Laptop Battery Technology
As far as battery technology for a laptop, what you've got is what you're stuck with for the most part as the charging electronics to different battery technologies are internal to the laptop itself.
That said, you've asked good questions about the terms used to identify batteries - mAh (yes, milliamp hours) and W (watts).
Watts are a standard way to measure power output of any electrical device. The best measure for a battery would be in Watt-hours, measuring actual energy capacity of the battery. (Watts = Volts * Amps)
A second-best measure would be the mAh measure which would indicate how much current the battery can supply over time at the specified voltage. (I used this figure frequently when selecting AA rechargeable batteries.)
I've not heard about voltage variations between batteries. Essentially the most efficient battery will be the one with the voltage that best matches what the computer's internal electronics were designed around. Any excess will be frequently lost as heat as the internal electronics convert the voltage to the proper level (which is probably not a figure specified by the manufacturer - they're more likely to supply a figure denoting the range of voltages the laptop will accept).
Bottom line for most batteries is that shelf-life is still a factor, so look for a reputable dealer with an indication of when the battery was manufactured since an older better specified battery may not have the capacity of a new battery with poorer specifications.
All batteries run on chemicals inside it. In notebooks, they always use Lithium batteries, so you don't have to worry about the technology (chemicals inside it).
What you can worry about is the capacity of the battery. In large batteries which include those for notebooks, you will always find the capacity in 'Ah' = Ampere-Hour not in 'mAh' = milliampere-hour. The bigger the number, the greater the capacity of the battery. More capacity, more time you can use your notebook.
The problem is that most notebook manufactures doesn't tell you the capacity in 'Ah'. The only information you have is the number of cells inside the battery. More cells -> more chemical -> more time you can use the notebook.
What the value actually means is that with a battery of 3 Ah (for example), you could drain 3 Amperes of current for 1 hour. So if your notebook drains only 1 Ampere of current, you battery would last for 3 times longer. But you mustn't worry about the calculations, because you will never know exactly how much your notebook drains, to make the calculations.
Voltage doesn't correlate in any way to the capacity of the battery and doesn't interfere with the lifespan of the battery,
Watts is a measure of power, not capacity, but you can use it to ascertain the capacity of the battery, because Watts = joules/second = energy/time. So again the bigger the number, the better.
For a deeper understanding (if you want), you can go to wikipedia.
This is what everything related to a Laptop Battery means:
Milli-Amp Hours (mAh) and Amp Hours (Ah)
1 Ah is 1000 mAh. So if you see a battery that states it's 7200 mAh it's just 7.2 Ah. (I'm guessing this was done as a marketing ploy). A 7200 mAh battery will supply 72 milli-Amps (7.2 Amps) for 100 hours or 1000 milli-amps (1 Amp) for 7.2 hours. In order to fully determine how a battery will do with your laptop, you must find out how much amperage your laptop uses and then back calculate the amount of hours that battery will supply the laptop. In short this means that the higher the number the greater amount of supply
Watts and Watt Hours
Watts (W) and Watt-hours (Wh) is a measurement of power that can be given over time. Meaning that a 100 Wh battery will supply 100 Watts for one hour, or 50 Watts for 2 hours, and so on. Since most battery manufacturer do not post a value of Wh or mWh, a simple way to calculate mWh is to take Milli-Amp hours (mAh) and multiply it by the Voltage output of the battery [mAh x V = mWh; Ah x V = Wh]. This means that the higher the number the greater amount of power supplied per hour
Cells
The amount of cells has an effect on the overall battery life, in that there are more cells to supply power. More cells will only result in higher values of either V or Ah and thus affecting the over all Watt-hour value.
Making Sense of it all
No one is really going to calculate exactly how much a battery is going to power their laptop. To make a simple comparison of all the different types of batteries is to best compare Watt-hours (Wh), since this takes into effect both voltage and milli-Amp hours, and doesn't matter the amount of cells within the battery.
Note: most, but not all, batteries have the same voltage for a particular model of laptop, so if your feeling lazy a look at simply mAh sometimes can be sufficient
Finally you must realize that this comparison is only valid for two batteries that are of the same age. An older battery with a higher Wh is going to perform less than a brand new battery of equal Watt-hour value. Also known to affect battery life is the surrounding temperature of the battery.
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