# Measuring the Capacity of a Battery

The capacity of a battery tells you how much charge it can store. The rechargeable AA batteries we sell in the REUK Shop for example are rated with a capacity of 2,900mAh (=2.9Ah). This means that they can theoretically provide a current of 2.9A for one hour, 1.45A for two hours, or 290mA for ten hours. In reality batteries do not respond in such a linear way – a 2,900mAh battery would not provide 29mA for 100 hours, nor 2,900mA for one hour.

Battery manufacturers use a discharge load of 0.1C or one-tenth of current capacity when rating their batteries. Therefore, a battery which can provide 300mA for 10 hours would be rated at 10×300 = 3,000mAh.

0.1C has been chosen by manufacturers as it shows battery capacity in the best light. A faster discharge rate would result in less energy being extracted from the battery, and therefore the measured capacity would be lower. If you are using batteries in energy-hungry devices such as digital cameras, the real world capacity is lower than that published.

### Measuring Battery Capacity

The mAh / Ah measurement is not particularly useful in the real world. What we are interested in is the amount of energy stored in a battery since it is this energy we need to power our devices. Stored energy is measured in Watt-hours – the same units used to measure our domestic electricity consumption (where 1,000Wh = 1kWh = 1 unit of electricity).

In order to measure the stored energy in a battery a power resistor is used as the load, and a fully charged battery is fully discharged through it. By measuring the voltage across this resistor at regular intervals during the discharge process it is simple to calcuate the total energy dissipated and therefore the total energy which had been stored in the battery.

Using Ohm’s Law we can calculate the current flowing through the resistor since we know the voltage across it (I = V/R). Instantaneous power is given by multiplying the measured voltage by the calculated current.

If we measure the instantaneous power to be 5.89 Watts at 10:39:30pm, and then 5.88 Watts at 10:39:40pm (i.e. 10 seconds later) we know that for the 10 second interval between readings, the power being dissipated was around 5.89 Watts. 10 seconds is 0.002778 hours and so during those 10 seconds, 5.89 * 0.002778 = 0.0164 Watt-hours of energy were dissipated (taken from the battery and lost as heat from the power resistor).

By taking readings every 10 seconds until the battery is completely discharged, and adding up the energy dissipated in each 10 second interval, we can calculate the total energy taken from the battery and dissipated in the resistor and therefore the total energy that was stored in the fully charged battery.

### Converting from Watt-hours (Wh) to Amp-hours (Ah)

Having measured the real energy capacity of a battery, it is interesting to convert it into the more common Amp-hour units. This is done using the Ohm’s Rule that Power = Voltage * Current, and therefore that Energy (power * time) = Voltage * (current * time). The voltage is displayed on batteries – e.g. 1.2V for a NiMH rechargeable, and we have measured the energy, therefore we have the information we need to convert to Ah.

If, for example, you measured 2.940Wh of energy in a 1.2V AA rechargeble NiMH battery, then:

 2.940Wh = 1.2V * ?Ah ?Ah = 2.940Wh/1.2V = 2.45Ah = 2,450mAh.

### Power Analyzer Obviously, you would not want to spend many hours manually taking voltage readings every 10 seconds, therefore a power analyzer is a very useful tool. We used the Power Analyzer PRO as it does everything automatically. The fully charged battery is connected to one side, and the power resistor is connected to the other. Every 0.3 seconds it measures the voltage and current, displays instantaneous power, and calculates and displays the total Watt-hours of energy dissipated since the discharge began.

With the power analyzer connected to a PC via the provided USB cable, it is possible to export the collected data to a spreadsheet so that discharge curves can be plotted, additional calculations made, and batteries from different manufacturers compared accurately.

### Other Datalogging Options

If you do not have a power analyzer then a Raspberry Pi, or an Arduino or Picaxe microcontroller can also be programmed to be used as a datalogger with the results outputted either to an LCD display, or via the serial connection to a PC where they can be plotted and analysed.