For information about the mass-luminosity relationship, click here.

This calculator can solve for radius or mass.

What is the event horizon of a black hole with 10 solar masses?
Click “Radius” then enter “10” in the “Enter Star Mass” box.
Click calculate and the Schwarzchild Radius is
29,533 meters or 29.533 kilometers.

What is the mass of a black hole that has an event horizon of 25 kilometers?
Click “Mass” then enter “25” in the “Enter Schwarzchild Radius” box.
Click “Calculate” and the answer is 8.4652 solar masses or 1.6833 x10³¹ kilograms.

Before we discuss the Schwarzchild radius, we first should discuss black holes.
A star spends a great deal of its life fusing hydrogen into helium. In order to do this, a star must possess a gigantic amount of mass (and thefefore gravity) to produce the tremendous temperature and pressure required for nuclear fusion.

In fact, a star with a mass that is less than 1.60 x 10³¹ kilograms (.08 the mass of the Sun) will never produce sufficient gravity to fuse hydrogen into helium.
When a star begins the process of nuclear fusion this produces the light we see from our own Sun and all the stars we see in the sky.
Nuclear fusion also creates the energy to provide an outward pressure, preventing a star from collapsing into itself due to its own gravity.
As long as the star has enough fuel to produce this outward pressure, a star will continue to exist.

When a star runs out of nuclear “fuel”, the outward pressure declines and the star undergoes gravitational collapse.
Depending upon how much mass the star has, this collapse can lead to dramatically different outcomes.

A star with a mass .08 to .50 of the Sun, becomes a white dwarf.

A star with a mass .50 to 1.5 of the Sun increases in size, becoming a red giant, forming a planetary nebula, finally becoming a white dwarf.

A star with a mass 1.5 to 3.2 of the Sun increases in size, becoming a red super giant, then turns into a supernova. When a star’s mass is this great, the gravitational collapse produces so much force that atoms can no longer exist and they become neutrons. Hence, a neutron star is formed. If the neutron star is rapidly rotating, then it is a pulsar.

When a star has a mass of 3.2 Suns (or greater), the gravitational collapse creates a red super giant, then the star turns into a supernova. As the star collapses, the gravitational pressure becomes so intense that not even neutron structure can be retained and the star becomes a black hole, whereby the escape velocity is greater than the speed of light and not even light itself can escape that fierce gravitational field.

The Schwarzchild radius is named after Karl Schwarzchild (1873 – 1916), a German astronomer who was the first to formulate this concept.
When a star becomes a black hole, it has actually become a gravitational singularity surrounded by an event horizon.
The gravitational singularity is something we cannot describe with the usual physical dimensions because it has no physical dimension at all and its density is infinite!
What we can describe is the event horizon which surrounds the gravitational singularity.
The event horizon is not a physical object but it is rather a sphere in which light may enter but cannot escape.

Solar Diameter = 1.39 x 10⁹ meters.

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