Schwarzschild Radius Calculator

The Schwarzschild radius is the critical radius at which, if a given mass were compressed, it would form a black hole. The event horizon is the surface at this radius from which nothing, not even light, can escape. Formula: r_s = 2*G*M/c^2, where G = 6.674e-11 N*m^2/kg^2, M is mass, c = 2.998e8 m/s. For the Sun: r_s = 2.95 km. For Earth: r_s = 8.87 mm.

The event horizon is the boundary of a black hole beyond which events cannot affect an outside observer. At the Schwarzschild radius, the escape velocity equals the speed of light. Once an object crosses the event horizon, no information about it can reach the outside universe. The event horizon is not a physical surface; an infalling observer would not notice anything special when crossing it (in their local reference frame).

A mass becomes a black hole when compressed below its Schwarzschild radius. The critical density for collapse is: rho = 3*M / (4*pi*r_s^3) = 3*c^6 / (32*pi*G^3*M^2). For a stellar mass black hole (M = 10 solar masses): critical density is roughly 2e17 kg/m^3 (nuclear density). For a supermassive black hole (M = 10^9 solar masses): the critical density is much lower, comparable to water.

The Planck length (l_P = sqrt(hbar*G/c^3) = 1.616e-35 m) is the scale at which quantum gravitational effects become important. The Schwarzschild radius of a Planck mass (2.18e-8 kg) equals twice the Planck length. Below this scale, general relativity and quantum mechanics must be unified (quantum gravity). Current physics cannot describe the singularity inside a black hole at scales below the Planck length.

Stephen Hawking predicted that black holes radiate thermally due to quantum effects near the event horizon: T_H = hbar*c^3 / (8*pi*G*M*k_B), where k_B = 1.38e-23 J/K (Boltzmann constant) and hbar = 1.055e-34 J*s. For a solar-mass black hole, T_H is about 6e-8 K, essentially zero. For a Planck-mass black hole, T_H is about 7e32 K. Lighter black holes are hotter.