There are a few different ways to 'measure' batteries, here are the ones I will be comparing
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Size
This is pretty straight forward, how big are the batteries? Lead acid batteries don't get much smaller than C-cell batteries. Coin cells don't get much larger than a quarter. There are also standard sizes, such as AA and 9V which may be desirable. -
Weight and power density
This is a performance issue: higher quality (and more expensive) batteries will have a higher power density. If weight is an important part of your project, you will want to go with a lighter, high-density battery. Often this is expressed in Watts-hours per Kilogram. -
Price
Price is pretty much proportional to power-density (you pay more for higher density) and proportional to power capacity (you pay more for more capacity). The more power you want in a smaller, lighter package the more you will have to pay. -
Voltage
The voltage of a battery cell is determined by the chemistry used inside. For example, all Alkaline cells are 1.5V, all lead-acid's are 2V, and lithiums are 3V. Batteries can be made of multiple cells, so for example, you'll rarely see a 2V lead-acid battery. Usually they are connected together inside to make a 6V, 12V or 24V battery. Likewise, most electronics use multiple alkalines to generate the voltage they need to run.
Don't forget that voltage is a 'nominal' measurement, a "1.5V" AA battery actually starts out at 1.6V and then quickly drops down to 1.5 and then slowly drifts down to 1.0V at which point the battery is considered 'dead'. -
Re-usability
Some batteries are rechargable, usually they can be recharged 100's of times.
