Is sizeof a function or an operator?

Question

Why do we say sizeof(variable) is an operator, not a function?

It looks like a function call and when I am thinking about the meaning of operator, it appears to me something like + or - or * and so on

Answer 1

It's an operator, and you don't need to use brackets, except "when the operand is a type name, it must be enclosed in parentheses". This is a syntax restriction, but should not be confused with a function call.

See the last example below from the GNU documentation:

size_t a = sizeof(int);
size_t b = sizeof(float);
size_t c = sizeof(5);
size_t d = sizeof(5.143);
size_t e = sizeof a;

Without parentheses for a type name, you may see an error like this, with the gcc compiler:

test.c:7:20: error: expected expression before ‘int’
    7 |  size_t s = sizeof int;
      |                    ^~~

But doing sizeof 12 or sizeof a is fine.

Answer 2

It's an operator because it doesn't take arguments like a function does. It operates at the syntax level.

f(int) is not a valid function call, but sizeof(int) is a valid use of sizeof.

It can also operate on variables or types, it's quite flexible by design, which is something an operator can do as it's baked deep into the C syntax.

More details can be found here.