Clearing up the question of battery capacity in electronics

TechTuesday_Big

Because mobile electronics are so pervasive, it is important for users to understand how to compare batteries. While most people are familiar with, for example, “gigabytes” as a measure of hard drive space and have a more instinctive appreciation for phrases like “4G speeds,” the nomenclature used to gauge the amount of energy capcity in a battery is still a bit of a mystery. This is exacerbated by some outdated industry practices that are throwbacks to when a single battery technology dominated any given energy sector. Most companies use capacity measurements that aren’t consistent from one battery technology to the next. So how do you compare and choose your battery pack? We’ll try to unshroud some of the mystery here.

How industry makes measuring battery capacity confusing
Most products show battery capacity measured in “amp-hours” (Ah) and milliamp-hours (mAh), where 1000mAh = 1Ah. Amp-hours is a measure of “current capacity”, not “energy capacity”.  This is a subtlety, but it is important.  Amp-hours only tells half the capacity story.

What is an amp-hour?  An amp is a measure of electrical current, and the hour indicates the length of time that the battery can supply this current. A 2.2Ah battery can supply 2.2 amps for an hour.  If the battery must supply more amps, because a bigger device is connected, it will last for a shorter period of time; if the battery is supplying less amps, it will last longer. The problem with this method is that it doesn’t give a complete picture of the total energy stored.  It is easy to find cases where two different batteries with the same number of amp-hours will have completely different amounts of total energy.

How Goal Zero measures battery capacity
The correct unit for measuring energy capacity of a battery product is called watt-hours. Watt-hours signifies that a battery can supply an amount of watts for an hour. For example, a 60 watt-hour battery can power a 60 watt light bulb for an hour. The same battery would run a 5W phone for 12 hours and power a 1W LED light bulb for 60 hours. Watt-hours is a simple and consistent way to measure the capacity of any battery pack, whether it’s a Nickel Metal Hydride (NiMH), AA battery, the 12V lead acid battery in your car, or the lithium ion battery pack on your laptop.  Goal Zero offers battery packs in all of these configurations, and they are easily comparable by looking at the watt-hours rated to each one.

What is the difference between watt-hours (Wh) and amp-hours (Ah)?
The equation for power is
watts = amps x volts
and for energy the equation is
watt-hours = amp-hours x volts

Amps is only half of the equation.  Since different batteries may have different voltages, amp-hours is only useful for comparing products that have the same battery configuration.
If you want to be sure that you’re getting the right results, use watt-hours for an apples-to-apples comparison.

What if I don’t have watt-hours?
To get a good grasp of the actual energy capacity, without access to the watt-hour rating of a pack, you can do a quick calculation to generate the watt-hours. First, find out the Ah rating of the battery pack (if it’s given in mAh, take that number and divide it by 1000 to get the Ah value). Second, find out the battery type or chemistry and then the typical voltage for that type. Here’s a short list of the most common types of batteries and their voltages:

3.7V per lithium-ion cell (cell phones use a single cell (3.7V), laptops typically use 3 cells in series (11.1V)
3.2V per lithium-ion iron phosphate cell (multi-cell LiFePO packs are typically configured as 4-cell or 12.8V)
1.5V per alkaline cell
1.2V per NiMH and NiCad cell
2.1V per lead-acid cell (car batteries are 6-cell (12.6V) and some golf carts are 3-cell (6.3V))

Finally, multiply the voltage (V) by the amp-hour (Ah) rating of the battery/pack to get watt-hours (Wh) and then compare.

For example, the Switch 8 Solar Recharger is 3.6V and 2.2Ah (2200 mAh) By multiplying those two together you get 7.92W. Will the Switch 8 charge your iPhone? well, the iPhone 5 has a 1440 mAh (1.4Ah) battery at 3.7V for 5.18W — yes!

*Did you know that the number at the end of each Goal Zero battery pack signifies the approximate amount of energy (measured in watt-hours) available in that that specific battery? Guide 10= 10Wh, Yeti 1250=1250 Wh, etc. Making it easy to find the battery pack for your power needs!

42 Comments

  1. Andrew Swensen 3 years ago

    Good article and, I agree, it’s important to clear up this confusion.
    Two things I am wondering about. First, should not the units in the last paragraph be Wh instead of W? (3.6V * 2.2Ah = 7.92Wh & 3.7V * 1.4Ah = 5.18Wh)? Second, I am always baffled by how the Wh became a unit at all. A Watt is a rate of energy consumption/dissipation (unit energy per unit time). Specifically it is one Joule/second; Joules being a unit of energy. So we take a unit of energy (J) and divide by a unit of time to get a Watt (W), then we multiply the Watt by a unit of time and call it a Watt-hour but it has the same dimensions as energy. Why the heck don’t we just call a Joule a Joule? It’s like measuring your displacement in miles, dividing that displacement by the time (in hours) it takes and calling that velocity, and then saying that if it takes you 2 hours to get home at 60 mph, then you must live 2 mph hours away. Sorry, pet peeve. Glad you wrote this.

