Amp hours to Watt hours- Conversion of Ah and Wh
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Amp hours to Watt hours- Conversion of Ah and Wh
Amp hours is a common unit of measurement in energy storage, UPS, solar energy and other fields to measure the capacity of batteries. Watt hours is also a common unit of measurement to measure power. In fact, there is a conversion relationship between the two. In many scenarios, the battery capacity comparison requires the conversion of Ah units to Wh. This article attempts to explain the concept of Ah and Amp hours to Wtt hours conversion.
Understand Amp-hours (Ah)
To understand Amp-hours to Watt hours, we first need to understand the definition of Amp-hours. I suggest that you do not use an overly academic approach to understand the definition of Ah, because understanding this definition is only to better serve our daily work. I suggest using some common daily examples to help better understand it. Here is an example:
The above is an example from daily life. We have a water tank containing 5L of water. One day we want to install a hose on it, and the water flor rate of this hose is 1L/hour. Then it can be expected that after 5 hours, there will be no water in the water tank. The water tank is essentially similar to a battery. It stores water for external use. If the water is released at a certain rate for a certain period of time, the water in the tank will be exhausted.
Now imagine the water tank as our battery, which has 5Ah (Amp-hours) of electricity. Then we have a machine that runs at a current of 1A. Is the power consumption of this machine similar to the process of draining water from the water tank hose? A battery capacity of 5Ah means that it can support a load with a current of 1A for 5 hours. Please note that the premise here is that the voltage of the machine is the same as the voltage of the battery. This detail will be introduced in the subsequent Watt-hours section:
Let’s express it as a formula:
Battery Capacity(In Ah) = Current(A)*Time(hour)
Based on this formula, let’s look at the example in the figure above. If we have a load that runs at a current of 1A, and our battery is 5Ah, what will happen after running for 5 hours? Obviously, the load consumed 5Ah of battery power in 5 hours, and the battery will be fully discharged.
Battery Capacity Used = Current(A)*Time(hour)
= 1A*5hours
= 5Ah
Battery Capacity Left in Battery = Battery Capacity Initial – Battery Capacity Used
= 5Ah – 5Ah
= 0Ah
Amp-hours Real Case
The picture above is a typical VRLA battery, the voltage of this battery is generally 12V. We can see from its datasheet that its battery voltage is 12V, and its battery capacity in Amp-hours is 50Ah.
Suppose we use this battery and a 12V 1A LED light to form a basic circuit, how long can this battery power the LED light?
We have already got the following formula in the previous chapter, so we only need to change it to calculate how long this battery can power the LED light.
Battery Capacity(In Ah) = Current(A)*Time(hour)
Time(Hour) = Battery Capacity(In Ah)/Current(A)
= 50Ah/1A
= 50hours
Therefore we can calculate that this battery can power the LED light for 50 hours.
What if we use a more powerful LED light? We can also use the formula to calculate:
Time(Hour) = Battery Capacity(In Ah)/Current(A)
= 50Ah/2.5A
= 20hours
Ah to Ah Conversion
After the previous example, we have understood the meaning of Amp-hours. But please note that all the previous calculations and explanations have a premise, that is, the voltage of the battery and the voltage of the load are the same, so we can calculate in this way. But if the voltages of the two are different, then we need to use Watt-hours to compare. This involves Amp hours to Watt hours Conversion.
As shown in the figure above, we have a 12V50Ah battery and a 24V1A LED light. Because the voltage of the LED light is different from the battery voltage, we cannot use the battery to drive the LED light directly. We need to add a DC12V to DC24V converter. So how do we calculate how long the battery can drive the LED light?
First of all, please note that the formula we described above: Battery Capacity (In Ah) = Current (A) * Time (hour) has a premise that the voltage of the load and the voltage of the battery are the same. But in our current example, the voltage of the load power supply and the battery are different. At this time, we can’t use this formula directly to calculate, we need to use Ah to Wh conversion.
First of all, we need to understand that there is a premise when using Ah as a unit to measure battery capacity. For example, if we have a battery A with a capacity of 12V50Ah and another battery B with a capacity of 12V25Ah, then we think that the capacity of battery A is twice that of battery B. The premise here is that their voltages are the same. For example, when we calculate the power supply of a 12V1A LED light with a 12V50Ah battery as follows:
Time(Hour) = Battery Capacity(In Ah)/Current(A)
= 50Ah/1A
= 50hours
The voltage used by the LED lamp here is the same as the battery voltage, both are 12V, so we can calculate this way.
At the time, when the load voltage is different from the battery voltage, we cannot calculate this way. We need to convert Ah to Wh. Wh is the true benchmark for representing power. Wh is determined by two parameters of the battery, voltage and ampere-hour. The formula is as follows:
Battery Capacity(In Watt-hour) = Battery Voltage(V)*Battery Capacity(In Ah)
This formula may seem confusing when you first encounter it. Let’s take a simple example. First, let’s put aside the concepts of Wh and Ah and look at the following example:
Now we have two rectangles, rectangle A is 50cm long and 12cm wide, and rectangle B is 24cm long and 10cm wide. How many rectangles of B can fill the area of A?
We have learned this calculation in elementary school. It is to calculate the area for comparison. The size of the area is obtained by multiplying the length of the rectangle by the width.
We use the area comparison method to understand the relationship between battery capacity, voltage, current, and time. If a 24V10A LED light runs for 1 hour, how big a battery do we need? We need a battery with a voltage of 24V and a capacity of 10Ah. If we apply the formula to calculate its capacity:
Battery Capacity(In Watt-hour) = Battery Voltage(V)*Battery Capacity(In Ah)
= 24V*10Ah
= 240Wh
We continue to use the area method to understand, then the capacity of a 12V50Ah battery is:
Battery Capacity(In Watt-hour) = Battery Voltage(V)*Battery Capacity(In Ah)
= 12V*50Ah
= 600Wh
Battery Capacity LED Light Need for One Hour(In Watt-hour） = LED Light Voltage(V)*Battery Capacity Needed for One Hour (In Ah)
= 240Wh
So that means the LED Light can run 600/240 = 2.5 hours.
Summary of Amp-hours to Watt-hours Conversion
Summarizing the knowledge we have described in the previous article, the summary is as follows:
(1) When comparing the capacities of two batteries, if their voltages are the same, their sizes can be determined directly by comparing the capacities marked in Ah.
(2) When the battery and load voltages are the same, the load runtime can be calculated using the following formula:
Battery Capacity(In Ah) = Current(A)*Time(hour)
(3) When comparing batteries, Wh to Ah conversion is required. First, calculate the battery capacity in Wh of each battery, and then compare them by Wh. The formula can be used:
Battery Capacity(In Watt-hour) = Battery Voltage(V)*Battery Capacity(In Ah)
(4) The battery and load voltages are different. To calculate the runtime that the battery can support for the load, you need to calculate the power required by the load for one hour in Wh, and then calculate the battery capacity in Wh. Then you can calculate the runtime.
In short, Wh is the ultimate benchmark for measuring the capacity of a battery or the load it can discharge over a certain period of time.
