## 18650 Lithium Battery Calculator

D.I.Y. guys want a fast calculator to help on their custom 18650 battery design, however, since things are complicated with different voltage and capacity of each cell, we think those of you who are designing the battery packs should know some basics of lithium 18650 battery design.

18650 Battery packs achieve the desired operating voltage（ie: Total Battery Pack Voltage） by connecting several 18650 cells in series( S in short ); each 18650 cell adds its voltage. Parallel( P in short) connection attains higher capacity by adding up the total ampere-hour (Ah) to help you further understand how it works, pls read the  explanation below:

#1 For a series connection, batteries with almost the same voltage and capacity are connected to raise the voltage of the final battery packs. The positive terminal of the first battery is connected to the negative terminal of a second battery and so on until the desired voltage is reached. The final voltage is the amount of all the battery voltages added together while the final capacity(Ah) remains unchanged.

#2 As for the parallel connection, batteries with almost the same voltages and capacities are connected together to increase the capacity of the overall battery pack. The positive terminals of all batteries are connected together, or to a common conductor, and all the  negative terminals are connected in the same way. The final voltage remains unchanged whilst the capacity of the assembly is the sum of all the individual cells together for the parallel design.

Let’s use a Lithium-Ion 18650 3.7V 2.6Ah( 2600mAh) for example.

1S1P 18650 pack that’s 3.7V 2.6Ah battery pack

2S1P 18650 pack that’s 7.4V 2.6Ah battery pack

1S2P 18650 pack that’s 3.7V 5.2Ah battery pack

2S2P 18650 pack that’s 7.4V 5.2Ah battery pack

Many 18650 battery packs may consist of a combination of series(S) and parallel(P) connections.

For Laptop batteries with 11.1V 4.8Ah battery pack, it commonly has three 3.7V 18650 battery cells in series (3S) to achieve a nominal 11.1 V and two in parallel(2P) to boost the capacity from 2.4Ah to 4.8Ah. As you can see it will be a configuration called 3S2P, meaning three cells in Series and two in Parallel.

When size limitations are considered, there is much more we need to consider, see below battery examples.

Stop here and check if you can figure them out, because here are the answers:

Simple?

Now let’s calculate another 11.1V 100Ah 18650 battery pack, let’s see how many cells would be needed: 11.1V/3.7V=3, so that’s 3S 100Ah/2.6Ah=38.5 so we can use 38P(98.8Ah) or 39P(101.4Ah)

Most guys will use 3S38P so that’s 114 cells in total(3*38=114)

How are we going so far???

What If we drop the mAh rating from 2.6Ah to 2.2Ah(which is more common for 18650 type batteries), I now need 135 cells in total with 3S45P configuration to get the same total capacity of 11.1V 100Ah(actual capacity is 11.1V 99Ah).

The math:11.1V/3.7V=3 100Ah/2.2Ah=45.5

What if we use Lifepo4 18650 cells(which are rated 3.2V 1.5Ah)? we would need 264 cells in total with 4S66P configuration to get the same total capacity of 11.1V 100Ah(actual capacity is 12.8V 99Ah).

The Math: 11.1V/3.2V=3.5 people normally use 4S to boost voltage,

100Ah/1.5Ah=66.6

What will happen if Watt/Hour(Wh in short) are involved?

If you have, for example, 2Ah lithium ion 18650 cells then each of those stores 7.4Wh (3.7V*2Ah=7.4Wh) of energy and you need 136 of them (1000/7.4 ~ 136) for a 1kWh battery. 136 in parallel will give you a 1kWh battery at a nominal voltage of 3.7V.

If you want higher voltage, and you probably will, you have to put them in series. 7s is a typical minimum for a Home UPS battery. 136 cells can’t be evenly distributed over 7 packs in series, you then need 140 cells for a 7s20p setup.

All the above are examples, there are plenty of other possibilities. It’s almost impossible to put this into an automatic calculator which provides meaningful results because almost all of this depends on variables the calculator doesn’t know or that they have to be put in, in the first place. It is easier to calculate this yourself.

## Ebike Battery Pack Calculator

The ebike battery pack calculator is fairly simple, using the following Fomula:

Battery Capacity Required (Wh) = Power Demand per distance traveled (Wh / mile or km) x Typical Distance Traveled (miles or km)

Calculation of the ebike battery is quite complex as the motor output is changing all the time, ie related watt-hour demand (Wh / mile or km) of the motor is changing all the time, to list a few factors below:

A Light Driver VS heavy player
B Flat Terrain VS Hilly Terrain
C Continuous Riding VS Frequent Start (Start consumes more power)
D Summer VS Winter

To help simplify your calculation, below is our table for your general reference

Constant Riding, 9-12 Wh/km (14-20 Wh/mile)
Frequent Start, 14-20 Wh/km (22-33 Wh/mile)

Let’s use an actul example to explain

For a 48V ebike that we want a minimum of 30 km riding range.
that’s 10 wh/km* 30km=300wh (it ranges from 9-12wh/km, we use 10wh/km as example)