Schwarzschild Radius Calculator Formula

Understand the math behind the schwarzschild radius calculator. Each variable explained with a worked example.

Formulas Used

Schwarzschild Radius

radius = 2 * 6.674e-11 * mass / pow(299792458, 2)

Radius (km)

radius_km = 2 * 6.674e-11 * mass / pow(299792458, 2) / 1000

Mass (solar masses)

mass_solar = mass / 1.989e30

Variables

VariableDescriptionDefault
massBlack Hole Mass(kg)1.989e+30

How It Works

Schwarzschild Radius

The Schwarzschild radius defines the event horizon of a non-rotating black hole.

Formula

r_s = 2 G M / c²

For a solar-mass black hole, r_s ≈ 2.95 km. The radius scales linearly with mass.

Worked Example

A 1-solar-mass black hole (M = 1.989e30 kg).

mass = 1.989e+30
  1. 01r_s = 2 G M / c²
  2. 022 × 6.674e-11 × 1.989e30 = 2.654e20
  3. 03c² = (2.998e8)² = 8.988e16
  4. 04r_s = 2.654e20 / 8.988e16 ≈ 2953 m ≈ 2.95 km

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