I'm building an electric skateboard and the speed controller is supposed to be connected with a 25v 2000mah battery. If I connect my 25v 6450mah battery too it will it damage the speed controller or the motor? I know voltage is really what I should worry about, but something feels off about the wattage going up by so much.

 

No. Check the units. "mah" stands for milliampere hours, and it is a measure of battery capacity. Battery capacity has nothing whatever to do with watts. Watts are determined exclusively by the load. For example, your 2000 mah battery can supply 2000 mA for 1 hour, or 200 mA for 10 hours, or 20 mA for 100 hours. What you don't know is the voltage after those discharge periods. They may or may not be the same. Some batteries object to being rapidly discharged, others don't. Get the picture?

 

Oh ok, so from what your saying is that assuming it doesn't discharge the battery too quickly I should be ok?
Thanks for the quick response!

 

Here's an oldie but a goodie. Written just for you.
https://forum.allaboutcircuits.com/threads/ohms-law-for-noobies-or-the-amp-hour-fallacy.69757/

 

You can think of it like putting a 3 times larger fuel tank on the skateboard. As long as the voltage is the same and the new battery is designed to supply the current required by the motor, you can now go 3 times longer.