​Ebike Battery Math: Volts, Amps, Amp Hours, Watt Hours

December 5, 2015

These days, awesome ebike battery packs constructed of quality 18650 cells are available to average bike builders thanks to  advances in 18650 DIY pack building  methods and vendors such as Luna Cycle who have begun offering quality affordable packs to kit buyers for the first time. 

The battery pack is probably the most expensive component of your ebike, so its best you understand what you are paying for before making a big battery or ebike purchase.

But if you are a newbie, selecting a battery for your new ebike build can be an overwhelming endeavor with all these weird numbers to consider. This guide will attempt to make it easier. Consider Volts, Amps, Amp hours (Ah), and finally Watt hours (Wh) when picking your battery. This article will break them all down. With some simple math you can keep yourself from being ripped off when making a purchase from some slick snake-oil selling ebike vendor. Never have the need to ask how fast or how far it will go again. By using some simple math, you will have an accurate idea of the expected range and power expectancy of any pack.

Volume and Weight



The first one is easy one to quantify because we all have been taught volume and weight since grade school.  The girl in the picture holds a 20ah 52 volt battery pack which holds a kilowatt of energy (1000 watt hours) and weighs around 12 pounds. A pack holding that much juice 10 years ago would be made of lead acid and would be heavier than a car battery and we would need a different and much bigger girl to even lift it up.

The most precious commodity we have as ebike builders is space, and…none of us want to carry a lot of weight when we ride because we want our bike to feel like a bike and not some heavy motor bike. How large and how heavy a pack should be is one of your biggest considerations. As technology progresses, ebike packs that can take you many miles are being compressed into smaller sizes and lighter weights, so that now in 2015? even a back-pack battery can take you for a long ride. Look and feel the weight of a battery pack, and decide now what size you can put up with…because its not just the high cost of quality lithium you need to consider…size and weight are also big hurdles to care about.

So…you want your battery pack to be light and small?

You want it to be powerful?

You want it to be safe?

And you want it to be cheap?

Good luck.  Elon Musk of Tesla is building an entire “gigafactory” in the desert  of Nevada to try to establish all those things.  And if his vision is correct it will change battery performance and pricing and actually make it possible to check all the items in the above list.




At the time of this writing you would be lucky to get two of the listed battery pack characteristics, and you are definitely not going to get all 4 items on that list. Although ebike packs have gotten much more power-dense and affordable…we all agree it could get better. For now, buying a battery pack is about compromises. If you want to go far, and you want it to be powerful its gonna be a bit big and heavy. If all you want is cheap and powerful, buy a lead acid pack. If you want light and cheap, go with Hobby King LiPo’s but only if you are knowledgeable, and know the safety risks. Ebike battery buying is all about deciding how big a pack you are gonna put up with to achieve your needs.




Lets say you got an existing ebike you are trying to revamp with a new 18650-cell battery pack, or you just bought a cheap China ebike kit off eBay, and you’re looking for a battery for it…the first question you need to know is…what is the voltage of your controller and motor?

Picking the wrong voltage battery is the only thing that could do serious damage to your ebike motor and controller if you pick the wrong one. Get the voltage right and you can’t go wrong with the rest.

A 36-volt controller and motor in general requires a 36-volt pack. All controllers allow a range of voltages before they pop so it’s highly probable you could go to a 52-volt battery even though your controller is rated for 48 volts. (read article on the benefits of 52v battery) By overvolting your 48V controller and motor with a 52V battery you get a nice performance gain with a low chance of frying your controller. Upping the voltage of your battery slightly is the easiest way to get a performance gain on an existing electric bike set up. 

So once you have the voltage selected, now you have to make one of your biggest decisions…how big do you want your battery to be? How much range do you want? And remember the more range, the larger and heavier the battery.

Amp hours-


The 18650 pack above is made up of Pansonic PF cells and is the Tesla S battery pack. It is 85kWh , about 170 tiimes as large as a typical eibke pack. Today ebike builders learn from the technology Tesla is pioneering to make safe and large pack.


The Amp-hour rating is how much energy capacity is in your pack. But the true energy capacity you also need to consider voltage. For example the pack above is for a Tesla and is made up from cells from the the same Panasonic company that Luna Cycles uses. The more Amp hours, the further you will go. But that gigantic pack is only a little more than 200 Amp-hours. Does that mean its only 10x as big as a 20-Ah pack?  No. You also need to consider voltage and the above pack is 375 volts. (enough volts to fry chickens). So right here is where it gets a little tricky….you can’t compare pack energy capacity with just the Amp-hours.

