The basic formula used in analyzing _thin-walled spherical pressure vessel_ is:

stress = PD / 4t

where P is the pressure inside or outside, D is the inner diameter, and t is the wall thickness.

therefore:

t = PD / [(allowable stress of the material) * 4]

Note that this formula is only applicable if D/t >= 10

Note also that allowable stress in acrylic is 10,000 psi @ **room temperature**. This changes when you submerge this in water, so might want to consider this too.
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Edit:
The unit of measurement in the formula is:

For English system: stresses should be in _pounds per sq.inch (psi)_ while dimensions should be in _inches (in.)_

For SI system: stresses should be in _megaPascal (MPa)_, and dimensions should be in _millimeters (mm)_