My PC is on the bench so the front case fan (a 120mm Noctua) around 12 inches from my right ear and the Wraith Spire is silent when you are just surfing etc. My front case fan at the slowest speed makes more noise (a very low hum). Under maximum load when everything spins up it makes some noise but it isn't deafening, i'm running the CPU-z stress test as i write this (processor is at 56.4c) and i still comfortably hear the radio which is 5 feet to my left, i can mainly hear air rushing in to the case because the front fan has spun up, when i walked about 8 feet away i couldn't hear the PC over the radio.
Playing X-Com on the highest settings at 1080p with a lowly GTX 750Ti is runs at 150fps and no fans spin up at all. That said it isn't the worlds most taxing game is it.