    • Author
      goalzero 3 years ago

      Hi Andrew. We agree, and we’re constantly reevaluating how to best communicate these standards, while making sure they fit our brand/naming conventions/legacy products/etc. Thanks for stopping by and leaving your feedback at Solar Life.

    • Sam C 2 years ago

      Andrew you are incorrect in your definition of Watts.

      W = Power (it is instantaneous) as in 2V x 2A = 4W or this is what the instant load would be

      Wh = Energy (it is Power over time) as in 4W x 2hours = 8Wh or this is what the load would consume over 2 hours

      You are correct that the last paragraph should be in Wh based on the variables that were given.

      • Marc 2 years ago

        Sam,

        You’re calling out Andrew, but you’re both saying the same thing. Andrew has it right; a Watt is a Joule/s, which is a much better definition then just ‘instantaneous power’. Also, Energy is the integral of Power in regards to time. By saying ‘Power over time’, you get the classic W/h which is not energy.

    • Mark 2 years ago

      I think you mean If it takes you 2 hrs at 60 mph to get home you live 120 mph-hours away.

  2. Aaron Schellenberg 3 years ago

    I was impressed with the article describing energy capacity of batteries. I am a Mechanical Engineering professor and am always pleased to see concepts described clearly and simply. Well done!

    Andrew, I was also delighted with your insights about the awkward nature of the Watt-hour unit. I find it difficult to help engineering students understand kWh units on their electric utility bills because they are expecting energy units in Joules or Btu. It is a little challenging helping them understand that a kWh is an energy unit rather than a power unit. Well stated!

    • Author
      goalzero 3 years ago

      Thanks for the feedback Aaron.

  3. valena wodoslawsky 3 years ago

    How many watts are in aa battery. I have not been able to find this answer.

    • Author
      goalzero 3 years ago

      Hey Valena, here’s some info on our AA rechargeable batteries:
      2300 mAH (2.3 watt-hours Ah)
      1.2 Volts
      You can find our batteries here

      Our customer service team is great about answering questions, so feel free to give them a call at 888-794-6250. Thanks.

  4. larry mathes 3 years ago

    Valena,

    !. 2300 mAh (milliamp-hours) = 2.3 Ah (2300 /1000), and 2.3 Ah * 1.2 volts = 2.76 watt hours (Wh) NOT 2.3 Wh as given in the answer above by goalzero.

    2. The formula for finding watts is ‘Watts = amps * volts’. Note: the ‘*’ in the formula denotes the multiplication operation. However, none of the batteries I’ve seen give the amperage of the battery (it would be given in milliamps or 1 thousandth of an amp). I have a ‘smart’ battery charger which gives me the milliamps of the charged batteries.

    3. BUT, Valena, YOU DON’T NEED TO KNOW THE WATTS OR AMPERAGE OF A BATTERY.
    YOU DO NEED TO KNOW TWO THINGS: (a) the total mAh (milliamp-hours) of the batteries you’re putting in the device and (b) the mA (milliamps) the device draws per hour.

    I have a light that requires four AA batteries. I used batteries that had 2400 mAh each, for a total of 9600 mAh. The device draws 1500 mA per hour. 9600 divided by 1500 is 6.4 hours of use before the batteries are completely devoid of charge. But after about 5.5 hours the light gets very dim, and I change the batteries for a freshly charged set.

    Valena, and goalzero, I hope this information is of some use.

    homealone

    • Author
      goalzero 3 years ago

      Thanks for catching that error Larry. We’ve corrected our comment. Check your inbox for a gift from us.

    • John Lam 5 months ago

      Hi Larry,

      No. 3 is incorrect . 2400mAH batteries are always 2400mAH when connected in series. Since your light draws 1500mAH, the 4 batteries can only last for 1.6 hours theoretically. Practically, voltage drops after a certain time of operations, and the light glows dimmer and dimmer without visually noticeable in the early stage as light intensity is logarithmic to human eyes. Until the light glows so dim that you change the batteries after 5.5 hours.

