How to calculate if an asteroid will hit the earth?

There is essentially no chance of any given asteroid ever hitting the Earth, because those with orbits that made them likely to hit the Earth have already hit the Earth. So it's not something you really need to worry about.

If you're just curious... well, really, you don't want to know that badly. It comes down to solving n-body gravitational equations, and for any reasonably sized n (i.e. larger than, say, 3) there is no known exact solution except in special cases, so you have to use numerical methods and hope the interesting bits don't get lost in rounding errors.