How loud/obvious is a wizard casting a spell?

Question

Some spells have somatic and vocal components, that's well known.

How loud must a wizard talk? How obvious/wide should his gestures be?

Some spells that would be awesome would be fairly limited if you need to shout them (ex: mage hand, range 30ft).

Answer 1

There's no restriction on volume, but gestures are pretty obvious.

The Player Basic Rules p79 says:

Verbal: Most spells require the chanting of mystic words... the particular combination of sounds, with specific pitch and resonance.

Somatic: Spellcasting gestures might include a forceful gesticulation or an intricate set of gestures.

Note that volume is not listed as important. The wizard must speak loudly enough to clearly enunciate her mystic words; a low voice would work, but a whisper might not be clear enough. Gestures are either forceful or intricate, which would be pretty obvious if visible.

A Dexterity check using the Stealth or Sleight of Hand skills is the way to go if you want to speak clearly but quietly or if you want to hide forceful or intricate gestures. If the wizard doesn't care if anyone notices, don't bother with a check; nearby people notice, as appropriate to the story. If the wizard does care, she should make a check with the normal rules.

Answer 2

It is up to the DM, but the casting is noticeable

In 5e nowhere does it define anything specifically defining the volume of spells or how grand gestures have to be. These kinds of details are left entirely up to the DM to decide.

Verbal (V)

Most spells require the chanting of mystic words. [...] the particular combination of sounds, with specific pitch and resonance.

[...]

Somatic (S)

Spellcasting gestures might include a forceful gesticulation or an intricate set of gestures. [...]

This is all the detail we get from the rules. Clearly, gestures must be made and sounds must be produced, but the exact extent of beyond being audible and visible is not solidly layed out.

It is worth noting that the rules do even say that there is a potential range of how obvious the somatic component might be, so it may even depend on the spell.

Jeremy Crawford has shed some light on the intent for verbal components though (in an old unofficial tweet):

The verbal component of a spell must be audible to work. How loud is audible? That's up to the DM.

One thing is sure though: both the verbal and somatic components are definitely noticeable however. We know this because there is at least one class feature, a Sorcerer's Subtle Magic metamagic, whose only purpose is to make them not noticable:

When you cast a spell, you can spend 1 sorcery point to cast it without any somatic or verbal components.

In the end, your DM will have to decide how they want it to work in their world.

Answer 3

It would certainly depend on the spell, but I'd say most of the time he's obvious enough. Though there is no real guidance on this, all of the spell caster art has them being quite vociferous in their casting.

So if you want to make a perception check out of it, DC5 or so.

Now if a character were trying to cast a spell without being seen or heard (something the rules do not currently support), I'd make them make a stealth check prior to attempting the spell. This would effectively be them trying to cast while whispering and making more subtle motions. The DC of the spell would be the passive perception of all creatures around, and particularly bad failures may result in no spell being cast at all.