Schwarzschild Radius Calculator

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Expert Verified by: David Chen, Physics Researcher & Data Analyst

The Schwarzschild Radius Calculator is a specialized physics tool designed to determine the event horizon of a non-rotating black hole based on its mass. Whether you are calculating the singularity threshold for a star or a planet, this tool provides precise astronomical results.

Schwarzschild Radius Calculator

Leave empty to solve for Radius.
Leave empty to solve for Mass.
Enter one variable to calculate the other.

Schwarzschild Radius Formula:

$$R_s = \frac{2GM}{c^2}$$

Source: Wikipedia – Schwarzschild Radius | NASA – Black Holes

Variables:

  • $R_s$: The Schwarzschild Radius (the radius of the event horizon) in meters.
  • $G$: Gravitational Constant ($\approx 6.67430 \times 10^{-11} \text{ m}^3\text{kg}^{-1}\text{s}^{-2}$).
  • $M$: The Mass of the object in kilograms.
  • $c$: The Speed of Light in a vacuum ($\approx 299,792,458 \text{ m/s}$).

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What is a Schwarzschild Radius Calculator?

The Schwarzschild radius calculator is a tool used to find the physical threshold at which an object’s mass would be so compressed that its escape velocity equals the speed of light. This boundary marks the “point of no return,” or the event horizon of a black hole.

By understanding the Schwarzschild radius, scientists can predict the size of event horizons for stars of different masses, including supermassive black holes at the center of galaxies and theoretical primordial black holes.

How to Calculate Schwarzschild Radius (Example):

  1. Identify the mass of the object (e.g., Earth’s mass is $5.972 \times 10^{24} \text{ kg}$).
  2. Multiply the mass by $2G$ ($2 \times 6.674 \times 10^{-11}$).
  3. Divide the result by the square of the speed of light ($c^2$).
  4. For Earth, the result is approximately $0.00887 \text{ meters}$, or about 9 millimeters.

Frequently Asked Questions (FAQ):

What happens if a star is smaller than its Schwarzschild radius? It becomes a black hole because its gravity is strong enough to prevent light from escaping.

Does every object have a Schwarzschild radius? Yes, every object with mass has a theoretical Schwarzschild radius, but only extremely dense objects can reach it.

Can the radius be negative? No, mass and distance are physical values that must be positive in this context.

How does mass affect the radius? The relationship is linear; doubling the mass of an object will double its Schwarzschild radius.

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