Watt hours (Wh) can be converted to Amp-hours (Ah) using the formula Ah = Wh / Voltage, where voltage refers to the nominal voltage of the battery.

What is an Amp Hour? 

An amp hour also shown as aH is a measure of amps over time. If one amp is flowing for one hour, then that is an amp hour worth of current flow. In the context of battery ratings, an amp hour indicates how many amps a battery can deliver over a period of time. It is calculated by testing the battery with a constant current load and measuring how long it takes for the voltage to go from fully charged to LVC (Low Voltage Cutoff). If the test current was 700ma and the cell lasted for 5 hours before its voltage reached LVC, then that means the cell is good for 3.5 Ah.

700ma Test Current x 5 hours run time = 3500maH(3.5Ah)

This means that a 3.5Ah cell can deliver 700ma for 5 hours, and it also means that it can deliver 3.5 amps for 1 hour, and so on. But really, what does that mean? How much power is that? You can’t know that without knowing about voltage. 

What Is A Watt Hour?

Now that we have a clear understanding of what a watt is, we can move on to watt-hours. A watt-hour also shown as wH is just like an amp hour, it's the number of watts that are transferred over the course of an hour. If a load of 500 watts is run for 30 minutes, then 250-watt hours will have been used. A watt hour incorporates both the current (amps) and the force driving that current (voltage).

Why Watt-Hours Matter

The real-world implications of watt-hours versus amp-hours are significant, especially when comparing batteries for different devices or applications.

Consider two batteries, each with a capacity of 100Ah. Battery A operates at a voltage of 12V, while Battery B operates at 24V. Based on amp hours alone, these batteries seem identical. However, when we consider watt-hours, Battery A has a capacity of 1,200Wh (100Ah x 12V), while Battery B has a capacity of 2,400Wh (100Ah x 24V). Despite having the same ampere-hours, Battery B can deliver twice as much energy as Battery A due to its higher voltage.

The watt-hours metric becomes even more important for applications like electric vehicles or DIY power wall systems because the power requirement isn't just about the amount of charge, but also about the work that charge can do, which is determined by both the current and voltage.

Amp hours may be the more commonly discussed metric, but if you have an understanding of watt-hours, you will have a more comprehensive understanding of a battery's capacity. This is because watt hours take into consideration both the amount of charge a battery can deliver (amps) and the 'pressure' or force driving that charge(voltage).

Effect of Discharge Rate on Battery Capacity

Regardless of how efficient your charge process is, if you are doing high drain discharge, you are not going to get the rated capacity of your cells. This means that whether you calculate using amp hours or the more informative watt-hours, it will always be less if your discharge rate is high. 

Batteries will have a lower capacity when they are discharged quickly. This is due to Peukert's Law, which states that the faster a battery is drained, the less overall capacity it will have. This means that the real-world capacity of a battery will always be lower than its rated capacity if it's used above 0.2C.

Understanding battery capacity goes beyond just looking at the amp hours. Factors such as voltage, watt-hours, battery efficiency, the measure of internal resistance, and discharge rate all play a significant role in determining how much energy a battery can realistically provide. As such, the watt-hour measurement is a more holistic approach to understanding and comparing battery capacities. By taking into account all these factors, you can make better-informed decisions when choosing a battery for a particular application.

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Conclusion

Comprehending battery capacity is more complex than simply evaluating amp hours (Ah), which only denotes the amount of current a battery can output over a specified period.

A better metric to consider is watt-hours (Wh), which takes into account both the current (amps) and the driving force behind that current (voltage). To truly understand a battery's energy capacity, you have to understand what these units mean-amp hours, volts, and watt-hours.

Also, the capacity of a battery is not static and fixed but instead dynamic and changes. It is influenced by its efficiency and discharge rate. Battery efficiency represents the proportion of energy that can be extracted from a battery compared to the energy expended in charging it, with some energy invariably lost in the process. The discharge rate also is linked to the overall capacity, with higher discharge rates resulting in lower observed capacities. So, when gauging battery capacities, take into account all these factors-amp hours, voltage, watt-hours, efficiency, and discharge rate.

We hope this article helped you learn everything about why there is more to capacity than amp hours. Thanks for reading!