Watt hours –

juiced rider

The ebike above is the Juiced Rider which is one of my favorite commercial electric bikes, because it really does have a huge battery pack. I know because I can do the Ebike math. You can buy the Juiced Rider with up to 48V / 32-Ah which is a whopping 1536 Watt hours (1.5 kWh) which (thanks to math) I know this bike could actually have a very real 100-mile range. 

However its hard to identify such a spectacular ebike without ebike math because the industry is full of gross exaggerators, and its hard to believe when someone says his ebike he is selling you will take 100 miles on a charge…but the top of the line Juiced Rider is one that really can.

One of the “gotchas” ebike sellers can get you with is to sell you on a high Amp-hour pack, but not tell you its low voltage. For example a 36 volt 10-Ah pack does not have near the range of a 52V / 10-Ah pack. To do a comparison of ranges of two different packs, they must be the same voltage, in which case all you would need is the Amp-hour rating to compare the difference. But…if the two packs are two different voltages then you must calculate Watt-hours.

Watt hours are calculated by multiplying the volts by the Amp-hours. So a 36 volt 10-Ah pack has 360 watt hours and a 52V 10-Ah pack has 520 watt hours. (read our article on calculating range)  Once you get to 1000 watt hours, its called one-kilowatt, and that’s how electric car packs are measured. Most ebike packs do not get too far over a kilowatt because now, just the pack is going to weigh over 20 pounds and you start leaving bicycle range. Once you know how to calculate watt hours you can fairly well know what you are paying for in a battery pack. Now we get to the fun part…deciding on how much power we want!


fast ebike


This is the power rating of the pack…how much power it will put out. If you multiply the amps by the volts you will get the wattage your battery is capable of. For example, a 30-amp 52 volt pack is capable of 1500 watts plus. In general you probably want to choose a higher amperage battery over a lower amp battery. You can’t burn out your controller with a high amperage battery because your low amp controller will just suck whatever amps out of it that it needs. If you get a battery  rated for low amps…your controller might not get all the amps it wants, which will just mean you will go slower so no harm is done. But if you want maximum speed and power that your set-up is capable of, you want a battery that is rated for at least as high amps as your controller is rated for. If you want to be future proof get an even higher amp-capable battery pack than what your controller is rated for, in case you upgrade the controller, or some day build (or buy) a more powerful ebike.

Tools for Measuring the above numbers

watt meter


There are several great measuring devices to keep everyone honest when it comes to getting the amp hours you paid for etc. The $30 Watt Meter is a very inexpensive way to measure amp hours in a pack and so is the $135 Cycle Analyst. These devices measure the energy as its depleting from the pack and act like a very accurate fuel guage which tells you exactly when your bike will run out of juice and then you can easily calculate how efficient you and your bike are. Why do no ebike manufacturers provide these convenient gadgets on their bike? They do not want you to have an accurate Amp-hour guage…guess why?

Charging Math



OK, so now what about charging? Are you getting a fast charger or a slow charger? How long will it take to Charge your battery? Well that’s an easy one.  You need to pick a smart charger that is compatible with  your batteries chemistry and the voltage of your battery. Charging with the wrong voltage  or wrong type of charger is a fire risk and should never be done.

If  you divide the amp hour rating of your battery by the amp rating of your charger, that is how long it will take you to fully charge your battery. However, all good lithium smart chargers dial back the charge at the end of the charge cycle, so they take a little longer than what they are rated for. So for a 10 Amp-hour battery it will take a 5-amp charger a little more than 2 hours to charge your pack. With a 1-amp charger it will take 10 hours. The larger the battery, the safer it is to charge at high amps. For example, charging at 5 amps is fast for a 10 Amp-hour battery, but…not so fast for a 20 Amp-hour battery. When you charge your battery fast, all the time it will greatly reduce your batteries life expectancy. We recommend you stick to slow charging (4 hours or more) or go with a charger that can switch between fast and slow charges like the Luna Charger.

Now, if you have a 10-Ah battery and you have a 5-amp charger…that is a super fast charger for that pack. One way you can tell is if when charging, does your pack get warm?…if it gets fairly warm, you are degrading the life of your cells, and its time to invest in a slow charger.

