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.

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.