Schwarzschild metric
The critical radius at which a massive body becomes a black hole, i.e., at which light is unable to escape to infinity: R_s = 2GM / c^2, where G is the gravitational constant, M is the mass, and c the speed of light. The formula can be approximated to R_s ≅ 3 x (M/M_sun), in km. Therefore, the Schwarzschild radius for Sun is about 3 km and for Earth about 1 cm.
Gravitational radius
Schwarzschild radius
Limiting radius of black hole