Ebike Math; Now You Got it

Now do the ebike math…which pack is bigger? Its all about math…not guesses on how far your pack will take you. A Sondors Ebike pack is 36 volts 9-Ah, so it contains 324 watt hours and based on that, you can guess how far the pack is going to take you. If you ask Sondors how far his pack will take you he has to exaggerate his mileage number because that is how the ebike industry has been doing it for years and its hard to compete with a bunch of exaggerators by suddenly being honest. Its a dumb question to ask an ebike salesman how far his bike will go…if you ask a dumb question expect an exaggerated dumb answer. 

So once you have all these numbers down you have the basic knowledge on how to compare packs based on real numbers…and you will never again ask “how far will it go” or “how fast will it go” because you will have math to back you up…and know exactly what you are paying for when buying an ebike (or ebike battery).



End of Story

I will give you one great example to end this story of how ebike math could possibly save you big bucks. Recently, one of my Luna Cycle customers went into a Arizona dealers shop with two of my 52V 20-Ah triangle packs. Happy with the amazing deal he got on the Luna pack ($700 each for over 1000 watt hours). He was doing good, but his mistake was going into this gigantic dealers shop with super inflated snake oil pricing, thinking he could get a cheap battery install. The dealer convinced him that the 52 volts might burn out his “E-rad Bafang” so the warranty would not be covered…not true! the Bafang BBS02 (it’s proper name) is rated to handle safely a 52 volt battery. 

So the dealer sells him on a “E-Rad”48V 10-Ah pack inside of a sexy dolphin case with a price tag of $1000 that will give him “50 miles plus” range. The dealer convinces him that the 1000 watt hour  Luna Cycle battery is big and bulky and will give him half  the range of the dealer’s $1000 400 watt hour pack. The customer eats a high hazmat charge to ship two perfectly good Luna Cycle packs back to Luna Cycle…Luna Cycle accepts the return, thinking karma will pay at the end…obviously this is different than typical ebike exaggerating…this is an example of a dealer lying to a customer. No ebike sales man could  honeslty argue his half sized pack will get double the range of a full sized real pack. 

So, if this customer knew ebike math he would have no problem calculating that he was being bamboozled. There is no way a 400 watt hour battery is going to double the range of a  1000 watt hour  battery no matter what snake oil it is filled with. And if the customer believed that Luna was making up its amp hour rating he could easily get a watt meter and test the battery himself and know which dealer is BS-ing and which one is the real deal…

Luna Cycle decided to one up the dealer….and  now has the same sexy  slim dolphin cased battery with better cells that dealer sold for $1000 at less than half the price ($420) and the Luna pack stacks 648 watt hours into the same case because we  use better and more power-dense cells. (Panasonic NCR-B). We  also one-upped the dealer by re-designing the pack to fit more cells, and more watt hours, and offering a 52V 13.5-Ah version which has over 700 watt hours. 



Luna Cycles "Shark" Pack

Luna Cycles “Shark” Pack


But no matter how sexy that ebike battery looks (actually it kind of looks like a dildo) Never judge a battery pack  by the cover…use math to figure out watt hours and even figure out how much each battery cost per watt hour. Use testing equipment to verify you got the battery you paid for.

But its not just about Math and raw numbers. Next comes Chemistry. Quality power-dense cells like the Panasonic NCR-B or high amperage cells like the Samsung 25R  have the bleeding edge chemistry and can be twice as expensive as other Samsung or Panasonic cells. Chinese cells are super cheap, but ineffective because they haven’t figured out yet how to make decent chemistry.  

But, to get that amazing energy density which is watt hours to size and weight….you are going to need to pay for top quality name-brand cells using the best chemistry. 

But 18650 chemistry is a different story for a different day.


Written by Eric, December 2015

Eric has been involved in the electric bike industry since 2002 when he started a 6000 square foot brick and mortar Electric Bike store in downtown San Francisco. He is a true believer that small electric vehicles can change the way we operate and the way we think.


  1. U friggin ROK!! Always breakin it down for us, so we understand what we are saying to our guests and customers!!! Thanku, thanku!!

  2. Perfect timing!!! My A2B batteries are toast. I want this 52v battery and controller!

  3. I had the same experience as the poor slob in your article who returned the two batteries. The guy from Arizona E-bike superstore bragged about how superior his mid-drive was to the competitors’ and how using a battery from em3ev would void the warranty. Luckily, I could feel the slime coming over the phone and decided then and there never to buy anything from that source.