      When the 4 batteries are connected in parallel, you are then right that the capacity is 9600mAH, but then the voltage is only 1.2V and can never drive your light at all.

  5. Don Mac 3 years ago

    volts x ah =watts… thank you thank you. I spent hours trying to get a straight answer to the question of how many batteries I need for my solar array.

    • Ron 2 years ago

      No, I believe volts x amps = watts; volts x amp-hours = watt-hours, or divided by 1,000 = kilowatt-hours

  6. JW 3 years ago

    So I take it that if the stock battery is 710mAh, any replacement that’s at least that is ok (if it fits the charger and battery compartment). But if the stock battery is 7.2 volts, is it ok to use a 7.4 volt replacement?

  7. Aaron 3 years ago

    Typo?
    “For example, the Switch 8 Solar Recharger is 3.6V and 2.2Ah (2200 mAh) By multiplying those two together you get 7.92W.”

    Should be 7.92Wh?

  8. Dave 2 years ago

    This does not apply to all batteries though.

    for example Exide – world leading battery manufacturer tell you what the watt hour of each battery is.

    There standard wet lead acid 80Ah (ER350) battery is rated @ 350Wh and this guarantees to be able to produce this.

    12.6V x 80Ah = 1008 watt hours

    however the Gel battery (ES900) is also an 80AH 12V lead acid battery but Gel

    this is a huge difference and you would be very disappointed if you calculated it like

  9. Chris 2 years ago

    Great read!

    One more question. I’ve heard that often a battery’s wh rating is not actually what you get. Do manufacturers list the USABLE wh or should the given rating be reduced as the entire capacity of the battery should not be used to avoid the risk of damaging the battery?

    Thanks in advance!

  10. Thomas Varghese 2 years ago

    Thanks a lot for making the difficult things so easy.
    Really appreciate your simple and lucid style of writing.
    Please can you answer if the following Statement is correct or not :
    “The Total Watt Hours from a Battery is the Sum of the Watt Hours of the individual Cells contained in the Battery.”

    Please correct me if I am wrong.
    Regards,
    Thomas

  11. Wh capacity of a battery is the correct Concept, because it gives how much energy battery has and battery can supply for doing any work. All the time we expect to know about the amount of work battery can undertake during its discharge cycle. Since energy is the measure for work done, we must know the stored energy in a battery at any instant. Since watt is the instantaneous energy (joules per second) available in the battery to undertake work at a given instant you know the exact status of the available energy. Voltage and current changes from instant to instant and no electronic devise can adjust battery voltage (DC voltage) automatically like AC voltage. Battery voltage changes as per the status of battery and current demand. Therefore Watt Hour if known can show exact status of the battery capacity for utilization.

  12. Cindydude 2 years ago

    I just want to thank you for this helpful information.

  13. agbradford83 2 years ago

    How much does resistance factor into the equation?

    IE: I have a Li-Ion battery that measures 4.5 Ah with 13 v for 58.5 Wh and an appliance that consumes 5.5 W (12v)… How many hours of operation will I get out of my battery? 58.5 Wh /5.5 W = 10.6 hours but that does not account for losses due to resistance.

  14. Ian 2 years ago

    So what if you have a battery with no AH rating listed on it. How do you calculate the AH with out puting a known load on it and seeing how many hours it takes to drain the battery?

  15. Mike 2 years ago

    Hey,

    Would anyone know the Battery watt hour (Wh) measurement for a 17 hour lithium ion battery ?

    Thanks in advance!

    Mike

  16. DW 2 years ago

    Real life question: I want to drive a 2-10hp 48v dc electric motor which in turn will drive a boat impeller on a small lightweight craft. I’m used 12v cat 29-31 lead acid batteries with around 125 AH. In this application their weight is prohibitive so I’m interested in finding out what I will need in a lithium ion type configuration to do the job. Realizing that the cost for lithium batteries is substantially higher I need more than a weight advantage to justify the extra dollars. What is the power storage advantage to lithium ion batteries in a case like this and how many, with what characteristics, lithium ion batteries would you suggest?

  17. Sridhar Shetty 2 years ago

    How to estimate residual AH capacity of an alkaline battery based on its voltage?

  18. Manos 2 years ago

    Hi there

    I would like to purchase a diving flashlight and I would like to know how to calculate of how long it will last me.
    The features of flashlight are :
    1. Li-ion battery 2x 4000mAh 18650 Protected rechargeable battery
    2. Emitter Type: CREE XM-L2 LED (6000lm)
    3. LED Quantity:3

  19. SB 2 years ago

    OMG thank you GoalZero.

