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From my knowledge, a big mass (planet star etc) can bend the fabric of spacetime. Is there a formula that we can use to work out how much it bends?

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It's not really a fabric, but anyway: yes, that formula is the Einstein field equation,

$$G^{\mu\nu} = \frac{8\pi G}{c^4} T^{\mu\nu}$$

Here $T^{\mu\nu}$ is the stress-energy-momentum tensor, a collection of 10 numbers which describe the contents of space, and $G^{\mu\nu}$ is the Einstein tensor, a function of the metric tensor, which is a collection of 10 numbers that describe the "shape" of spacetime. Whatever quantity you would like to use (for example, the scalar curvature) to characterize the amount by which spacetime is "bent," you can calculate it from the metric tensor.

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