# Calculate battery life

I would like to know how to calculate battery life when using an LED strip. The LED strip is powered by 8 AA batteries in series. LED Current Draw = 260 mA. LED power consumption: 3.1 W. LED Operating Voltage range: 9-14.8 VDC. Please see attached images for battery datasheet.

This is my calculation, but I'm not sure if it's correct:

Battery Life = (Battery Capacity)/(Load Current) = 2000 mAh /260 mA = 7.7 Hours

This is for one battery, and the lights are powered by 8 batteries, so is the total battery life = (7.7)x(8) = 61.6 hours ?

• Thanks for doing your homework before asking. It is a well written question. – mkeith Nov 19 '17 at 22:06
• You should be more precise. How are the LED strip and the 8 batteries are connected? All batteries in parallel is not possible, 1.5 V is too low for a LED strip. If all 8 batteries are in series, the capacity is 2000 mAh for them, no multiplication with 8. With 8 cells in series, the voltage at start will be 12 V, but at finish of discharge only 8 * 0.8 V = 6.4 V. You should look in the datasheet of the LED strip for the minimum operating voltage. If this voltage is 10 V for example, one cell may be discharged only to 1.25 V and the capacity is smaller than 2000 mAh. – Uwe Nov 19 '17 at 22:08
• @Uwe Thank you for your answer. 8 AA batteries are in series and the minimum operating voltage is 9 VDC. – A.K Nov 19 '17 at 22:18
• If minimum voltage is 9 V DC, the cells may be discharged to 1.125 V. In the discharge diagramm not 10 hours at 250 mA, only about 6 hours. – Uwe Nov 19 '17 at 22:29
• We really need to have the datasheet for the LED strip, or at least the V-I curve (which you could measure with your bench top power supply.) We also need to know what kind of a converter you are using, and its efficiency (datasheet would be best, or measurements at least). With your partial question, our attempted answers are also partial, sorry to say. – MicroservicesOnDDD Jan 1 at 20:40

I would like to know how to calculate battery life when using LED strip. The LED strip is powered by 8 AA batteries. LED Current Draw = 260 mA.

Right. The batteries will be discharged at 260 mA. This is close enough to the 250 mA of the third bar on the capacity chart so we can assume 2000 mAh capacity.

This is my calculation, but I'm not sure if it's correct. Battery Life = (Battery Capacity)/(Load Current) = 2000 mAh /260 mA = 7.7 hours.

Correct.

This is for one battery, and the lights are powered by 8 batteries, so is the total battery life = (7.7)x(8) = 61.6 hours?

You were doing fine up until this. Here's the way it works:

• One cell gives 2000 mAh at 1.5 V.
• Two cells in parallel gives 4000 mAh at 1.5 V. (But this is not your configuration.)
• Two cells in series gives 2000 mAh at 3 V.
• Eight cells in series gives 2000 mAh at 12 V.

Run time = 2000mAh / 260mA = 7.7 h.

We can cross-check this with the energy capacity which is given by V x mAh.

• Each cell has an energy capacity of 1.5 x 2000m = 3000 mWh.
• Eight cells have a capacity of 8 x 3000 = 24000 mWh = 24 Wh.
• Using your figure of 3.1 W the run time is 24 / 3.1 = 7.7 h.

The result is 7.7 h in both cases.

• For including the cross-check... Bravo! I love seeing this, as it increases my confidence in the answer, as well as reminding me to do so on my own, as taught in school. Excellent! – MicroservicesOnDDD Jan 1 at 19:35
• For a converter with 80% efficiency, that 7.7 hours gets reduced to 7.7 * 0.8 = 6.16 hours, and a linear solution at 40% efficiency would be much worse at only 3.08 hours. Unfortunately, we are not told the efficiency of the converter, but I leave this for those who aren't thinking about the "efficiency factor". For battery powered applications, efficiency can matter a lot! – MicroservicesOnDDD Jan 1 at 20:05

Calculating battery life is pretty simple, just look at the units. Battery capacity is rated in mAh so 2000mAh can provide 2000mA for 1 hour, or 1mA for 2000 hours, etc.

Battery Life [hours] = Capacity [mAh] / Average Current [mA]


For example

Capacity [mAh] / Average Current [mA] = Battery Life [hours]
2000 mAh   /        260 mA        =     7.7 hours


You can pretty much ignore the Wh rating on the battery. It's like the mAh rating but it accounts for the fact that the battery voltage isn't constant over the battery's life.

As for series and parallel:

         | Capacity | Energy | Voltage   | Max Discharge Current
| mAh      | Wh     | V         | mA
----------------------------------------------------------------


For example, using 2000mAh AA batteries:

           | Capacity | Energy | Voltage   | Max Discharge Current
| mAh      | Wh     | V         | mA
----------------------------------------------------------------
Single     | 2000     | 3000   | 1.5V      | 500
2xSeries   | 2000     | 6000   | 3V        | 500
2xParallel | 4000     | 6000   | 1.5V      | 1000


Note from the datasheet though that the expected capacity changes based on the discharge rate. You get 3000mAh at 25mA but only 1500mAh at 500mA.

For your situation, you would need 6-8 batteries in series to reach 9-12V which would give you 2000mAh or 7.7 hours.