# How to calculate battery energy

### Definition

Battery energy is the electric energy stored in a battery cell or battery pack. It shows the capacity of the battery to provide electric energy for a prolonged period of time. The higher the battery energy the longer the time it can supply electric energy. A typical battery stores chemical energy and converts it to electric energy when it’s connected to an electrical load (consumer).

Image: Battery cell

Battery energy is sometimes referred as battery capacity, which is not very accurate. To clarify things, there are two types of “battery capacities”:

• battery current capacity, also called battery capacity, measured in amperes-hour [Ah]
• battery energy capacity, also called battery energy, measured in joules [J], watts-hour [Wh] or kilowatts-hour [kWh]

Go back

### Formula

If the battery consists of a single cell, the battery energy formula (equation) is:

Ecell = Ccell · Ucell
(1)

where:

• Ecell [Wh] – battery cell energy, in watts-hour
• Ccell [Ah] – battery cell (current) capacity, in amperes-hour
• Ucell [V] – battery cell voltage, in volts

For a battery pack, consisting of several cells, the battery energy formula (equation) is:

Epack = Ncell · Ecell
(2)

where:

• Epack [Wh] – battery pack energy, in watts-hour
• Ncell [-] – total number of cells within a battery pack

The unit of measurement for battery energy can be: joule [J] or Watt-hour [Wh] or kilowatt-hour [kWh].

Go back

### Ni-MH battery cell example

Calculate the energy content of a Ni-MH battery cell, which has the cell voltage of 1.2 V and current capacity of 2200 mAh.

Step 1. Convert the battery cell current capacity from [mAh] to [Ah] by dividing the [mAh] to 1000:

Ccell = 2200 / 1000 = 2.2 Ah

Step 2. Calculate the battery cell energy Ecell [Wh] content:

Ecell = Ccell · Ucell = 2.2 · 1.2 = 2.64 Wh

Go back

### Tesla battery pack example

A Tesla Model S battery pack contains 7104 individual battery cells. Calculate the total battery energy, in kilowatts-hour [kWh], if the battery cells are Li-Ion Panasonic NCR18650B, with a voltage of 3.6 V and capacity of 3350 mAh.

Step 1. Convert the battery cell current capacity from [mAh] to [Ah] by dividing the [mAh] to 1000:

Ccell = 3350 / 1000 = 3.35 Ah

Step 2. Calculate the battery cell energy Ecell [Wh] content:

Ecell = Ccell · Ucell = 3.35 · 3.6 = 12.06 Wh

Step 3. Calculate the battery pack energy Epack [Wh] content:

Epack = Ncell · Ecell = 7104 · 12.06 = 85674.24 Wh

Step 4. Convert the battery energy from [Wh] to [kWh] by dividing the [Wh] to 1000:

Epack = 85674.24 / 1000 = 85.67424 kWh

Go back

### Calculator

The battery energy calculator allows you to calculate the battery energy of a single cell or a battery pack. You need to enter the battery cell capacity, voltage, number of cells and choose the desired unit of measurement.

The default unit of measurement for energy is Joule. If you want the result displayed in another unit, use the drop down list to choose and click the CALCULATE button again.

Go back

### References

[1] David Halliday, Robert Resnick, Jearl Walker, Fundamentals of Physics, 7th edition, John Wiley & Sons, 2004.
[2] Benjamin Crowell, Light and Matter – Physics, 2007.
[3] Raymond A. Serway and John W. Jr. Jewett, Physics for Scientists and Engineers, 6th edition, Brooks/Cole Publishing Co.,2004
[4] Jiansong Li, Jiyun Zhao, and Xiaochun Zhang, A Novel Energy Recovery System Integrating Flywheel and Flow Regeneration for a Hydraulic Excavator Boom System, Energies 2020.
[5] Leo H. Holthuijsen, Waves in oceanic and coastal waters, Cambridge University Press, 2007.
[6] Kira Grogg, Harvesting the Wind: The Physics of Wind Turbines, Carleton College, 2005.