The Schwarzschild radius in astrophysics defines the radius of a black hole beyond which nothing, not even light, can escape the gravitational pull. It is derived from the solutions to Einstein's field equations in general relativity. The formula for calculating the Schwarzschild radius (r) is r = 2GM/c², where G is the gravitational constant, M is the mass of the object, and c is the speed of light. Understanding this concept is crucial in astrophysics, as it helps describe the behavior and characteristics of black holes and their effects on surrounding matter and energy.