How to calculate the time to empty a battery

Question

I am a computer developer, excuse me if the question is basic.

If a consumer takes 1600 mA, how long will it take for it to empty a 12 Ah battery? Is it as simple as 12/1.6?

Answer 1

To a first approximation, yes that is how many hours.

To get a more accurate number you have to look at the cutoff voltage (limited by the minimum voltage the device being powered can operate at, or perhaps the minimum voltage that you can discharge a rechargeable battery to before damage to the battery occurs).

The capacity changes with the rate of discharge (usually getting worse at higher discharge rates, but at very low discharge rates the self-discharge becomes as factor).

Temperature also plays a role- at low temperatures capacity can be significantly less.

Note also that it many loads do not draw even a somewhat constant current for the entire discharge time. An example of such a load would be a fixed load on a linear regulator. Since the output voltage of the regulator is fixed the load current is independent of the input voltage. Even so, many times the load will vary significantly as transmitters or motors start and stop or the device goes into sleep mode.

A resistive load draws less current as the battery voltage drops. An incadescent filament has less variation in current as the voltage drops. A modern switching supply will draw more current as the voltage drops to maintain constant output power, and even a bit more than that since efficiency is typically lowest at minimum input voltage.

So it's actually fairly complex to get a real number for the battery life. One good way to confirm the numbers is to measure the battery capacity under standard datasheet conditions using a programmable digital load, and then measure the device operating time on the same battery in simulated usage.

Answer 2

The simple answer 12/1.6 is not entirely true. The 12ah rating is likely the nominal capacity based on nominal 20 hour discharge rate, and includes recommended cut-off voltage. The 20h discharge rate of a 12Ah battery is 0.6A, so 1.6A discharge rate is almost 3X larger.

Here is a battery specification example, from today's questions. From the example, 3x discharge rate over the nominal rate will result in about 80% of nominal capacity. So the estimate is 12/1.6 * 0.8 = 6 hours.

However, batteries differ in purpose and design, and may have different definitions of nominal discharge rate, so the estimation will vary depending on specifications.

Answer 3

12aH battery means that it can provide 12amps of current for one hour. That means if you have a device which is consuming 12amps, so your battery will get discharged in an hour. If you have a device which needs 1amps, then your battery will last long for ~12hrs.

So as you said, a consumer takes 1600mA (1.6A), it will last long for ~7hrs

Answer 4

Due to the numerous variables in amp-hour [Ah] discharge time, the battery industry has standardized on a 20h discharge rate at 25'C for a constant current discharge rate. As discussed in other answers and comments if the expected discharge time is less than 20h, then the Ah capacity reduces and visa versa. As @Sphero mentioned, there many nonlinear load types and thus not always constant current. As @Ali refers to actual battery SLA specs this is the most accurate way and one sees that other variables such as Temperature and discharge profiles effectively reduce the efficiency and capacity. @gbarry states accurately that this is most likely the best case.

Increasing battery temperatures, although increases capacity somewhat in most battery chemistries, it also rapidly decreases life.

So for a Rule of Thumb you can use the Ah calculation to get an approximations for time from Amps then reduce by x% for discharge times less 20h and y% for lower temperatures and z% for age and condition of battery.

This stackup of uncertainties for capacity reduction are dominated by battery brand quality, chemistry and life cycle expectancy in total lifetime Ah. This life cycle can vary from 500 to over 10,000 cycles and 10 years such as batteries used in Mitsubishi e-cars.

• For LiPo's for example you can almost double the life cumulative Ah capacity by only using it between 50 & 75% which is inconvenient for most people yet partially adopted in the charger profile for Lenovo laptop chargers.