Calculating Battery Run Time

There are a number of factors which must be considered when calculating the expected run time of a cell or battery; it is not simply down to taking the rated values of the battery and using standard electrical equations to work out run time. These parameters are outlined in our ‘Choosing the right battery pack’ section; this section will outline the more specific mathematics which goes into the calculation of battery run time.

Calculating the individual cell run time is fairly straight forward, if you can get access to a datasheet for that cell then that will give you information regarding discharge characteristics and you may be able to read the information straight from the datasheet;  when dealing with a battery pack the process is more complex. The idea being to work with the electrical specifications for the pack and reduce it down using the pack properties to work out what is seen by each individual cell in the pack; then the cell datasheets can be used to calculate run time.

Voltage
The important voltage value is the Cut-Off Voltage of the application i.e. at what voltage will the device/application stop working. When cells are rated, a specific cut-off voltage is stated to which the cell is designed to work to, if the cell is taken below this voltage it may be damaged. Alternatively, if the cut-off voltage is higher than that of the cell then some useful battery energy will not be utilised.

When looking at NiMh and NiCd, cut-off voltage is generally rated at 0.9V - 1V per cell, this also applies to Alkaline cells (nominally rated at 1.5V). When dealing with packs, these values need to be multipled by the number of cells in the pack that are connected in series. For more information see the example at the bottom of th page.

Current
The important factor here is the current being drawn from the pack, the key details are:

• The type of current drain, is it constant or pulse current,
• The duration of the drain current, if pulse currents are involved both the duration and frequency of the pulses needs to be taken into account.

The constant current drawn from the pack is the important value; each cell will have a maximum continuous discharge rating. The cell may also have a moximum pulse discharge current rating depending on the type of cell. These values must not be exceeded or the damage to the cell could be caused; this isn't the only consideration when designing a pack.

The amount of drain current has an affect on the capacity of the battery, the rated capacity is rated against a specified discharge current. A general rule of thumb is the closer to the drain current is to the capacity, the less capacity that will be available to utilise, you may see use made of 'C rate' when charging and discharging are discussed. The C rate is the capacity rating of the battery and is used relative to the charge or discharge rate of the battery. This rate is represented as a fraction of this value, e.g. take a battery with a capacity of 2000mAh, 1C (or C) = 2000mA, 0.2C = 400mA, 3C = 6000mA. At each of these different C rates, the characteristics of the battery will change, a good cell datasheet will outline these characteristics.

Again, these vales need to be traslated to a battery pack, so in order to work out the current drain seen at each cell, divide the total drain current by the number of cells which are connected in parallel.

After you have worked out the Cut-off voltage and current drain for each cell, this can be matched to the characteristics on cell datasheets and approximate service life can be estimated. Apart from this there are further considerations as mentioned earlier such as storage characteristics, operational temperature and drain current characteristics all have a bearing on operational life.

Example 1: Battery pack specifications
Nominal Voltage 6V
Nominal Capacity 2000mAh
Chemistry NiMh

Application specifications:
Cut-off voltage 4.5V
Drain Current 400mA

Number of cells in pack = 5
Number of series connections = 5
Number of parallel connections = 1

Cut-off voltage of each cell = 4.5/5 = 0.9V
Drain current seen by each cell = 400/1 = 400mA

Example 2: Battery Pack Specifications

Nominal voltage 14.4V
Nominal Capacity: 66Ah

Application specifications:
Cut off voltage 12V
Drain Current 600mA

Number of cells in pack = 16
Number of series connections = 4
NUmber of parallel connections = 4

Cut off voltage of each cell = 12/4 = 3V
Drain current seen by each cell = 600/4 = 150mA