Schwarzschild Radius Calculator

The Schwarzschild radius is the radius at which a mass becomes a black hole. If compressed below r_s = 2GM/c^2, not even light can escape. Earth Schwarzschild radius is just 9 mm.

⚫ Black Holes📐 r = 2GM/c²🔭 Astrophysics
Mass (kg)
Or Solar Masses
Please enter valid values.

Formula & Reference

VariableSymbolFormulaUnits
Schwarzschild Radiusrsrs = 2GM/c²m
G constantG6.674 × 10⁻¹¹ N m²/kg²N m²/kg²
Speed of lightc2.998 × 10⁸ m/sm/s
Solar massM☉1.989 × 10³° kgkg

Step-by-Step Examples

Example 1
Sun as Black Hole

M = 1.989e30 kg (1 solar mass).

  • r_s = 2*6.674e-11*1.989e30/(2.998e8)^2
  • r_s = 2.953 km
✓ Sun would need compressing to ~3 km radius
Example 2
Earth

M = 5.972e24 kg.

  • r_s = 2*6.674e-11*5.972e24/(8.988e16)
  • r_s = 8.87 mm
✓ Earth Schwarzschild radius = 8.87 mm
Example 3
10 Solar Mass Black Hole

M = 10 solar masses.

  • r_s = 10 * 2.953 km = 29.53 km
✓ 29.5 km event horizon radius

Real-World Applications

⚫
Black Hole Physics
Defines event horizon — the point of no return for all matter and light.
📶
GPS Corrections
Gravitational time dilation near Earth (related to r_s) affects GPS satellite clock corrections.
🔭
Stellar Evolution
Stars above ~20 solar masses may collapse to black holes when nuclear fuel is exhausted.
🌀
Cosmology
Observable universe Schwarzschild radius is comparable to its actual size — a deep cosmological puzzle.

Common Mistakes to Avoid

⚠️
r_s is not the physical size

r_s is the radius IF compressed to a black hole. Normal objects are much larger than their r_s.

⚠️
Mass must be in kg

1 solar mass = 1.989e30 kg. Use solar masses input box for convenience.

⚠️
Non-rotating (Schwarzschild) black holes

Formula is exact only for non-rotating, uncharged mass. Rotating black holes require Kerr metric.

Frequently Asked Questions

What is the event horizon? ▾
The surface at r = r_s where escape velocity equals c. Nothing inside can escape, not even light.
What happens at the event horizon? ▾
To a distant observer, infalling objects appear to freeze there. The infalling observer notices nothing special locally — they cross it normally.
Do black holes grow? ▾
Yes. Absorbing mass increases M and proportionally increases r_s. Supermassive black holes (10^9 M_sun) have r_s larger than our solar system.
Can anything escape a black hole? ▾
Hawking radiation: quantum effects allow black holes to emit thermal radiation and slowly evaporate. For stellar black holes, this takes longer than age of universe.
What is primordial black hole? ▾
Hypothetical tiny black holes formed in early universe. A black hole of mass 10^12 kg has r_s = 1.5e-15 m (nuclear scale) and evaporates via Hawking radiation today.

Related Physics Calculators

🌍 Gravitational Force🚀 Escape Velocity🌍 Gravitational Time Dilation🛸 Orbital Energy⛛ Mass-Energy

Formula Explorer connections

Interpretation: This relationship connects mass, distance, orbit or spacetime behavior through gravitation and astrophysical scaling. Assumption: Many calculations assume spherical bodies, point masses, circular orbits, weak fields or Newtonian gravity; relativistic regimes require the stated correction.

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