How does the size of a cube area of effect work?

I was wondering what exactly does X-foot cube mean in a spells range description.

Let's look Thunderwave for example. It says:

A wave of thunderous force sweeps out from you. Each creature in a 15-foot cube originating from you must make a Constitution saving throw.

We took that to mean, all points a square 15 feet from the caster. Or does it mean a 15×15 foot square with the caster in the middle?

Let P be the player and X a 5 foot block that the spell affects.

We decided it to be:                    Or is it Really:

     xxxxxxx                        xxx
xxxxxxx                        xPx
xxxxxxx                        xxx
xxxPxxx
xxxxxxx
xxxxxxx
xxxxxxx


It's not quite your first option, but you do have a lot more choices than your second option. In particular, the caster does not need to be at the center of the cube.

15 foot cube means 15 feet is the length of a side. "Originating from" puts the origin anywhere on any face of the cube, which I take to mean it could be along the bottom side or on a corner (or mere inches from a corner).

So it could be any of these options, or slide it around pretty much anywhere, so long as the cube is 15×15×15. And if you're not working with a grid, go ahead and rotate it however you want.

XXX  XXX  XXX
XXX  XXX  XXX
XXX  XXX  XXX
P  P  P

XXX  XXX  XXX
XXXP XPX PXXX
XXX  XXX  XXX

P  P  P
XXX  XXX  XXX
XXX  XXX  XXX
XXX  XXX  XXX


Note that the center option would work if you put the point of origin along the bottom face of the cube.

For the exact text, see page 204 of the PHB.

• Note that unless the caster is creating the cube above them, centering the cube puts the caster inside the cube, and subject to damage. – T.J.L. Mar 2 at 18:54