# Can the amount of ampere hours in a car battery be determined by it's output in volts?

Let say an average car battery has a 48 amp-hour capacity. Is it possible to determine how many ampere hours are left in a battery if the volts are known? What about if they are lower (e.g., 8 V) than a completely discharged battery (i.e., 11.9 V)? - and if so, how is it determined mathematically?

Edit #1

I'm trying to calculate how long it would take to charge a car battery from 11.89 V to 12.65 V, but my battery charger only provides it's output as 1.25 A. If a battery is at 11.89 V then does that mean it has 0 ampere hours? What about if it has 8 V, is it still 0 ampere hours still?

The work that a battery can do is measured in watt-hours. You observe that a high or low voltage across the terminals somewhats reflect the state of charge of the battery. That is true, but it's not a reliable measurement of anything else. Batteries of different ages, or with different chemistries and internal surface areas will perform differently (and nor would you want to completely discharge a car battery, as they are not meant for "deep cycling").

The answer is that yes, it can be, to some extent, according to battery university. However, the battery should rest for 24 hours, which may be impractical. Note that most cars have a low continuous current drain on the battery. So, ideally, the battery should be disconnected from the car, meaning you lose your radio stations.

The other difficulty is temperature compensation. The open circuit voltage is not only a function of the state of charge, but also a function of the temperature.

For example, for starter batteries with antimony, approximately 0% is 11.89V (can be lower as well if the battery is totally flat), and 100% is 12.65V. So, even though the state of charge went from approximately 0% to 100%, the open circuit voltage changed only very little. However, these values are valid only if the temperature of the battery is 26 degrees Celsius. Note also that these values are for batteries with antimony. Most batteries these days have calcium instead of antimony, and thus, the voltages are slightly different.

Edit #1:

If the battery is at or below the empty voltage (which for lead acid antimony batteries is at 11.89V, but the battery can in theory be at any voltage between 0V and 11.89V and it is in any case approximately empty), and has 48 Ah capacity, a 1.25A charger will fully charge the battery in approximately 38.4 hours (just divide the Ah of the battery by the amperes of the charger), but I would add few hours more because the end of the charging occurs at constant voltage, not at constant current. So, in about two days, you should have a fully charged battery.

• So for lead acid antimony batteries, if the voltage is below 11.89, does that mean the capacity in ampere-hours is still below 0 right? So as long as the voltage is greater than 11.89 V, the capacity should reflect > 0 ampere-hours? I'm wondering if the correlation is 1:1. – Narcotixs Feb 14 '17 at 3:13
• Well, the voltage versus charge graph is so vertical at that point, so very minor changes in charge lead to huge changes in voltage. So, e.g. battery at 6V has a tiny bit less charge than a battery at 11.89V. Both are practically devoid of charge. – juhist Feb 14 '17 at 7:53