I was just wondering in general relativity how you would be able to calculate how strong gravity is? I know that you can calculate spacetime curvature, but how do you calculate the force of gravity in general relativity?

What you actually calculate from a given state of an object (position and velocity) and a known spacetime structure is the acceleration on the object. The relevant equation is called the "geodesic equation". The concept of forces as in "F=ma" is mostly used in non-relativistic, non-QM physics.

In GR gravity isn't actually a force. Geodesic motion is "natural" motion, i.e. the motion that something exhibits if there are no forces around to mess with it. You can find things like "the normal force required to keep an object on the surface of the Earth" through a slightly tedious calculation of proper acceleration by taking the magnitude of four-acceleration. But "force of gravity" has no real meaning in GR.

But then what would the acceleration be of an object in a gravitational field in general relativity?

Edited August 7, 201312 yr by Endercreeper01

But then what would the acceleration be of an object in a gravitational field in general relativity?

I did in fact mention the term "geodesic equation" on purpose. Google it, look it up on Wikipedia, check this this text (eq. 31), ... .