## Tuesday, 28 January 2014

### Which metric should we use to compute the capacity of my battery: mAh vs. mWh?

You probably remember the following formula from your science class:
Watt = Volts x Ampere
if you multiply it with time, you get energy instead of power
Watt x Hour = Volts x Ampere x Hour
or in the case of a AA battery
miliWatt x Hour = Volts x miliAmpere x Hour
the short version:
mWh = V x mAh

If the voltage (V) of a AA battery were constant over time, we could either use mWh or mAh to compute the battery capacity.
Since it drops as the battery empties, it would be more accurate to use mWh. While this is the scientific way of doing it, in some cases, mAh provide a better estimate of the battery ability to power your device:
• Devices using a voltage regulator: these devices use a voltage regulator to decrease the voltage provided by the batteries to a value supported by the electronics. This means that as long as the voltage from the batteries is high enough, the current consumed by the electronics will be the same as the current provided by the battery. In this specific case we therefore only need to know the mAh a battery can provide above a given cut-off voltage where the voltage regulator stops working (and the batteries must be replaced).
• In the case of a simple torch where the light bulb is a resistor, the current consumed will vary with the voltage of the battery. In this case mAh is probably a bad metric.
• More complex electronic devices might include a dc-dc converter (step up or step down) regulating the output voltage. The current drawn at the input (battery side) of these regulators varies with
• the input voltage (battery voltage),
• the power consumed by the electronics and
• the regulator efficiency (which also varies with input and output voltages).
In this case as well, the electronics draws a certain power and the current pulled from the battery will vary with the voltage it provides.
As a conclusion, I would recommend using energy (mWh) instead of current (mAh) to measure the capacity of your cells unless:
• You have a voltage regulator at the input of your circuit (and you know the cut-off voltage)
• You have a very linear battery, such as NiMh batteries (in which case if does not make a big difference).
Conclusion: we will therefore keep on using both!