The maths behind "charge status" and amp-hours being different

The (SI) unit of energy is the Joule, symbol J. It represents the total amount of energy available within a system, be it a litre of diesel, a kg of coal, the energy in a coiled spring or the energy in a battery. If a system has 1 Joule of energy available it makes no differernce how fast or slow we use that available energy. We will still get 1 Joule.

The (SI) unit of power is the Watt, symbol W. It represents the "rate of doing work". Or the rate of converting one form of energy to another, say electrical energy into heat energy.

1 Watt = 1 Joule per second. So if we use 1 Joule every second we are using 1 watt of power. Irrespective of how long that goes on for. So if we use 1 Watt for 1 second we will have used 1 Joule of energy, if we use 1 Watt for 10 seconds we will have used 10 Joules of energy.

Therefore 1W=1J/s

We can therefore also write 1Ws=1J. In english this reads as "one Watt-second equals one Joule". Therefore a Watt-second is a unit of energy (not power).

Therefore a watt-hour is a unit of energy.

Now if we are talking about an electrical system consisting of a power supply with a fixed voltage we can see that the watt-hours is directly related to the amp-hours because the voltage is constant. In this case, as we already know that watt-hours are units of energy, we can also state that amp-hours are directly proportional to units of energy.

However in the case of a lead acid battery, as the battery becomes discharged the terminal voltage falls. This means that the amp-hours are not directly related to the watt-hours available. Therefore the amp-hours are

not related to the Joules remaining in the battery and therefore not a good representation of the available energy remaining in the battery.

SmartGauge "state of charge" display is related directly the the energy (in Joules) not the amp-hours.

The voltage of a fully charged lead acid (flooded) battery is about 12.7 volts, and that of a discharged battery is about 11.4 volts. This is a variation of about 10% which means that the amp-hours figure will be in error by up to about 10% from the actual energy (in Joules) remaning in a battery.