What is Lithium Battery C-rate and How to Calculate it?
The C rate is particularly important when the battery is used as the energy carrier of electric tools, especially electric vehicles. C rate can determine battery operation time. If you omit this key point when you are choosing a battery, your will get a poor experience.
There are 10 hours to be full charged
Vihicle battery is out of power
Climbing a steep hill the car is going to slide down
Obviously, we don’t want to see these scenes above. Batteries with low C-rate makes the charging take a long time. While high C-rate can immediately provide a large current in order to give a great traction power for your device. However, battery with high C-rate can not provide power for a very long time like Low C-rate does. In addition, batteries with high C-rate discharge fierce have possibility to cause batteries to be aging soon and even cause security questions. Thus, it is necessary for you to have a clear look about lithium battery C-rate.
1.What is lithium battery C-rate?
A C-rate is in order to show the discharge rate of a battery relative to battery’s maximum capacity. When describing batteries, discharge current is often expressed as a C-rate in order to normalized against battery capacity. C-rate is often very different between batteries because of different electrolyte, different ions conductivity and battery internal resistance and etc.
2.Function of C-rate
The charge and discharge rate of lithium batteries determines how fast a certain amount of energy can be stored in the battery, or how fast the energy can be released from the battery.
3.Limitations of Lithium Battery C-rate
However, in many occasions, we need a high C-rate battery. Nowadays, lithium battery is widely used in various fields because of its excellent advantages. In order to achieve better development of lithium-ion batteries, we need to understand what factors are limiting the battery’s rate performance. We mainly start from following aspects.
3.1 The lithium ion diffusion ability of anode and cathode will limit C-rate
The speed of disembedding and embedding of lithium ions in the positive or negative active material, in other words, the rate of lithium ions running out of the positive or negative active material, which is an important factor affecting the charge and discharge rate.
Every marathon game, there are many players participate. For the road width is limited, its probable to cause mutual crowded and prolong running team although all athletes start at the same time. Because the team finally become a super long front. Some reach the finish line quickly, some arrive a few hours late, some pass out and stop eating halfway through.
The diffusion and movement of lithium ions in the positive and negative poles is basically similar to marathon athletes. They have their own running route which seriously restrict the finish time of the game. Therefore, it is better for athletes to run 100 meters, the distance is short enough, everyone can quickly reach the finish line. In addition, the track should be wide and straight enough. In this way, thousands of ions rush together to the finish line, the game ended quickly. Then we get excellent performance of C-rate.
As for the positive material, the thickness of the active material should be small to improve the compaction density of the positive material, which is equivalent to shortening the distance of the race. In the active substance, there should be enough pore clearance to set aside channels for lithium ions to compete. At the same time, we should optimize the structure of the cathode material and change the distance and structure between particles to achieve uniform distribution. Although increasing the compaction density and increasing the particle gap are contradictory, a balance needs to be found to achieve the optimal lithium ion migration rate.
The idea of the anode material is similar to positive material. It mainly starts from the structure, size, thickness and other aspects of the material to reduce the concentration difference of lithium ion in the anode material and improve the diffusion ability of lithium ion in the anode material.
3.2 Ionic conductivity of electrolyte
Lithium ions play a race in anode/anode materials, but the race in electrolytes is swimming.
Lithium ions bounce back and forth between the anode and the cathode, swimming in a “swimming pool” of electrolytes and battery shells. The ionic conductivity of the electrolyte, like the resistance of water, has a great influence on the speed at which lithium ions swim. At present, organic electrolytes used in lithium ion batteries, no matter liquid electrolyte or solid electrolyte, have low ionic conductivity. The resistance of electrolyte becomes an important part of the battery resistance, and its influence on the high rate performance of lithium ion battery cannot be ignored.
