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The Schwarzchild radius of a black hole is linearly dependent on its mass. The relationship is

rs = 2GM / c2

where G is the Newtonian gravitational constant, m is the mass of the black hole, and c is the speed of light. The Schwarzchild radius works out to be 2.95 km per solar mass.

There is nothing at all mysterious about this formula. It comes from the standard classical formula for escape velocity

ve = sqrt(2Gm / r)

by substituting c for the velocity and then solving for r.

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13y ago
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11y ago

The Schwarzschild radius for a black hole whose mass is equal to 133 million solar masses would be:

r = 2MG/c2

r = [(2)(2.65x1038kg)(6.67x10-11 N·m2·kg-2]/[(3.00x108m/s)2]

r = 0.39x1012 m

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10y ago

A four solar-mass black hole would have a gravitational radius (Schwarzschild radius) of about 11.8 km.

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11y ago

The Schwarzschild radii of a black hole with 1 million solar masses would be 2.95x109m.

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