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What is an Amp Hour and How to Calculate Battery Capacity

An Amp-Hour (ampere-hour, Ah) is a way of describing a battery's capacity - how long it will run before it is drained down. But I can be be more specific: the amp-hour rating for a given battery is the maximum amperage that can be drawn continuously until the battery is completely discharged, flat, empty, drained, dead, over a specific time period.

How Are Amp Hours Determined?

Battery manufacturers complete tests on their batteries to give them an Amp-Hour rating. A typical time period for a test is 20 hours, but it varies - batteries are tested over different periods, such as 24 hours, 75 hours, even 100 hours.  But as you'll see below, a 100 Amp-hour battery tested over a 100 hour period (i.e. 1 amp drawn for 100 hours) will not have the same capacity as a 100 Amp-hour battery tested over a 20 hour period (i.e. 5 amps drawn for 20 hours). It turns out that if you drew 1 amp continuously from the 20 hour test battery, it would last for 110-120% longer than on the 100 hour test battery. I'll (try to) explain that later.

Let's Do an Example Calculation

Suppose you have a 100 Amp-hour battery, tested over a 20 hour period. 100 Amp-hours divided by 20 hours = 5 amps. That means that the battery manufacturer claims the battery can sustain a 5 amp load for 20 hours until the battery is completely dead.

That's great, but now put it into realistic terms. For starters you don't want to drain a battery to it's completely flat, empty, dead state as it will significantly reduce the life of the battery. A good rule of thumb (battery type depending) is that you should only drain a battery down to 40% of it's original capacity, or in other words you've only got 60% of the battery to use. This number should be stated by the manufacturer in the documentation.

Back to the 100 Ah, 5 Amp load example: We said you had 20 hours of time when drawing 5 amps, but in fact you only have 60% of that time, so 20 hours x 60% = 12 hours.

Up until now, what we have said is true because we have used the same amperage over the same time period at which the battery was originally tested (20 hour rate). So what if you took your 100 amp-hour battery, but wanted to draw 10 amps from it until it was at the safe discharge level (60%)?

Do the math: 100 Ah / 10 Amps x 60% = 6 hours, right?

Wrong.

The More Amperage You Draw, the Lower the Battery Capacity

That's right, the effective amp hours available drops with the more amps you draw.  All of a sudden that 100 Amp-hour battery is not what it says it is. Ok, back to the numbers, lets try to keep this clear:

Using the 100 Ah, 20 hour test battery, at 5 amps draw, you get the full 100% of the battery rating (that's how the battery was tested in the first place, so you should get all 100%!). But step up the amperage to 10 Amps, and you will lower the capacity of the battery by about 10% (or 90% remaining).

That makes 100 Ah x 90% = 90 Ah / 10 Amps draw = 9 hours x 60% (max safe discharge number) = 5.4 hours. And that's quite a difference from the 6 hours you thought you had.

Where Did I get the 90%?

I'm going to stop here and leave you hanging - except to say that there's a relationship defined called Peukert's Equation, and that's where the approximate 90% comes from.  The Peukert Equation quantifies the above phenomenon so that you can predict how much time you'll actually have on a battery given a specific discharge rate.

What's Next - How About A Helpful Tool?

My guess is that if you're still reading this your about ready to start figuring out how many batteries you need, and you could really use a little help with the calculation.  You might have gone to the Wikipedia site above to investigate what Peukert had to say, but exponents aren't really your thing, and you can't find your calculator anyway.

 

43 Responses to What is an Amp Hour and How to Calculate Battery Capacity

  1. nick says:

    im wanting to run 2x1000watt electric motors that draw 48v to run. thats roughly 20.8amps?
    my real question is if i want to run them at full go for 6hrs what amp/h battrey would i be looking at.
    thanx in advance

    • Mr. Mei Cruz says:

      Sir,
      Please send me a copy of your reply to nick’s question (dated Sept23,2009). My question is somewhat related to his case problem.

      • Nick says:

        Well i never got a reply and its been several years, lets say the project never went off the planning stage but i did get answers to my question elsewhere. Mr. Mei Cruz if you need help go to http://www.benson-search.com and go to contact us and send me an email. glad to help

    • Pro says:

      u need at least 125AmpHour for one motor

  2. adam says:

    Hi, I am trying to chose a bettery. One battery is 7.5 Ah tested at 20 hours, the other is the same Ah but tested at 10 hours. Which one is preferable? Thanks!

