What is the most efficient way to get the actual allocated size in memory of std::map?

std::map provides an std::map::size function which only returns the number of elements.

Assuming an std::map of int/std::string pairs, one may get the actual allocated memory per pair using sizeof(int) and str.capacity() respectively and then sum them up per insert. This causes lots of overhead.

An alternative would be to take a random sample of pairs and num of elements to estimate the total capacity, optionally apply some theory of estimation (maximum likelihood, confidence interval).

I need some "capacity" function for the std::map. Is there a better way then the two approaches mentioned above?