  4. I’ve got a VoltOn bike I bought largely due to recommendations from this site. It was a good purchase and I’ve enjoyed the bike for just over a year now. So first off, thanks!
    Now that I’ve got myself into shape I’d like to be able to take longer rides and have considered buying a second battery to carry with me so I could swap them out after the first one is discharged. But I wonder if it is possible to buy a triangular pack that could plug in to the charge port on the bike and add to the distance I can travel without having to switch out the battery from the locked enclosure on the bike. Is that something Luna can do?

  5. My battery is about 6 years old, and has outlived 2 motors, a frame, cycle analyst 1, and 3 throttles. I’ve actually built a much stronger bike around this 48v 13ah battery, and now I need a much bigger battery to utilize, well honestly to find out of I was successful in the build, it’s been ready for 72v for a year now. …but I can’t afford the $2,000 for a plug and go battery… so hopefully I can make sense of all thism…lmao

  6. Hi,
    I purchased a Shark Pack. 36V 13Wh. Battery has Pos(+) and Neg(-) wires. I want to replace a yamaha battery but I find the Yamaha one has 3 wires. Do you know what is the third one? Pos, Neg and ?¿

  7. Maybe it would be smarter to just get in better shape so you extend YOUR range. You’ll have to eat better, sleep well, rest your muscles well, but the end result is you’ll feel a lot better, look a lot better, age a lot slower and live a lot longer. Ebikes now are geared towards out of shape people. Look at the upright styles of most of them. Looks like they are designed for senior citizens with stiff backs. They should focus on aerodynamics for fit people so instead of riding 10 miles to work each day, with electric motor supplementation, they can now go 20 miles. Either way they are pedaling hard. What about recumbent ebikes? Efficiency cannot be attained without careful consideration of weight and aerodynamics. And the faster you go the more crucial aerodynamics becomes. Think of how it feels riding when you have a wind behind you. You would feel like that a lot more if the aerodynamic factor of your body and bike was better. Your legs are not so much of the problem. Its your upper body that is like a flat wall pushing into the wind.

    • lol you are a racist cunt, and i hope you get syphilis, and all your offspring as well. Go fuck yourself and eat some shit you fucking goof.

    • You’re making a fool of yourself. Not everyone is as able as everyone else. Extenuating circumstances could include things such as age, natural physical ability, prior injuries sustained, weight, maybe even something simple like number of prior wars you have attended. Any and all of these could drastically effect riding distance. Stop worrying why people want something that you are too narrow minded to even be able to contemplate why. Upright stance on a bike is meant to make longer rides more comfortable. Google “Tour” bikes and keep your mouth shut until you have anything worthwhile.

      • Wow, what a nice attitude. Brian, you completely missed the gist of my post. I was referring to the vast majority of ebike users that I see all the time. The reason most get one is just because they are NOT in very good shape because they don’t push themselves physically. And I notice you didn’t comment on the points I made about aerodynamics….function over convenience. Of course there are circumstances that warrant modification of these parameters but its vital for any good design to pursue function first, convenience second. Make it work for the vast majority of people then alloy for flexibility to adapt to others. I believe those are precepts of good design.

        • 20 miles is not a great distance to ride period, your confusing the reason for having an electrically assisted or powered bike which in most cases is multi-factorial. I don’t want to turn up to work invigorated by a 10 mile bike ride (read hot and sweaty) I want to get there fresh and not have the stress of driving a car on already congested roads. I often ride century’s and do time trials and see the benefit of aerodynamics on both bikes, but never have I been on a group ride or an iron man where someone is touting the benefits of having an electric motor attached to their bikes. You have assisted or electric bikes for a totally different reason and if you are bragging about having the ability to ride 20 miles with power assist you are not understanding the concept. I can ride 100 miles comfortably and get off and run a Marathon, but I still put my ‘out of shape’, ‘not pushed physically’ body on an bike with no focus on aerodynamics and I love it, because I understand the difference people have for buying these types of bike, you however have yet to grow up and see the world as it is.

