Schwarzschild Radius Calculator
Find the event horizon radius of a black hole.
Results update as you type.
How it works
The Schwarzschild radius defines the size of a black hole's event horizon, and this calculator computes it for any mass. You enter a mass, and it returns the Schwarzschild radius in meters and kilometers. The radius is twice the gravitational constant times the mass, divided by the speed of light squared. Its physical meaning is striking: it is the radius to which you would have to compress a given mass for its escape velocity to reach the speed of light, at which point not even light could escape and the object would be a black hole. Every mass has a Schwarzschild radius, but for ordinary objects it is fantastically small; compressing the entire Earth to a black hole would require squeezing it to a radius of about nine millimeters, and the Sun to about three kilometers. Only when enormous mass is packed into a tiny volume, as when a massive star collapses, does an object actually cross within its Schwarzschild radius and form a black hole. For real black holes, the Schwarzschild radius marks the event horizon, the boundary beyond which nothing can return. Astronomers use it to characterize black holes of all sizes, from stellar remnants to the supermassive black holes at galaxy centers. This calculator handles non-rotating, uncharged black holes described by the Schwarzschild solution. The mass must be positive. Enter a mass to find its Schwarzschild radius.
Rs = 2GM / c²
The Schwarzschild radius is twice the gravitational constant times the mass, divided by the speed of light squared. It is the radius of the event horizon: if all of an object's mass were compressed within this radius, its escape velocity would equal the speed of light and it would become a black hole from which nothing can escape.
Source:General relativity
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Worked example
How to use this calculator
- 1
Enter your values
Enter mass.
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Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Schwarzschild radius updates instantly as you type — no button to press.
Frequently asked questions
What is the Schwarzschild radius?
The Schwarzschild radius is the radius at which a given mass would become a black hole, marking the event horizon. It equals twice the gravitational constant times the mass divided by the speed of light squared. If all of an object's mass were within this radius, its escape velocity would equal light speed and nothing could escape.
Does every object have a Schwarzschild radius?
Yes, mathematically every mass has a Schwarzschild radius, but for ordinary objects it is absurdly small. Earth's is about nine millimeters and the Sun's about three kilometers. An object only becomes a black hole if its mass is actually compressed within this radius, which does not happen for normal matter under ordinary conditions.
What is the event horizon?
The event horizon is the boundary of a black hole located at the Schwarzschild radius. It is the point of no return: anything crossing it, including light, cannot escape the black hole's gravity. The event horizon is not a physical surface but a boundary in spacetime beyond which events cannot affect an outside observer.
How big are real black holes?
Because the Schwarzschild radius is proportional to mass, black holes range enormously in size. A stellar black hole of a few solar masses has a radius of tens of kilometers, while a supermassive black hole of billions of solar masses at a galaxy's center can have a radius larger than our solar system. The calculator scales to any mass you enter.
Does this formula apply to all black holes?
This calculator uses the Schwarzschild solution, which describes a non-rotating, uncharged black hole. Real black holes usually rotate, and rotating black holes are described by the more complex Kerr solution, which has a different horizon structure. The Schwarzschild radius remains an excellent approximation and the standard reference scale for black hole size.