    I’m so sick of the industry trying to use “current-hours” as a measure of battery capacity when it means absolutely nothing.

    I think it is proof that the idiocracy has arrived.

  20. Mark 2 years ago

    Anyone here love MATH?
    Great read, but I still am unsure if I’m calculating this correctly. I’m a off grid home, and my current batteries are not keeping up to our off grid demands, and I’m looking to upgrade my batteries. I just want to be sure my upgrade is actually a UPGRADE.
    My current solar system is inverted at 48volts. I have acid batteries that are each 6 volts with 230ah. 6v x 230ah=1380Wh. However I have 3 rows of 8 wired in series and then paralleled to give me 48volts, out of my 6 volt batteries. So I suspect that changes my Wh calculations to the following.
    230ah x 48volt=11,040Wh (but I have three rows of this) x 3 =33,120Wh
    The battery I am looking to purchase is a huge salt water battery boasting the best/newest technology available in batteries. It’s a 48 volt 500ah battery which calculates to 24,000Wh
    As per these calculations is that to mean I would actually be downgrading?
    Thanks all you mathematicians !!

    • Lonnie 1 year ago

      Mark, what I read is that you are using (24) 6v batteries in a configuration that produces 48volts from three banks, tied together to give you 33,120Whrs. This has got to be a headache to watch over all those batteries and manage the different fluid levels in each battery, plus the amount of copper to tie them all together. Now, you have found a single 48 volt battery that comes close to your requirements, but only putting out 24,000Whrs. First and foremost, when talking about using solar energy storage, you never want to completely deplete your batteries. And, 50% is really the lowest you want to go on rechargeables, otherwise you will cause irreparable damage to them. You probably have a few batteries that are not holding up their part of the load. So, if the original configuration was not keeping up with your requirements, what would make you think a smaller storage capacity would? Depending on your load requirement, drives the storage capacity. You would be better off with at least two of those salt water batteries in parallel giving you 48,000Whrs.

    • Achraf 1 year ago

      Yes you’re downgrading, but this battery seems like a more efficient approach, so just buy 2 of these 48v 500Ah and install in parallel to make it an upgrade.

  21. Mark 1 year ago

    Watts (Power) is not an instantaneous measure. It is a measure of work performed over time.

    It’s the amount of energy dissipated OVER a specific amount of time. If no time passes, no power can be produced. When people talk about Watts, they implicitly mean 1 J/sec. So if you say something is using 100 Watts, that’s a rate of energy used over that 1 second.

    A Joule already contains a factor for voltage (It’s a unit of Volt-Coulombs). So ratings in Power (W) (energy per second) over time are silly.

    Just rate your batteries in Joules. It’s a direct measurement for how much energy is stored. If you really need to know Watt-hours, then just diving the Joules by seconds.

    1W = 1J over 1sec.

    So 3600J battery, can supply 3600W for 1 second.
    Or 60W for 1 minute.
    Or 1 Watt for one hour (1 Watt-hour)

    To get back, just multiply Wh by 60 to get Joules.
    1 Watt-hour means 1 J/sec for 3600 seconds.

    Joules plus instantaneous current ratings for charge/discharge tell you everything you need to know in a simple form.

    • Mark 1 year ago

      Sorry, one mistake to correct:

      To get back, just multiply Wh by 3600 to get Joules.
      1 Watt-hour means 1 J/sec for 3600 seconds.

  22. Mark 1 year ago

    Real world example:

    Nominal voltage: 3.2V
    Capacity: 20Ah (64Wh)
    Weight:750g

    This is 230KJ (230,400 Joules)
    And the energy density (by mass) is: 409 J/g

    Energy density is the single most important value as it sums up how much energy you’re carrying per unit of weight, and allows you to easily compare different batteries which might be different weights.

  23. Leo Luis 1 year ago

    Thanks but no matter how much i try, i wont understand.

    I jst want to know. can I use a 3.7 850hm lipo batt in my dm007 quad? i have a few of them from another quad but the original one for the dm007 is a 7.4 400mh. Will it spoil the quad? will be enough power for the quad to lift off?

  24. Engr. Enyinda Nath Okey 1 year ago

    This tutorial makes a lot of sense. I have always imagined why, an inverter would be rated at 4kVA 24V and another rated at 4kVA 48V. It is clear in the long run, that the 48V dc inverter would produce a longer time of load sustainability than the 24V dc system, not minding that the power (kVA) ratings are same.

  25. Alex G 12 months ago

    The most important way to compare batteries is not just Wh, but $/Wh (is it worth the money).

