# Battery calculator

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## Principle and definitions

### Capacity and energy of a battery or storage system

The capacity of a battery or accumulator is the amount of energy stored according to specific temperature, charge and discharge current value and time of charge or discharge.

Even if there is various technologies of batteries the principle of calculation of power, capacity, current and charge and disharge time (according to C-rate) is the same for any kind of battery like lithium, LiPo, Nimh or Lead accumulators.

### Configuration of batteries in series and in parallel : calculate global energy stored (capacity) according to voltage and AH value of each cell

To get the voltage of batteries in series you have to sum the voltage of each cell in the serie.

To get the current in output of several batteries in parallel you have to sum the current of each branch .

Caution : do not confuse Ah and A, Ampere (A) is the unit for current, Ampere-hour (Ah) is a unit of energy or capacity, like Wh (Watt-hour) or kWh or joules.

The global capacity in Wh is the same for 2 batteries in serie or two batteries in parallel but when we speak in Ah or mAh it could be confusing.

Example :

– 2 batteries of 1000 mAh,1.5 V in series will have a global voltage of 3V and a current of 1000 mA if they are discharged in one hour. Capacity in Ampere-hour of the system will be 1000 mAh (in a 3 V system). In Wh it will give 3V*1A = 3 Wh

– 2 batteries of 1000 mAh,1.5 V in parallel will have a global voltage of 1.5V and a current of 2000 mA if they are discharged in one hour. Capacity in Ampere-hour of the system will be 2000 mAH (in a 1.5 V system). In Wh it will give 1.5V*2A = 3 Wh

That is why it is better to speak in Wh (Watt-hour) rather than Ah (ampere hour) when you speak of capacity of a pack of batteries with elements in series and parallel, because capacity in Watt-hour is not linked to the voltage of the system whereas capacity in Ampere-hour is linked to the voltage of the pack of batteries.

### Rating capacity and C-rate

C-rate is used to scale the charge and discharge current of a battery. For a given capacity, C-rate is a measure that indicate at what current a battery is charged and discharged to reach its defined capacity.

A 1C (or C/1) charge loads a battery that is rated at, say, 1000 Ah at 1000 A during one hour, so at the end of the hour the battery reach a capacity of 1000 Ah; a 1C (or C/1) discharge drains the battery at that same rate.

A 0.5C or (C/2) charge loads a battery that is rated at, say, 1000 Ah at 500 A so it takes two hours to charge the battery at the rating capacity of 1000 Ah;

The Ah rating is normally marked on the battery.

Last example, a lead acid battery with a C10 (or C/10) rated capacity of 3000 Ah should be charge or discharge in 10 hours with a current charge or discharge of 300 A.

## Formula to calculate Current available in output of the battery system

How to calculate output current, power and energy of a battery according to C-rate?

The simplest formula is :

I = Cr * Er

or

Cr = I / Er

Where

Er = rated energy stored in Ah (rated capacity of the battery given by the manufacturer)

I = current of charge or discharge in Amperes (A)

Cr = C-rate of the battery

Equation to get the time of charge or charge or discharge “t” according to current and rated capacity is :

t = Er / I

t = time, duration of charge or discharge (runtime) in hours

Relationship between Cr and t :

Cr = 1/t

t = 1/Cr

### Why is it important to know the C-rate or C-rating of a battery

C-rate is an important data for a battery because for most of batteries the energy stored or available depends on the speed of the charge or discharge current. Generally, for a given capacity you will have less energy if you discharge in one hour than if you discharge in 20 hours, reversely you will store less energy in a battery with a current charge of 100 A during 1 h than with a current charge of 10 A during 10 h.