Schwarzschild Radius Calculator
Find the event horizon radius for any mass, and see how it compares to that object's actual size.
Calculator verified • Last updated: August 2026
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Size Comparison
The blue dashed circle is the object's actual radius; the red dashed circle is its Schwarzschild radius, both centered on the same point and sized on a logarithmic scale since they usually differ by many orders of magnitude. An object becomes a black hole only once it's compressed inside the red circle.
The Schwarzschild Radius Explained
The Schwarzschild radius marks the size a mass would need to be compressed to for its escape velocity to equal the speed of light — the boundary of a black hole's event horizon.
rs: Schwarzschild radius, in meters (m) or kilometers (km).
G: the gravitational constant, about 6.674 × 10⁻¹¹ N·m²/kg².
M: mass of the object, in kilograms (kg).
c: speed of light, ≈ 3×10⁸ m/s.
This is the same expression as escape velocity's formula, solved for the radius at which escape velocity exactly equals c — any mass compressed within this radius becomes a black hole.
Worked Example: The Sun's Schwarzschild Radius
Using the calculator's default — the Sun's mass ( kg) — the Schwarzschild radius works out to about 2.95 km. Compare that to the Sun's actual radius of about 696,340 km, roughly 236,000 times larger — which is exactly why the Sun is nowhere close to being a black hole and never will be, regardless of what happens as it ages.
What It Would Take to Turn Earth Into a Black Hole
Earth's Schwarzschild radius is only about 8.7 millimeters — smaller than a marble — compared to its actual radius of about 6,371 km. To become a black hole, all of Earth's mass would need to be compressed into a sphere smaller than that marble, an utterly inconceivable feat with any known process; nothing in Earth's future evolution could ever cause this to happen naturally.
A Brief History of the Schwarzschild Radius
Karl Schwarzschild derived this exact solution to Einstein's general relativity field equations in 1916, remarkably just weeks after Einstein published the theory itself, while serving on the German front in World War I. For decades the radius was treated as a mathematical curiosity rather than something physically real, since no known process seemed capable of compressing matter that far — until 20th-century astrophysics confirmed that collapsing massive stars really do form black holes.
Common Schwarzschild Radius Mistakes
Assuming any object with a "Schwarzschild radius" calculation is close to being a black hole is a common misconception — every mass has a mathematical Schwarzschild radius, but it's only physically relevant if the object could actually be compressed that small, which essentially never happens outside of collapsed stars. Confusing the Schwarzschild radius with a black hole's actual physical "surface" is another mix-up; it's a boundary in spacetime geometry, not a solid surface. Forgetting that this formula describes a non-rotating black hole (a simplification) is a third common oversight — real astrophysical black holes typically rotate, which changes the geometry somewhat.
Black Hole Terms You Should Know
Event Horizon — the boundary at the Schwarzschild radius beyond which nothing can escape.
Solar Mass (M☉) — a unit of mass equal to the Sun's mass, commonly used for stars and black holes.
Singularity — the theoretical point of infinite density at a black hole's center, distinct from the event horizon.
Stellar Black Hole — a black hole formed from the gravitational collapse of a massive star, typically a few to tens of solar masses.
This calculator uses the simple non-rotating (Schwarzschild) black hole model; real black holes may rotate, which modifies the event horizon geometry (the Kerr metric).
Frequently Asked Questions
Does every object have a Schwarzschild radius, even ordinary things?
Mathematically, yes — the formula gives a nonzero result for any mass, including a person or a coin. But it's only physically meaningful as an actual event horizon if the object's real size is smaller than that radius, which never happens for ordinary objects; Earth's Schwarzschild radius is under a centimeter, vastly smaller than the actual planet. It only becomes relevant for objects compact enough to actually collapse within their own Schwarzschild radius, like massive collapsed stars.
What actually happens at the Schwarzschild radius?
It marks the event horizon — the boundary beyond which nothing, not even light, has enough escape velocity to get back out, because the required escape speed there equals or exceeds the speed of light. Crossing it isn't like hitting a physical wall; for a large enough black hole, an observer might not even notice anything unusual locally, but once inside, every possible future path leads only further inward, with no way back out.
Could the Sun ever become a black hole?
No — the Sun doesn't have nearly enough mass to collapse into a black hole under its own gravity once it exhausts its nuclear fuel. Stars need roughly 20+ times the Sun's mass to end their lives as a black hole; the Sun will instead become a white dwarf, a much less extreme but still very dense stellar remnant, well before gravity could ever compress it inside its own Schwarzschild radius.