Schwarzschild Radius Calculator

Calculate the Schwarzschild radius (event horizon) of a black hole from its mass. Includes solar mass presets, Hawking temperature, photon sphere, ISCO, and tidal forces.

kg
Schwarzschild Radius
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Schwarzschild Radius —
In Astronomical Units —
Extended More scenarios, charts & detailed breakdown ▾
kg
Schwarzschild Radius (m)
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Schwarzschild Radius (km) —
Professional Full parameters & maximum detail ▾
M☉

Key Radii

Schwarzschild Radius —
Photon Sphere (1.5 r_s) —
ISCO (3 r_s) —

Physical Properties

Hawking Temperature —
Mean Density at r_s —

How to Use This Calculator

  1. Enter the black hole mass in kg or use the solar masses tab.
  2. Use Famous Black Holes tab for Sgr A*, M87*, and stellar-mass examples.
  3. Professional tier adds Hawking temperature, photon sphere, ISCO, and density at the Schwarzschild radius.

Formula

r_s = 2GM/c²  |  G = 6.67430×10⁻¹¹, c = 299792458 m/s

Photon sphere: r_ph = 1.5 × r_s  |  ISCO: r_ISCO = 3 × r_s

Hawking T = ℏc³ / (8πGMk_B)

Example

Sgr A* (4.3×10⁶ M☉): r_s = 2 × 6.674×10⁻¹¹ × (4.3×10⁶ × 1.989×10³⁰) / (299792458)² ≈ 1.27×10¹⁰ m ≈ 12.7 million km

Frequently Asked Questions

  • The Schwarzschild radius r_s = 2GM/c² is the radius of the event horizon for a non-rotating black hole. If an object is compressed below its Schwarzschild radius, it becomes a black hole.
  • Earth's Schwarzschild radius is about 8.87 mm — roughly the size of a marble. If Earth were compressed to less than 9 mm diameter, it would become a black hole.
  • The Sun's Schwarzschild radius is about 2.95 km. If all the Sun's mass were compressed into a sphere less than 3 km across, it would form a black hole.
  • Hawking radiation is thermal radiation theorized to be emitted by black holes due to quantum effects near the event horizon. Temperature T_H = ℏc³/(8πGMk_B). Smaller black holes are hotter and evaporate faster.
  • ISCO stands for Innermost Stable Circular Orbit. For a Schwarzschild (non-rotating) black hole, ISCO = 3r_s = 6GM/c². No stable orbit exists closer to the black hole.

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Sources & References (5) ▾
  1. Event Horizon Telescope — M87* and Sgr A* Papers — Event Horizon Telescope Collaboration
  2. NASA Black Hole Resources — NASA
  3. NIST Physical Constants — G and c — NIST CODATA
  4. OpenStax Astronomy, Ch. 24: Black Holes and Curved Spacetime — OpenStax
  5. Thorne, K. — Black Holes and Time Warps (1994) — W. W. Norton / Kip Thorne