The battery on my laptop is not as good as it used to be. If the battery is it 98% at 3:07 and then it's at 87% at 3:16 how fast is it running out of power? How would I write an equation for this? TIA

3:07 - 98%
3:16 - 87%

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    $\begingroup$ You would probably want to get a few more measurements because we can't really say what sort of equation would best fit the situation with just two times. $\endgroup$ – DMcMor Dec 23 '15 at 23:21

There are infinitely many equations that fit those two data points. But that is not what you asked. You asked "how fast is it running out of power?" That is a rate-of-change question, and the average rate of change can be calculated from just two points.

If you know two data points $(x_1,y_1),\ (x_2,y_2)$, then the average rate of change is defined as


In your case that is

$$\text{AROC}=\frac{87-98}{(3\cdot 60+16)-(3\cdot 60+7)}=-\frac{11}{9}\approx -1.22$$

So your battery lost $1.22$ percent per minute.

The consequences of this depend on whether the rate of loss of charge is constant. Since that is unknown, I'll refrain from making predictions.


you have two points here: $(0,98)$ and $(9,87)$ (after subtracting the rest of the minutes off), so you can shoot a line through them via:


where $m$ is the slope (how fast the battery is draining) and $b$ is the y-intercept

so you have:


so $m=\frac{-11}{9}\approx -1.2\%$ per minute

if the battery use is constant, the battery will be dead at approximately 4:27


If the battery was a perfect power source and behaved linearly, charge and discharge times could be calculated according to in-and-out flowing currents, also known as coulombic efficiency.

As I do not know context of this question (school problem or just looking at the icon in your computer), I am providing you with the following sites for additional information:




That batteries have a finite life is due to occurrence of the unwanted chemical or physical changes, or to the loss of the active materials of which they are made. Otherwise they would last indefinitely. These changes are usually irreversible and they affect the electrical performance of the cell.


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