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) / 1000Mass (solar masses)
mass_solar = mass / 1.989e30Variables
| Variable | Description | Default |
|---|---|---|
mass | Black 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
- 01r_s = 2 G M / c²
- 022 × 6.674e-11 × 1.989e30 = 2.654e20
- 03c² = (2.998e8)² = 8.988e16
- 04r_s = 2.654e20 / 8.988e16 ≈ 2953 m ≈ 2.95 km
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