Calculate the Schwarzschild Radius of a Black Hole
Calculator for the radius of a black hole's event horizon from its mass. Every mass has a Schwarzschild radius to which it would have to shrink to become a black hole. The event horizon is the limit beyond which nothing can escape the black hole's gravitational force, including light, which is why it is black.
The Schwarzschild radius is calculated as
In practice, this formula is often used for the radius in meters and the mass in kilograms, which also this calculator uses:
Examples: the earth as a black hole would have a radius of almost 9 millimeters, the sun almost 3 kilometers. A human would have a radius of about a tenth of a yoctometer (∼ 0.1 * 10-24 m).
The Schwarzschild radius is a simplification and applies to black holes that do not rotate and are uncharged, i.e., electrically neutral. The first property, in particular, will be difficult to find in reality, since celestial bodies generally have a strong tendency to rotate.
The event horizon is a boundary in space and time; it is described by the general theory of relativity, which Albert Einstein developed in 1915. For every object with a mass greater than or equal to the Planck mass, i.e., 0.00000002176 kilograms, there is a theoretical Schwarzschild radius. If the object with this mass were smaller than a sphere with this radius, it would become a black hole. The smaller the volume of a black hole, the higher its density; very massive black holes have densities in the range of normal matter and below. Sagittarius A*, for example, the black hole at the center of our Milky Way, with 4.2 million solar masses and an event horizon of 24.5 million kilometers, has a density about four times that of water, more than aluminium, less than titanium or iron.
Last updated on 06/30/2025. Author: Jürgen Kummer
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