Understanding Watt Hours and Amp Hours

Watt hours (Wh) and amp hours (Ah) are two important units of measurement in the electrical world, providing insights into energy storage and consumption. Converting between these two to determine battery pack capacity is straightforward and can be done using Ohm's law. If, for example, your project needs a 1,200-watt-hour battery, the number of amp hours can be deduced by dividing the watt-hours by the battery's nominal voltage. So, if you're building a 12-volt battery, a hundred amp hours of cells are needed to deliver 1,200-watt hours.

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Getting Practical: From Theory to Application

Applying these concepts to real-life scenarios makes the calculation more tangible.

If your battery cell has a capacity that's already known, this information can help determine the number of cells needed to reach the desired amp hours. As an example, if you're using 3 Ah cells and need to reach a target of 100 Ah, 34 cells would need to be connected in parallel. To achieve 12 volts, at least three cell groups connected in series are necessary, meaning 102 cells would be required for the project. 

It’s also important to consider that the nominal voltage of a 3S NMC lithium-ion battery is actually 11.1 volts. So, 102 Ah will actually provide 1132.2-watt hours of energy.

How To Convert Watt Hours To Amp Hours

Here are a few more examples. Let's say you have a 48-volt electric bike battery that can store 500 watt-hours of energy. If you want to find out the Amp-hours (Ah) of the battery, you would use the formula Ah = Wh/Voltage.

Ah = 500Wh / 48V = 10.42Ah

So, the 500Wh battery is equivalent to a 10.42Ah battery at 48 volts.

Now, consider a 12-volt RV battery that has a capacity of 100 amp-hours. To find the watt-hours stored in this battery, you would use the formula Wh = Ah * Voltage.

Wh = 100Ah * 12V = 1200Wh

So, a 12V 100Ah battery can store 1200Wh of energy.

Different Voltage Levels

Next, let's consider a scenario where you're trying to choose between a 24V battery system and a 48V battery system for your DIY powerwall project, and both are rated at 100Ah. How do these options compare in terms of watt-hours?

For the 24V system:

Wh = 100Ah * 24V = 2400Wh

For the 48V system:

Wh = 100Ah * 48V = 4800Wh

Although both systems have the same Amp-hour rating, the 48V system can store twice as much energy because it operates at a higher voltage.

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Accounting for Efficiency and Power Loss

It’s important to remember that no system is 100% efficient. Any heat generated in wires, battery connectors, or regulators equates to power loss. Incorporating an additional 10-15% into your calculations to cover these losses is prudent.

Lithium-ion batteries are particularly efficient when not being charged or discharged at extreme rates, reaching efficiency levels close to 99%. Because of this, any efficiencies in your system will more than likely be due to charge and discharge regulators. 

Amp Hours, Watt Hours, and Nominal Voltage

The watt-hours rating is an estimate based on the nominal voltage over time and the current the battery can deliver. These figures are not exact, and it's vital to consider fluctuations. A 12-volt lithium-ion battery, for example, has a max charge voltage of 12.6 volts. If it's delivering 10 amps at 12.6 volts, it's providing 126 watts. Over one hour, that's 126 watt-hours; over ten hours, it's 1,260 watt-hours. However, the voltage will not remain constant throughout this period. By the third, fourth, or fifth hour of continuous 10-amp delivery, the voltage will have dropped from its original level.

This is why nominal voltages are used in these calculations. The nominal voltage of a 12-volt battery is 11.4 volts. Hence, to accurately estimate the capacity of a battery pack in amp hours and watt hours, it's essential to use the nominal voltage in your calculations.

Watt Hours Vs Amp Hours

So, which one is more useful, watt hours or amp hours? Well, if you are comparing two systems that have the same nominal voltage, then amp hours can be just as useful as watt hours. Remember, the total amount of power (watts) is the voltage times the current. To know the watt hours, you must first know the amp hours. 

If the two systems you are comparing have the same voltage, then you can easily use amp hours to compare them. For example, if you have a 5Ah 21V drill battery and a 2Ah 21V battery used for a portable soldering iron, its easy to compare the amount of total between in each system. The 5Ah battery contains 2.5X the energy as the 2Ah battery. 

But when comparing two systems of different voltages, this all goes out the window. For example, a 6Ah 36V ebike battery contains a whole lot more energy (216 watt hours) than a 8Ah 12V lawnmower starter battery (96 watt hours).

So, when comparing two random systems that may not have the same voltage, watt hours will always be more useful.