The capacity of a battery (or capacitor) is the amount of energy stored according to specific temperature, charge and discharge current value and time of charge or discharge. Let's look at some of the terminology and formulas used to give attributes to battery banks.
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.
Charging at a 1C rate, loads a battery that is rated at say – 1000Ah at 1000-Amps during one hour. To break that down; at the end of 1 hour at a 1C charge rate, the battery will have reached it's capacity of 1000 Ah. Therefor a 1C discharge rate will drain the battery at the same rate of discharge, so after 1 hour the battery would be dead and ready for a recharge.
Charging at a 0.5C rate, would charge that same battery that we said was rated at 1000Ah at 500-Amps so it will now take two hours to charge the battery at the rating capacity of 1000 Ah and so on.
Charging at a 2C rate will charge the 1000 Ah battery at 2000-Amps, so theoretically, the battery would charge in 30 minutes.
Further Example: a battery with a 10C rated capacity of 3000 Ah should charge or discharge in 10 hours with a current charge or discharge rate of 300-Amps.
C-rate is an important data point to understand because for most 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. Rapid discharge of a battery typically interferes with the efficiency of the battery to deliver power. There are ways to counter act this effect. For example in a Tesla Model S the designers engineered a complex cooling system to bleed off heat from the battery during rapid discharge events (like accelerating onto the freeway). By keeping the battery cooler, they are able to increase the battery bank efficiency during high output events. The same principals apply to large amperage loads applied to the battery bank, such as during a Fast Charge. The battery bank will store less energy current charge of 100-Amps during 1 hour period than with a current charge of 10-Amps over a 10 hour period. So we'd naturally thing that an over night trickle charge is better than setting out with a low battery and finding a fast charge point. But engineering again has worked to remedy the inefficiency that is introduced into the battery system, again by providing cooling to the battery bank during high amperage charging.
So how do you calculate output current, power and energy availability of a battery according to the C-rate? The simplest formula is :
I = Cr * Er
Cr = I / Er
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:
Er / I
t= time, duration of charge or discharge (runtime) in hours
Relationship between Cr and t :
1 / t
1 / Cr
Say we have a battery that has a 4S rating
S relates to how many cells are in series to create the total module voltage.
Our 4S battery differs from 2S (2 cells in series) or 3S (3 cells in series). Our hypothetical 4S battery has four cells hooked together from each of the individual cells positive & negative terminals. The first ( - ) and the last ( + ) are the terminals of our a battery module. The terminals in-between are interconnected to make up the series.