Description: What is the Schwarzschild Radius?

The Schwarzschild radius ($R_s$) is a critical radius associated with any mass $M$. It defines the boundary of the event horizon of a non-rotating, non-charged black hole. If a celestial object’s entire mass were compressed to a sphere with a radius smaller than or equal to its Schwarzschild radius, it would become a black hole.

In essence, the Schwarzschild radius represents the distance from the center of the black hole at which the escape velocity equals the speed of light ($c$). Nothing—not even light—can escape once it crosses this boundary. It is directly proportional to the mass ($M$) of the object, as shown in the formula: $$R_s = \frac{2GM}{c^2}$$ The constant $G$ represents the Gravitational constant ($6.674 \times 10^{-11} , \text{N·m}^2/\text{kg}^2$). This simple relationship highlights why more massive stars produce larger black holes when they collapse.

How to Use the Calculator

1. Enter Mass: Input the mass of the celestial object ($M$) in kilograms (kg) into the designated field. You can use standard numbers (e.g., $5.972 \times 10^{24}$ for Earth’s mass) or scientific notation (e.g., 5.972e24 or 1.989e30 for the Sun’s mass).
2. Calculate: Click the “Calculate $R_s$” button.
3. Review Results: The tool will instantly display the step-by-step substitution into the Schwarzschild formula and the final calculated radius ($R_s$) in meters (m), rounded to two decimal places.