`R_S = (2* G * "M" ) / c^2`

Enter a value for all fields

The Schwarzschild Radius calculator computes the Schwarzschild Radius based on the mass (M) of the object (e.g. black hole), the speed of light and the universal gravity constant.

INSTRUCTIONS: Choose units and enter the following:

• (M) Mass of Star (or other celestial object)

Schwarzchild Radius (R_s): The calculator returns the radius in meters. However, this can be automatically converted to compatible units via the pull-down menu.

The Math / Science

The formula for the Schwarzschild Radius is:

R_s = 2•G•M / c²

where:

• R_s is the Schwarzschild radius
• G is the universal gravity constant
• M is the mass of the celestial object.
• c is the speed of light

The Schwarzchild Radius, R_S, is the radius defining the maximum size of a star necessary to create a black hole.  In other words, a mass must collapse to a size having a radius smaller than this radius to become a black hole.

Any mass with a radius less than the Schwarzchild Radius will have an escape velocity greater than the speed of light, so even light cannot escape it's gravitational grasp.  The Schwarzchild Radius also defines the sphere sometimes referred to as the Event Horizon.  Since light cannot escape from a black hole, a Star of this dimension has a spherical surface inside of which we cannot see events occurring.

Input to this equation is M, the mass of the star.

Notes

Current theory suggests that a burned-out star of approximately three times the Sun's mass will collapse under its own gravity and form a black hole.  This equation then suggests that such a star, once collapsed, would have an event horizon of less than 6 miles (less than 9 kilometers).

So, what then would be the approximate density of such a three-solar mass black hole?  Greater than `2E^18 "kg"/m^3`.  That's more than 100,000,000,000,000 times denser than gold.

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