# Calculation of battery capacity, c-rate, charge and discharge current

## Calculator

Enter your own values in the white boxes, results are displayed in the green boxes.

Voltage of one battery = V
Rated capacity of one battery : Ah    =    Wh
C-rate :      or    Charge or discharge current I : A
Time of charge or discharge t (run-time) = h
Time of charge or discharge in minutes (run-time) = min

### Calculation of energy stored, current and voltage for a set of batteries in series and parallel

Number of batteries in a serie = elements
Number of series in parallel = series
Voltage of the storage system = volt
Current of the storage system = ampere
Capacity of the storage system (energy stored) = Ah    =    kWh

## Principle and definitions

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

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

### 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;
A 2C charge loads a battery that is rated at, say, 1000 Ah at 2000 A, so it takes theoretically 30 minutes 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 batterie with a C10 (or C/10) rated capacity of 3000 Ah should be charge or disharge in 10 hours with a current charge or discharge of 300 A.

### 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.

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

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