I had a realization yesterday...something I forgot because it has been ages since I installed a GPU...is my power supply up to the task?

It is a 360W PSU. My new card recommends a 450W. I see that manufacturers give a pretty wide variance, but I do not want to risk damage so I am wondering if I should get maybe a 500W. Any thoughts if it really matters? I only want to play FFXIV in a blaze of glory in the metaphorical sense, not the literal one.