As we have seen in earlier modules, the electrical power equals the current multiplied by the voltage. A battery delivers electrical power at a voltage $V$ for a given current $I$. Hence, the unit of power—the Watt (W)—is defined as:

In other words, 1 Watt (W) is the rate at which electrical work is done when 1 Ampere (A) flows through a potential difference of 1 Volt.

A commonly used analogy compares electrical current to flowing water. Current is analogous to a flow rate (liters per second), while voltage is analogous to a height difference (meters). The power produced by a hydroelectric plant is proportional to both the flow rate and the fall height (Current × Voltage). To convert from electrical power to electrical work, we integrate the power over time:

The unit for energy is the Joule (J), where $1\ \text{J} = 1\ \text{W} \cdot \text{s}$ (i.e. 1 Watt sustained for 1 second). In batteries we often use the term Watt-hour, which is 1 Watt delivered for 1 hour (1 Wh = 3600 J).

Batteries are also characterized by their total charge capacity:

Two common units for capacity are:

• Coulomb: the charge passed by 1 Ampere in one second.
• Ampere-hour: the charge passed by 1 Ampere in one hour.

The state of charge is the percentage of capacity remaining. For instance, if a battery has a capacity of 1 Ampere-hour, a state of charge of 50% means 0.5 Ampere-hour remains. Charging the battery by 0.5 Ampere-hour would restore it to 100%.

To describe the charging/discharging rate, the C-rate is used. A rate of $C/n$ indicates that it takes $n$ hours to fully charge or discharge the battery. For example, 1 C means 1 hour, 0.2 C (i.e. $C/5$) means 5 hours, and 2 C indicates 30 minutes.

Finally, the electrical work consumed or released during charge/discharge is given by

and the roundtrip efficiency η is defined as:

A good battery typically has a roundtrip efficiency above 90%.