retrolefty:
Yes that can be plugged directly into the external DC power connector on the mega board.Lefty
Even though this is true I would add a note based on personal experience.
The recommended voltage for Arduino Mega is 7-12V. A fully charged Lead acid battery holds 14.4V.
The input voltage limits are 6-20V.
This is not taking into account additional hardware attached to your arduino. So if you just have a mega running to see the led flash you are 200% OK. If you add an ethernet shield and some motorshields you may run into troubles.
In other words. Yes you can run from a 12 volt led acid battery. But when you have lots of power consuming shields or power consuming additional electronics the Mega may get overheated. In this case make sure your mega gets enough cooling (no closed box or walls around the mega, have it ly down on its long side, use a ventilator) or better use a switching regulator and power with a modified USB cable. The last option will make your solution run 2 times longer.
Note that it is the power converter on the board that gets (to?) hot.
Practically. Use the battery and have a feel from time to time to verify whether your power consumption is sustainable.
Best regards
Jantje