Raio Schwarzschild
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
About this calculator
The Schwarzschild radius calculator determines the theoretical radius of a black hole's event horizon using the formula r_s = 2GM/c². This value represents the boundary beyond which gravity prevents anything, including light, from escaping. Simply input the celestial object's mass in kilograms to get the radius in meters.
The formula incorporates the gravitational constant (G = 6.674×10⁻¹¹ N·m²/kg²) and the speed of light (c = 3×10⁸ m/s). Multiplying 2 by G and the mass (M), then dividing by the speed of light squared, yields the Schwarzschild radius. This is a fundamental calculation in astrophysics for black hole studies.
Use this tool for academic research, simulation projects, or understanding phenomena like black hole formation. Note: the result is a static approximation that ignores factors like object rotation (real black holes have Kerr radii) or electric charge, which require more complex models.
Example: For the Sun (mass ≈ 1.989×10³⁰ kg), the Schwarzschild radius is about 2.95 km. This doesn't mean the Sun becomes a black hole - it shows the critical radius if all its mass were compressed to that limit. Useful for comparing hypothetical celestial objects.
Frequently asked questions
Why is it called the Schwarzschild radius?
German physicist Karl Schwarzschild developed the exact solution for general relativity in 1916, describing ideal black holes. The radius is named after him in recognition of this pioneering work.
How does mass affect the Schwarzschild radius?
The radius increases linearly with mass. An object twice as massive will have a Schwarzschild radius twice as large, assuming the same density conditions.
What happens if an object exceeds its Schwarzschild radius?
If a physical object (like a star) collapses within its own Schwarzschild radius, it forms a black hole, with the singularity at the center and the event horizon as the visible boundary.
Does this calculator work for any type of mass?
Yes, but only for static spherical objects. For real black holes (with rotation or charge), use other formulas like the Kerr radius or Reissner-Nordström radius.