    • Robin says:

      Adam

      The battery tested at 10 hours would have more capacity than the one tested at 20 hours, assuming everything else is equal.

  3. ric recede says:

    if i will connect battery in series with the same AH
    will this mean that the BACK-UP time doubles-up at a given load?

    which will give more back up in this string of batteries connected in series to give a 48volts battery bank supply :

    Battery rating : 4volts 180ah x 12 pcs =48volts what’s
    the total ah?

    Battery rating = 12volts 180ah x 4 pcs = 48 volts what’s the ah?

    • Robin says:

      Ric

      No. If the batteries are in series the Ah rating does not change (assuming the batteries are all the same as in your examples).

      In your first example the batteries are in series, 4×12 volts @ 180 ah each = 48 v @ 180 ah.

      The same goes for the second example: 48 v @ 180 Ah.

      Clear?

  4. GDI says:

    Great article, thanks.

  5. Pawas says:

    Great work. Really helpful as u kept it simple. Thnx a lot

  6. mr watts says:

    hello, i recently caught some youths actually drinking battery acid. they have been arrested by the police and are now being charged !!

    • MarkyMark says:

      Being charged with what? Stupidity is not a crime…

      • Regomatic says:

        MarkyMark, did you happen to notice the submitter’s name? May have been a little clue there that this was his attempt at humor … if you’re still wondering about the youths though, I’d venture a guess they’re now fully charged and ready for ‘discharge’ should they get turned on! Good article by the way, Robin.

  7. Ric says:

    4 volt in series connection means you will get 4×12= 48 volt 180 Ah. IF 4 volt in parallel connection means you will get 4 volt 2160 Ah

  8. Steve says:

    Hi,
    How can I calculate the Run Time of my 12 volts 4 X 1000 CCA batteries if I need to run a 100 amp motor.
    I already thank you for your help.
    Steve

  9. amol says:

    hi,
    i have 12v / 7.5Ah batteries . for how much time can i draw a current more than 8A.

  10. Robin says:

    Without the actual battery spec it’s hard to say, but a rough calculation would be:

    7.5 Amp-hours / 8 Amps = 0.9 hours * 0.9 * 0.6 = 0.5

    So say approximately 0.5 hours or 30 minutes.  This depends on many things though as noted in the article, including temperature, battery test period, battery maximum discharge level, and battery type.

  11. Chris Butler says:

    Great article. I have 4 6volt batteries powering a 12volt system. Each 6volt battery has a capacity of 232 amp hours. Should I expect a total capacity per this example? 232 x 4 /2? For a total of 464 amp hours?
    Thanks

  12. Robin says:

    Chris – thanks.  And yes, I think you’ve got it!

  13. Chris Butler says:

    Cool!  I guess my brain DOES work sometimes! Thanks!

  14. Justin says:

    Thinking of ways to save gas money in this tough economy I am thinking of buying an electric mower-but I also want to put a tractor battery on it. The mower has a 12 amp motor. Im having trouble figuring what size battery I would need. I would like the mower to be able to run easily for an hour, maybe two hours max. Any suggestions on a battery size and how long you think it would last?

    • Robin says:

      Justin
      Is the mower an electric plugin that you want to convert or is it a newer battery powered model?

      What voltage does it run on and is it AC or DC?

      If you are looking to save money be careful for false economies. A new 24 volt battery mower might have two 20 amp hour sealed lead acid batteries – buying those will run you between 200 and 250 dollars. That’s a lot of gasoline!

  15. jey jumo says:

    i have bought a 12v x 17Ah battery which was seriesed up to give 240v dc. this was to be connected to a 10kva ups to give a 220v ac output and drawing a current of about 20amps. how long can this battery take before it is completely discharged.

    this same battery though new was completely drained to a level that some cells were giving as low as 1v dc. could this be a problem with the ups or what?

  16. regs says:

    sir..??..may i ask how many 20Watts, 12Volts Halogen Lamp can i load to a 200Ahr, 12VOlts battery if i am going to light the bulbs for only one minute per day? ynx.

  17. PRADIP BARMAN says:

    can u please give me an answre……….If the ceiling fan is on slow speed, does it consume less electricity?

  18. Carl Harrison says:

    Hi there,

    I’m very new to all these numbers, i hope you can help me with my new batteries?