In addition, we should focus on chemical and thermal stability of electrolytes. If the chemical stability of the electrolyte is not good, it is easy to oxidize and decompose on the surface of the cathode material, affecting the ionic conductivity of the electrolyte. The thermal stability of electrolyte has a great impact on the safety and cycle life of lithium ion battery, because a lot of gases will be generated when the electrolyte is decomposed by heat. On the one hand, it is a hidden danger to the battery safety, and on the other hand, some gases will destroy the SEI film on the negative electrode surface, affecting its cycle performance.
3.3 Internal resistance of the battery
Different materials and different shapes of conductive agents will affect the internal resistance of batteries. This affects battery magnification.
The wetting degree of electrolyte and anode materials will affect the contact resistance at the interface between electrolyte and electrode, thus affecting the rate performance of the battery. The total amount of electrolyte, viscosity, impurity content and porosity of anode and cathode materials will change the contact impedance between electrolyte and electrode, which is an important research direction to improve the rate performance.
4.How to Calculate C-rate of a Lithium Battery
Formula : “Cr=I/E”
Cr：C rate
I: It is the current of charge/discharge (Amps)
E: It is the rated energy of the battery (Ah) (amp hours)
Step 1:determine the rated energy storage of the battery.
In this problem the rated energy is found to be 200 Ah → E=200 Ah
Step 2: determine the current of charge or discharge.
This is found to be 50 amps → I=50 Amps
Step 3: Calculate it directly
Cr=I/E=50Amps/200Ah=0.25 C
So we get its C rate is 0.25 C.
It is easy to calculate as you turn your hands over. Right ?
A C-rate of 1C is also known as a one-hour discharge. A battery’s C rating is defined by the rate of time in which it takes to charge or discharge. You can increase or decrease the C rate and as a result this will affect the time it takes the battery to charge or discharge. The C rate charge or discharge time changes in relation to the rating. For example, 1C is equal to 60 minutes.
Here is a simple formula to calculate time.
Formula: “T=1/Cr”
T: charging or discharging time (hours)
Cr: C rate
Examples: just take mentioned example above as our example, according to “Cr=I/E”, we calculate “50amps,200ah” and get 0.25C. Then we convert it.
T=1/0.25=4 Hours
It means that it takes 4 hours to charge or discharge the battery with 200ah and in the current of 50amps. It is OK to convert into minutes. 4hours =240mins
According to this formula ”T=1/Cr”, we know that this formula just tell us the accurate time and the result is unrelated to “E”and “I”. It helps us to understand C rate easier.
Combine two formulas above, can help us understand C rate.
Compare differences when the same 18650 3000mah battery has different C rate
0.5 C rate 2 C rate 10 C rate
3000mah=3Ah 3000mah=3Ah 3000mah=3Ah
0.5C*3A=1.5A 2C*3A=6A 10C*3A=1.5A
1/0.5C=2 Hours 1/2C=0.5 Hours 1/10C=0.1 Hours
60*1/0.5C=120mins 60*1/20.5C=30mins 60*1/10C=6mins
Here is a chart about the C rate and the time with several data. It is easy for you to understand this formula.
| C rate | Time |
|---|---|
| 0.05 C | 20 hours |
| 0.1C | 10hours |
| 0.2C | 5hours |
| 0.5C | 2hours |
| 1C | 1hour |
| 2C | 30mins |
| 5C | 12mins |
| 10C | 6mins |
| 20C | 3mins |
| 120C | 30seconds |
That’s all about lithium battery C-rate and how to calculate it. Now, are you clear about how to calculate it? If you are interested in batteries or if you have any doubts on lithium batteries, you can leave a message about your doubts.
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From your explanation the following : “Cr=I/E=50Amps/200Ah=0.25 C So we get its C rate is 0.5 C. It is easy to calculate as you turn your hands over. Right ?..”
Is the C rate not 0.25 C 1/200 = 0.25 C ?
The calculation you make is 0.5C but it indicate as 0.5C (“so we get its C rate is 0.5C….”)
So charge time is 2 hours and should be 4 hours then
Or do i have it wrong ?
Yes，you are correct, already correct the page error