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Me and my dad have a disagreement about this. He thinks that if a person had a larger skull they would naturally have a larger brain. I think that he is assuming the evolutionary trend holds on an individual scale and that it is odd to assume that they would be correlated.

We are having a hard time finding information on the topic as everything is about skull or brain size when related to intelligence. Sorry if this is not the right place to ask this, please direct me to the right place if I have misjudged.

Who is right?

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As a disclaimer, first please remember that brain size is only partially related to intelligence, and that whenever this comes up with regards to humans you should remember the long and ongoing history of badly-justified racism on the topic. So let's ignore intelligence, and just focus on brains and skulls.

If a person has a bigger skull, then they have a bigger volume inside that skull (neglecting the question of thickness). There's not really much inside the skull besides the brain (average volume ~1350 $cm^3$) and the cerebrospinal fluid (average volume ~125 $cm^3$). There's quite a bit of difference in size between skulls (men's brains are on average ~200 $cm^3$ bigger than women's brains, and individual variation large as well). Folks with big heads don't have their brains sloshing around in massive amounts of cerebrospinal fluid (and it would be quite dangerous if they did!): that space is filled with brain.

Bottom line: in humans, a bigger skull generally means a bigger brain.

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