Schwarzschild Radius Calculator
Calculate the Schwarzschild radius — the critical radius at which a mass becomes a black hole. If an object is compressed within this radius, not even light can escape its gravitational pull.
Formula
rs = 2GM / c²
- rs — Schwarzschild radius (m)
- G — Gravitational constant = 6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻²
- M — Mass of the object (kg)
- c — Speed of light in vacuum = 2.99792458 × 10⁸ m/s
This formula is derived from Karl Schwarzschild's 1916 exact solution to Einstein's field equations of general relativity for a non-rotating, spherically symmetric mass.
Assumptions & References
- The object is assumed to be non-rotating and uncharged (Schwarzschild metric). Rotating black holes require the Kerr metric; charged ones require the Reissner–Nordström metric.
- The result is the event horizon radius — the boundary inside which escape velocity exceeds the speed of light.
- Gravitational constant G = 6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻² (NIST CODATA 2018).
- Speed of light c = 299,792,458 m/s (exact, by SI definition).
- 1 Solar Mass (M☉) = 1.98892 × 10³⁰ kg; 1 Earth Mass (M⊕) = 5.97219 × 10²⁴ kg.
- The Schwarzschild radius of the Sun ≈ 2.953 km; of the Earth ≈ 8.871 mm.
- Reference: Schwarzschild, K. (1916). Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie. Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften.