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

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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. 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 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 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 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 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