Schwarzschild Radius Calculator
Calculate black hole event horizon radius and gravitational field strength
Black Hole Calculator
Mass of the object that could form a black hole
Black Hole Properties
Enter mass to calculate black hole properties
Example Calculation
Solar Mass Black Hole
Mass: 1 Solar Mass = 1.989 × 10³⁰ kg
Gravitational constant (G): 6.674 × 10⁻¹¹ N⋅m²⋅kg⁻²
Speed of light (c): 2.998 × 10⁸ m/s
Calculation
rs = 2GM/c²
rs = 2 × (6.674 × 10⁻¹¹) × (1.989 × 10³⁰) / (2.998 × 10⁸)²
rs = 2.653 × 10²⁰ / 8.988 × 10¹⁶
rs = 2.95 km
Black Hole Physics
Event Horizon
Boundary where escape velocity equals light speed
Singularity
Point of infinite density at the center
Spacetime Curvature
Extreme warping of space and time
Black Hole Facts
Nothing can escape from inside the event horizon
Time appears to stop at the event horizon for outside observers
Stellar black holes: 3-20 solar masses
Supermassive black holes: millions to billions of solar masses
Earth's Schwarzschild radius would be ~9 mm
Understanding the Schwarzschild Radius
What is the Schwarzschild Radius?
The Schwarzschild radius is the radius of the event horizon of a black hole - the boundary beyond which nothing, not even light, can escape. It's named after Karl Schwarzschild, who derived this solution to Einstein's field equations in 1916.
Physical Significance
- •Defines the "point of no return" around a black hole
- •At this radius, escape velocity equals the speed of light
- •Marks the boundary of the observable universe around a black hole
- •Determines the "size" of a black hole
The Schwarzschild Formula
rs = 2GM/c²
- rs: Schwarzschild radius (event horizon radius)
- G: Gravitational constant (6.674 × 10⁻¹¹ N⋅m²⋅kg⁻²)
- M: Mass of the black hole
- c: Speed of light in vacuum (2.998 × 10⁸ m/s)
Important: The Schwarzschild radius is proportional to mass - doubling the mass doubles the radius.
Formation of Black Holes
Black holes form when massive stars (typically > 25 solar masses) collapse at the end of their lives. When the core can no longer support itself against gravity, it collapses to a point of infinite density.
- • Stellar black holes: 3-20 solar masses
- • Intermediate black holes: 100-100,000 solar masses
- • Supermassive black holes: millions to billions of solar masses
- • Primordial black holes: any mass (theoretical)
Gravitational Effects
Near a black hole, gravitational effects become extreme. The gravitational acceleration at the event horizon is given by g = c⁴/(4GM), which depends inversely on the mass.
Paradox: Larger black holes have weaker gravitational fields at their event horizons. A supermassive black hole's event horizon might feel like gentle gravity!