    I have just bought a new lamp for shooting at night. The batteries are 2 x 12 volt 14 amp/hr, i think that means each one has 7 amp/hr? I would like to know how long each of them will power my lamp for? I sometimes run both the batteries on the lamp at the same time. Can you also tell me about charging them, just some timimgs would be nice as i have a 12 volt charger that comes with them? The lamp is a Light force 240mm Blitz model. As the two batteries combined weigh quite a bit i would like to take just the one out with me but only if the hours i get out of them are long enough.

    Hope you can help,

    Regards Carl.

    • Robin says:

      Carl, what bulb do you have in your lightforce 240? There should be a code with your unit like “GL03″ or something. This code tells you the power consumption of the bulb. The manufacturer lists 20, 30, 50, 75, and 100 watt bulbs. Also, is it wired as a 24 volt or 12 volt? Most of them are 12V, but there are a few 24 volt options as well.

  19. Doug says:

    Robin, thanks for these amp-hour explanations, it’s helpful. Might you be misspeaking, though, when you say “…that means that the battery manufacturer claims the battery can sustain a 5 amp load for 20 hours until the battery is completely dead”? Obviously a battery isn’t gonna put out 5 amps for 20 hours and then suddenly be “completely dead.” Instead, I assume it would still put out 4 amps for a while, then, 3 amps, etc. as it approaches “dead” status.

    • MMcGinty says:

      It depends on your definition of “dead”.

      In practice, assuming we’re talking about deep-cycle batteries, as the charge is depleted the voltage drops, but it still delivers whatever amps the load is drawing. The point at which it can no longer do that is what I consider “dead”. It may still show 9-10 volts under no load, but for a 12 volt battery that’s dead as a doornail.

      That said, bear in mind that I never test adequately-working batteries to the bitter end (on purpose, anyway.)

  20. tahir aziz says:

    its really helpful information for all of us .
    but i have a little problem if you help me in this regard i m very grateful to you,
    i have 800 amp load , and want 6 hrs battery backup .
    please suggest me the how much battery Ah capacity i required…?

    • Steven says:

      Here is my guess at your question:

      You want 800 amps for 6 hours, that comes to 4800 amps. Using the 60% rule state above I figure it would come to 8000 AH of capacity needed (4800/.6)

  21. rahul says:

    how should i calculate current from battery AH?
    i.e for eg. for 200AH battery,how much amount of current is available?

  22. sarojini says:

    Good morning sir,
    Is there any relation between voltage and amphour for selecting a battery.

  23. trinath says:

    i use a ups with rated KVA : 0.5
    minimum VAH : 84
    AVR for single phase AC
    160 V to 280 V input

    WHAT is the backup time ?
    Please reply soon

  24. trinath says:

    UPS rated KVA: 0.5
    minimum VAH : 168

    what is back up time ?
    Please reply via my e-mail

  25. Steven says:

    Here is a battery that I am considering purchasing but it does not appear to have the info needed to calculate the AH rating. Am I missing something?

    PLEASE reply to my email as well!!!!!!!!!!!!

    Battery Usage
    Deep cycle
    Cranking Amps at 0 Degrees F
    450 amps
    Cranking Amps at 32 Degrees F
    575 amps

    Reserve Capacity
    66 minutes
    Volts
    12 V

  26. Sandeep Malik says:

    Which is a better 12 Volt battery to be used for a heavy vehicle application:-
    120 Ah @ 5 hr rating
    or
    140 AH @ 20 hour rating?
    How does one compare the two?

  27. Ellmer says:

    Hi
    I have a trike made up of a robin reliant, i have put quite a lot of lights on it, that i might add they are not all on at the same time, but if i do use some aswell as the head lights the engine drops a lttle power. Now the battery has gone right flat as i havent been on it fore some weeks, i have had a look in the reliant book and the have 2 sorts of battery one is 12v 22amp hrs and the other is
    12v30amp hrs. i dont understand could you please let me know what i should buy as the one on the trike now is gone flat and i dont know how long it has been like it so just as well buy a new one. Please help as i dont want to go for a long ride and find that the battery goes flat on me.

    Thanks Ellmer

  28. Mitha says:

    My technician bought for me :
    4X150 watts panel
    Inverter 3000 watts 48 volt
    4 batteries each 200/10
    One regulator
    I wonder what he did is right. My regulator shows 53.5 v most of the time , sometime below that when power is cut. What capacity is this?
    thanks

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  30. [...] it (via its internal shunts) so it draws a maximum of 30 amps.  My battery is a Chinese-made 10 amp-hour, 48 volt Lithium Iron Phosphate (LiFePo4) pack that came as an option with the BMC kit. [...]

  31. Anonymous says:

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