What is the return type of sizeof operator?

C++11, §5.3.3 ¶6

The result of sizeof and sizeof... is a constant of type std::size_t. [ Note: std::size_t is defined in the standard header (18.2). — end note ]

You can also do a quick check:

#include <iostream>
#include <typeinfo>
#include <cstdlib>

int main()
{
    std::cout<<(typeid(sizeof(int))==typeid(std::size_t))<<std::endl;
    return 0;
}

which correctly outputs 1 on my machine.

As @Adam D. Ruppe said in the comment, probably the compiler does not complain because, since it already knows the result, it knows that such “conversion” is not dangerous