Question

How would you know if a cyclic organic molecule is planar?

Answer 1

When you look at the structure of a six-membered ring, if all the molecular geometries around each atom in the ring are `\mathbf(sp^2)`-hybridized, then the whole molecule is planar.

It's not always the case for rings of other sizes, but for six-membered rings, it usually is true.

...But if all bonds have 100% restricted rotation AND are restricted to be in one plane, then it's even more likely that it IS planar (even if one atom appears to not be `sp^2`-hybridized...). Pyrrole, furan, and thiophene are interesting five-membered ring examples of this.

With five-membered rings, having one heteroatom in addition to four `sp^2`-hybridized atoms helps, especially if that heteroatom has a smaller valency than carbon, but it doesn't guarantee anything.

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Here are a few examples of planar and non-planar six-membered rings.

Notice how the ring gets more planar with an increasing number of `sp^2` carbons. That usually is how it goes, but not always.

For five-membered rings, it's harder to find examples, but here are some examples that may contain heteroatoms:

For rings with more than six members, it becomes less likely that all `sp^2`-hybridized ring atoms is the only requirement for planarity. Here's an example of a non-planar molecule with all seemingly-`sp^2`-hybridized carbons in its flat structure:

Its actual structure is:

So how would you actually know for sure? Do some X-ray crystallography or X-ray diffraction and determine the structure.