    Just a hint: smaller power packs can get as good as $.50/Wh, while larger packs include expensive inverters (ex., offering 110V outputs) and price shoots up to like $.80/Wh – so it may seem like economy of scale is not working. Make sure you compare apples to apples.

    Also the weight of the battery is important for portable solutions – try calculating lb/Wh and you will notice vast differences between batteries. This is generally a good indication of the quality of battery technology used.

    Finally, number of recharging cyclies can be taken into consideration.

    Have fun shopping!

  26. Robert Corty 8 months ago

    Many many Smart Electronics folks Commenting! However, I see many flaws that were not nailed down one single time to my knowledge. Watt hours are a pretty horrible rate of measurement for capacity because it leaves one to wonder 1 major thing when comparing different devices of a multitude of Voltages. (Speaking in Direct Current) many gadgets operate on different voltages whether it be with different types of Cells* (AA, C,AAA (1.5valkaline-1.2vNIMH) or lithium 3.7 etc) or one of those in series to equal a multiplied Voltage (not capacity). So where many people failed… Sorry, it happens… Larry M, your 4xAA flashlight running on a high capacity NiMH AA @ 1.2 volts (he said rechargeable) likely (well positively) they are in series, which means aligned positive to negative with a open neg and pos terminal for device connection. So, your total nominal voltage is 4cells*1.2V= 4.8v and the capacity stays the same @ 2400mah. Should it have been in parallel, what you said would have been true.. I can make this assumption because of my knowledge with cells, electronics and Luminaires. So the point, when learning broad spectrum, Watt hours is silly unless you teach the person to look out for voltage, a major factor.. Watt hours given at 12V and 1.5v or 5v are totally different in every flipping way. Now one good way to use watts in general, is this.. load sizing.. if something needs 100 watts to operate properly and you need to know how many amps your supply will need to withhold given voltage drop and such… No matter what.. that something needs 100watts… So 120volts gets you 100 watts with .83 Amps or 830MA (milliamps) .. 100ft of drop cord has caused voltage drop to 110volts(safe operating range on Alternating current (AC) but now you must make sure your supply can carry the new Amp Load to still supply 100watts.. .83amps is now .91 or 910MA… Just an example as most any supply and drop cord can handle such small current/load.. So, if comparing capacity in the future.. Watt hours is great for direct current found in

  27. Mike 8 months ago

    I’m surprised this thread has been here for 2 years without anyone mentioning the big bugaboo I’m looking into. The capacity of a lead-acid battery (e.g. car) is severely affected by discharge (and charge) rates and depth of discharge. L-A batteries are good for something like 200-400 discharge cycles at 50% discharge (depending on if “deep cycle” or not and I don’t really know the number), and Li batteries more like 2000 cycles at 80% discharge and MUCH less affected by charge/discharge rate. Ah ratings on batteries are based on maintaining a nominal voltage over a 20 hour discharge. If I’m comparing capacity of (typical AGM-type) L-A to Li, what depth of discharge do I base the Li battery on? 80%?

  28. Bil 8 months ago

    I have a weak but very efficient laptop (Asus x205), and I was curious to know how it’s battery would compare on the mAh scale. According to the specs, it has a 38 Wh polymer battery. I can attest that it gets at least 10 hours on the battery. How is this possible (because does that mean it operates at 3.8 watts)? I became confused in trying to figure out both of these questions.

  29. Anonymous Commentator 7 months ago

    I was also very confused at the way they measured the total capacity energy stored in batteries vs capacitors .For instance if it is a 550 volts capacitor then it means that this capacitor can store up to 550 volts but when it comes to batteries then it is different. It seems like they are measuring the max DC output per hour than the actual total or max capacity of the power that’s been stored in the battery. For example, an AA battery has 1300 mah to 3500 mah according to wikipedia which is 1.3 volts to 3.5 volts AA battery but that does not make sense and it still does not tell how much power was been stored in an AA battery because then it is like they are saying that my clock with an AC input of 3 volts powered by one 3 volts dc AA battery would be dead in just an hour or the AA battery would go dead in just a matter of an hour since it would have all its max 3 volts capacity power withdrawn by my clock. That is crazy and it makes no sense at all. Actually, my clock with an AA battery can work for many months without going dead so I don’t understand why they said this. It’s very confusing indeed.

  30. Robert 5 months ago

    Excellent article! Very to helpful to a layman like myself when comparing different batteries rated in mAh and WH. You also helped me realize that one of the batteries I was comparing was a 2 cell instead of a 3 cell like the rest. Thank you! =)

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