Black Hole Size Calculator

Schwarzschild Radius Formula:

\[ R_s = \frac{2 G M}{c^2} \]

Schwarzschild Radius (Event Horizon):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Schwarzschild Radius?

The Schwarzschild radius is the radius of the event horizon of a black hole. It represents the boundary beyond which nothing, not even light, can escape the gravitational pull of the black hole. This concept was first derived by Karl Schwarzschild in 1916 as a solution to Einstein's field equations of general relativity.

2. How Does the Calculator Work?

The calculator uses the Schwarzschild radius formula:

\[ R_s = \frac{2 G M}{c^2} \]

Where:

\( R_s \) — Schwarzschild radius (meters)
\( G \) — Gravitational constant (6.674 × 10⁻¹¹ m³/kg s²)
\( M \) — Mass of the black hole (kilograms)
\( c \) — Speed of light in vacuum (299,792,458 m/s)

Explanation: The formula shows that the size of a black hole's event horizon is directly proportional to its mass. Doubling the mass doubles the Schwarzschild radius.

3. Importance of Schwarzschild Radius Calculation

Details: Calculating the Schwarzschild radius is fundamental in astrophysics for understanding black hole properties, gravitational physics, and testing theories of general relativity. It helps determine the minimum size an object must be compressed to form a black hole.

4. Using the Calculator

Tips: Enter the mass in kilograms. The gravitational constant and speed of light are pre-filled with standard values but can be modified if needed. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What happens at the Schwarzschild radius?
A: The Schwarzschild radius marks the event horizon - the point of no return where the escape velocity equals the speed of light.

Q2: Can anything escape from inside the Schwarzschild radius?
A: No, according to general relativity, nothing can escape from within the event horizon, not even light or information.

Q3: What is the Schwarzschild radius of Earth?
A: For Earth's mass (5.972 × 10²⁴ kg), the Schwarzschild radius is approximately 8.87 millimeters.

Q4: What is the Schwarzschild radius of the Sun?
A: For the Sun's mass (1.989 × 10³⁰ kg), the Schwarzschild radius is approximately 2.95 kilometers.

Q5: Do all black holes have the same density?
A: No, the average density decreases with increasing mass. Supermassive black holes can have densities less than water.