To calculate the factorial of a positive integer, you can use a simple loop to multiply the integer by all the positive integers less than itself. The factorial of 0 is defined to be 1. Here's a sample C++ program to calculate the factorial:

#include <iostream>
using namespace std;

int main() {
    int num;
    cout << "Enter a positive integer: ";
    cin >> num;
    int factorial = 1;
    for (int i = 1; i <= num; ++i) {
        factorial *= i;
    }
    cout << "The factorial of " << num << " is: " << factorial << endl;
    return 0;
}