Android Phone Battery Calculations

I recently received a new Samsung Galaxy S3. Coming to Android 4.1.1 from three years of iOS is quite liberating. The phone just gives you so many more customization options and control. Amongst all the new features though, I really like the power usage meter under Settings > Battery. It presents a nice graph that shows battery charge over time and the applications using the most power. I thought it would be fun to interpret the data a bit and calculate the “full charge time” and the charge rate in mA. My calculations are below:

Data

The last part of the graph is me charging via USB

The last part of the graph is me charging via USB

Calculations

(𝚫x, 𝚫y) = (85 px, 258 px)
graph is 720×661
axes are (17h 57m 47s = 64667s, 100%)
so (𝚫x, 𝚫y) = ((85/720) * 64667s, (258/661) * 100%) = (7364s, 39.03%)

That means the rate of charging is (39.03%/7364s) = 0.0053001% per second

That means for a full charge at this rate, it will require 100% / (0.0053001% per second) = 18870s = 5.241h = 5h 14m 8s

The capacity of the battery marked on the outside is 7.98Wh / 3.8V = 2100 mAh = 7560000 mAs
so the new 𝚫y = (258/661) * 7560000 mAs = 2950000 mAs

𝚫y/𝚫x = 2950000 mAs / 64667 s = 45.62 mA
𝚫y/𝚫x = 2950000 mAs / 7364 s = 400.6 mA

400.6 mA * 3.8 V = 1.52W

Remarks

The calculations should be correct. 5 hours seems reasonable for a full charge. What surprises me is what seems like a very low current – only 45.62 mA? Now I see the mistake. 400.6 mA seems like a much more reasonable charing current. It’s a nice round number too. I’m happy.

EDIT 2015-01-18: I now have a new Samsung Galaxy S5 and have noticed that the battery is physically larger and lasts a lot longer than the S3 battery. (10.78Wh vs 7.8Wh) I have redone this analysis and have come up with new charge rate of 2.898 W.

Some observations:

  • The new S5 battery has more capacity, but the energy density has not increased significantly.
  • The rate of charging has doubled!
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2 thoughts on “Android Phone Battery Calculations

  1. Eduardo

    You actually make it seem so easy with your presentation but
    I find this matter to be really something that I think I
    would never understand. It seems too complicated and very broad for me.
    I’m looking forward for your next post, I’ll try
    to get the hang of it!

    Reply
    1. Andrew Post author

      If I made it seem easy then that is good! You can follow along and eventually do such calculations yourself. All this requires is some high school physics knowledge.

      Reply

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