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Battery C Rating-Formula and Equation

# Battery C Rating-Formula and Equation

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Battery C Rating Explained

Battery c rating refers to the measure of the rate at which a battery charges and discharges. So the capacity of a battery is labeled and rated at the 1C current rate. This means a fully charged 10Ah battery provides 10 Amperes at a constant rate for a period of one hour. The same battery being discharged at 0.5C provides 10 Amps within 2 hours. Below is a chart showing the battery C rating.

Manufacturers usually rate lead acid batteries and alkaline batteries at a small 0.05c or a 20-hour discharge in order to obtain a good capacity reading. However, the batteries end up being overrated still because lead acid rarely attains a 100% capacity.

Battery C Rating Formula

The charging rate in Amps refers to the amount of charge added to the battery per a given unit time. The charging/discharge rates may be specified directly by giving the current. For example, a battery may be charged or discharged at 10 A. However, the charging/discharging rate is commonly specified by determining the total time taken for the battery to fully discharge. For such cases, the rate of discharge is therefore given by dividing the battery capacity (in Ah) by the total time taken for the battery to fully discharge/charge. For instance, for a battery with a capacity of 1000 Ah that discharges to its cut-off voltage in 20 hours, the discharge rate will be 1000 Ah/20 h = 50 A. Therefore, if the battery is a 24V battery, then the total power output will be  25A x 24 V = 600W.

NB; It is almost impossible to fully discharge a practical battery as this will reduce its lifetime or damage the battery. Thus the assumption that the battery is fully discharged is only theoretical.

The formulae is simple

t = Time

Cr = C Rate

t = 1/Cr

t = 60 minutes / Cr

0.5C Rate Example

2400mAh Battery

2400mAh / 1000 = 2.4A

0.5C x 2.4A = 1.2A available

1 / 0.5C = 2 hours

60 / 0.5C = minutes

2C Rate Example

2300mAh Battery

2300mAh / 1000 =2.3A

2C x 2.3A = 4.6A available

1 / 2C = 0.5 hours

60 / 2C = 30 minutes

30C Rate Example

2300mAh Battery

2300mAh 1000 = 2.3A

30C x 2.3A = 69A available

60 / 30C =2 minutes

The formulas below are useful to calculate the power, output current, energy and power of a battery using it’s C-rating as a basis.

Er = Rated energy (Ah)

Cr = C Rate

I = Current used to discharge or charge (Amperes)

I =CR x Er

Cr = I / Er

1.1. How To Find C Rating of Battery

Smaller batteries are mostly rated at the 1C rating, which is also referred to as the one-hour rate. For instance, take a battery with a capacity of 5000mAh, using a one-hour rate, then its 1C rating is 5000mAh. You can find the C rate of a battery on the battery data sheet and its label.

Battery C Rating Equation

How to Calculate the C rating of a Battery

A battery’s C rating is the rate of time which it takes to charge fully or discharge. You can increase or decrease the C ratitng, and this will therefore affect the time taken to discharge or charge the battery. 1C is equivalent to 60 minutes, 2C is equivalent to 30 minutes, and 0.5C is equal to 120 minutes.

Batteries have different capacities depending on which C rate you use. A 200Ah battery has different capacities at C/100 and at C/20. C-rates which are also called hourly rates, are based on the length of time of discharge. A rate of C/100 means that the capacity of the battery is determined by basing the calculation of the time taken to discharge it completely to be 100 hours. Meaning if you have a 1000 amp-hour battery bank, charging or discharging at 50 amps would be a C/20 rate (1000Ah divided by 50 A = 20 hours).

If you know the Peukert’s exponent, then you can easily calculate the battery’s capacity at any c  rating

Who is Peukert?  Peukert was a German scientist that first determined the formula that relates discharge rate and capacity of a battery, which manufacturers tend to omit from the specification sheets. The following is the capacity information of a C-Rate battery;

It = C x [C / (I x H)] k – 1; where

H = rated discharge time in hours

C = rated capacity at that specific discharge rate

I = actual discharge current in amps

K = Peukert exponent

It =  capacity usable at the discharge rate “I.”

You can calculate Peukert’s exponent for a battery even when the manufacturer provides you with two different discharge rates capacity ratings. Using a system that monitors a battery and logs data to a spreadsheet, the possibility to determine the C-rate at any instant. The strange thing is that your usable battery bank capacity is continuously changing. Consider a 48 V battery bank of 1,000 Ah in a system that is designed to provide 10 kWh equal backup energy per day. That 10 kWh of backup 208 Ah. This divided by 24 equals 8.7 A. Large loads used during those 24 hours increase the Peukert effects and thus reduce the usable capacity of the battery. However, this example is figured with no solar input since, on a sunny day, the C-rate of discharge will be even slower. On the contrary, folks working with electric vehicles must pay closer attention to Peukert’s law because a typical EV’s battery bank has a much lower capacity than one in a typical solar home because both battery bulk and weight have to be minimized as much as possible in automobiles.