counting letters in a string, excluding spaces

[dunnDolphin]

I'm trying write a bit of code that will count the number of letters in a name (first, middle, last) but not count the spaces. What I have here almost work, but it seems to ignore only the first space. (Yes, it also prints the name back words - silly I know).

#include <iostream>
#include <string>

int x;
int char_count = 0;

using namespace std;

int main ()
{
    string user_name;

    cout << "To see your name spelled backwards, enter your";
    cout<< " name here: " << endl;
    getline(cin, user_name);

    for (x = user_name.length()-1; x <= user_name.length(); --x)
    {
    cout << user_name.at(x);
    char_count++;

    if ( x == '\n')
    char_count--;

    }

    cout << "\n"<< char_count << " letters\n" << endl;


    return 0;
}

To see your name spelled backwards, enter your name here: 
Bill W Smith
htimS W lliB
11 letters

[LendraDwi]

if(name.at(x)==' ')continue

[anup30]

int len = user_name.length();
for ( int i=0; i< user_name.length(); i++ )
if ( user_name[i] == ' ') len--;

[dunnDolphin]

Thanks you!