650w is a safe bet.
That GTX 1080 is rated for 180w with a 500w PSU recommendation.
In theory, you should be ok. In reality, your PC will probably use 1/3rd less than what you expected. Ether way, it's never a good idea to push a PSU past 85% it's rated capacity for a prolonged period of time.
A modern UPS or Kill A Watt meter (link below) will tell you what the draw is.
http://a.co/fKM4D4G