Maybe you didn't read the OP's remark about his desire to run his Arduino from batteries. So you don't think that running an arduino off a 9-volt is not a good idea.
There are countless posts from people using 9V batteries, wondering why their projects don't work. Sure an Arduino by itself will last a long time on a 9V, but most projects add in a few LEDs or Motors which draw far more current than the Arduino.
Alkaline 9volt batt has 565 mAh and a lithium has 1200 mAh.
Capacity is directly related to how much current is actually being drawn. Take a look at this datasheet from Energizer:http://data.energizer.com/PDFs/522.pdf
1. It states 9V types are only good for Moderate Drain devices, like a clock.
2. As more current is drawn, the milliamp-hours goes down, fast.
3. Voltage drops below 7V (minimum for the on-board regulator to be stable), very quickly.
#3 is important because the 9V will have capacity left, but the output voltage will be too low to be usable.