How can you tell if Roblox is down or it's just your connection?

quick test: open roblox on your phone on mobile data, wifi off. if it fails there too, it's roblox. if it works, it's your connection or your pc.

Roblox runs its own status page, search roblox status and it's the first result. It's not always instant though, so if that says fine and you still can't join, check one of the outage tracker sites where players report problems, a big spike there is usually faster than the official page. If other sites and games work fine, don't touch the router.