C++ and Fortran interoperability

For my own entertainment I have decided to create a large scale physics engine. I have experience with Java and C++ but none with Fortran. My understanding of Fortran is that it is used in the scientific industry and is good for large calculations. I decided to use C++ for any gui, sound, user input, etc. that might be added while Fortran would handle the calculations. How easy is it to call Fortran methods from C++? I have googled the matter and haven't found much information. Despite not knowing Fortran I am determined to learn it no matter how strict the learning curve may be (assuming that I will get an appropriate performance increase). Is it practical to use Fortran in this way? Will I get a decent performance increase (for large calculations)? Is Fortran still used in the modern world or is it outdated?