampere-hours).
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 k-the 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, 1.1-1.25 for Gel, and 1.2-1.6 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 in-both 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 re-testing 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 Lead-Acid 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.