  8. Loved your article, your information is accurate and spot-on (unlike many of the articles I’ve read…) You even go so far as to specify batttery chemistry and the exact cell! ($5.75 per cell for sanyo’s 3500mah 10A 18650GA is the bleeding edge for longevity liion cells, a small upgrade to those venerable 18650B’s 😉 )

    Just wanted to inform you if you weren’t already aware, the teslas gigafactory will be churning out 20700 batteries, supposedly with a new chemistry that puts 4 AH in a normal 18650 😀

  9. “[…] 375 volts. (enough volts to fry chickens).” — uhm… This statement kind of makes you want to avoid reading this article… The current fries “chickens”, not voltage. Electroshockers that meant to “scare off” burglars may give ~1500 V. E.g., ~100 mA may stop your hart from beating, while 1 A may/will fry you. Though I can’t say how voltage affects current in this aspect: after all, small AA batteries can have ~2500 mA/~2.5 A.

    • so if i go grab both terminal of a 12v battery capable of pushing out in excess of 1000 amps, i’ll die?

      …no, i won’t, i won’t even feel a tingle. Both voltage and current are important factors, if you don’t have enough voltage, you won’t push enough amps.

      This is a sort of trend where people think they know the truth, and technically, it’s true, it’s not the volts but the amperage that can kill, but it’s not the whole truth.

      • Thanks for the info! I guess now I know why AA batteries do not kill people even though they have such a huge amperage. But can you provide link to some book/site where all this gets explained?

      • Amperage depends on the resistance of your load, they are inversely proportional. A 10 billion volt battery won’t put out a single amp until you put a load with a low enough resistance on it. Dry skin has an resistance of roughly 500,000 ohms or more, while wet skin can have as little as 150 ohms. If you touch a 12v with dry skin you’ll get a nice shock little of around 24 microamps, but if you touch it with wet skin you’ll be immediately shocked with 80 millivolts… some three orders of magnitude larger than with dry skin, and enough to cause muscle convulsions and possibly heart failure. Know your ohms law. It’s neither the volts nor the amps that kill, but both working together against the resistance that is you. (And 12v batteries can realistically only put out about an amp, just sayin’).

  10. You explain Ohm’s law well enough but didn’t stress “usable” battery storage. With a one kilowatt battery you lose 40% of it’s storage if you are trying to treat it well and get the most charges. I am using a 50V, 24.25ah battery that can store 1212.5 watt hours or 1.2kWh. Using battery management techniques means not fully charging the battery and also not fully discharging. Charging to only 80% and leaving 20% in the battery when finished, means I get 727.5 watt hours of usable storage out of a 1.2 kilowatt battery. Start with a 50V, 10 ah battery and your 500 watt hour battery gets small Fast when you subtract the 40% capacity for battery management. Common sense comes into play also but some readers like to latch onto some inane point like an inbred rottweiler, so let me also point out that 20 plus pounds of battery is not something you want on your back. Only people that want to Zooommmm around at high speeds or sit in the saddle for 5 or 6 hours at normal riding speeds need a battery over 1 kw but you do need to take into account battery management techniques or accept minimum battery life as the standard.

  11. Can anyone please tell me what happens if we connect 48v 20amph controller to a 48v 36amph battery.will the controller burn out or not?

    • First of all, controllers are measured in amps, not amp-hours. Amps measure power, while amp-hours measure capacity (actually Watts and watt-hours measure power and capacity, but those are simply amps*volts (or amp-hours*volts), or amps*48 in this case).

      The controller will not burn out as it will only ever draw up to 20 amps from the battery. The Battery doesn’t “push” amps into the controller, the controller “pulls” amps from the battery. The larger battery will simply be able to run for a longer time.

  12. You didn’t give the formula to calculate pack amps… I get how to calc AH, watt hours, volts and so on.. I wish someone would actually just show all the formulas in one place. I’ve gotten a lot of formulas that have helped me but I had to search all over the internet,

  13. Hi there I would like to know the price of Ebike battery math?

  14. good article but do you think you could keep the childish sexual remarks to yourself it does not look anything like a dildo and were is your mind for thinking it does clean up your act children read this stuff too dude now i have to explain to my 8 year old what a fricin dildo is thanks alot dude

  15. The battery thing drives me crazy. I have a 48V that uses 4 SLA 18ah batteries with a one year guarantee. They barley last 6 months. I want to go to a Lithium LiPro 48Volt 30ah battery. Can I do this on a 500 w hub motor. If not what is your best recommendation.



  16. Sorry I forgot to say it is a scooter

    Mark D

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