Appeal

Isn't it the current year 7 that's over by 1? So even if they were under that wouldn't help as those year 7s will be year 8 when OP's child would be due to start.

Oh and yes as the above poster notes, 5*180 = 900, suggesting the 6 th form
Is not included and they are currently under by 19 overall. But over in year 7, which is your issue.

Surely if the PAN is 180 then across five years you get 900 so it would be for those 5 years and across the 5 years they have 19 spaces. But none for Y7.
I don't think just picking at the numbers will win an appeal. The panel need to understand why the school needs to exceed the PAN further for your child rather than the other children wanting a place.

The sixth form can be included yes, but you would need the actual number in the current sixth form (years 12 and 13) to understand current numbers not the PAN.

A PAN of 30 would lead to 60 pupils in 6th form which seems low; this is more likely to be the PAN for those admitted from other schools I think, with the actual number on role higher. This may mean that the 6th form is not included in the net capacity as it would mean the school was significantly over net capacity if they are included. You need to check.

Either way, your problem is more that the year you want entry to is already over by 1. The schools case is more likely to focus on why adding another child to this year would be prejudicial to the education of pupils in that year. The fact that not all years are full doesn't make squeezing 32 into classrooms designed for 40 any easier.

If the sixth form is included in the PAN then it's included. You'd need to verify that with the school. In my area the sixth form is a different entity, but I'd be surprised if that was the case with just 30 students.

Looking at the figures though, I can't see your argument being successful. The "spare" places are in the upper years, there's no spare capacity in year 7 and that's what matters for your child as they need to be in the classroom with their own year group.

Do you know how many others are appealing? Unless you have other circumstances I'd say your only chance of success is if there are sufficient children (and space) for an additional class.