OrbitLab

Schwarzschild Radius Calculator

How small would this mass need to be to become a black hole?

Mass (kg)

Schwarzschild radius

2,953.994 m

Default mass shown is one solar mass

What you entered

Mass (kg): 1.989e+30

1
Rs = 2GM ÷ c²
2 × 6.674e-11 × 1.989e+30 ÷ 2.998e+8²= 2953.9938 m

Result

Schwarzschild radius: 2,953.994 m

If this mass were compressed inside a sphere of radius 2,953.99 m, it would become a black hole.

Schwarzschild radius by mass

The radius any mass would need to be compressed to in order to become a black hole: twice the gravitational constant times mass, divided by the speed of light squared.

Object	Mass	Schwarzschild radius
1 kilogram	1 kg	1.4852 x 10^-27 m
Earth	5.972 x 10^24 kg	8.8694 x 10^-3 m
The Sun	1.989 x 10^30 kg	2.9540 x 10^3 m
A 10 solar mass black hole	1.989 x 10^31 kg	2.9540 x 10^4 m
Sagittarius A*	8.55 x 10^36 kg	1.2698 x 10^10 m

Earth would have to be crushed to about 9 millimetres across, and the Sun to a 3 km radius. The radius scales linearly with mass, so the supermassive black hole at the centre of our galaxy has an event horizon larger than Mercury's orbit.

The point of no return

The Schwarzschild radius is the size a mass would need to be compressed to for its escape velocity to exceed the speed of light — inside this radius, not even light can escape, defining a black hole's event horizon.

Every mass has one, even you

In principle any mass has a Schwarzschild radius (Earth's is about 9mm), but ordinary matter is nowhere near dense enough to collapse to that size — only the crushing gravity of a collapsing massive star can actually achieve it.

Frequently asked questions

What is the Schwarzschild radius of a 10-solar-mass black hole?

Rs = 2GM/c² ≈ 2 × 6.674×10⁻¹¹ × (10 × 1.989×10³⁰) / (3×10⁸)² ≈ 29.5 km. A stellar-mass black hole is roughly city-sized.

How is the Schwarzschild radius different from the escape velocity calculator?

The escape velocity calculator finds the speed needed to escape a body of given mass and radius. The Schwarzschild radius calculator finds the radius at which that escape velocity equals the speed of light — the boundary defining a black hole.

What is the Schwarzschild radius of the observable universe's mass?

The observable universe contains about 10⁵³ kg. Its Schwarzschild radius is roughly 13.7 billion light-years — intriguingly close to the actual radius of the observable universe, a coincidence that has fueled cosmological speculation.

Can anything escape from inside the event horizon?

No. Inside the Schwarzschild radius, all paths in spacetime lead inward. Even light, the fastest thing in the universe, cannot escape — which is why we call it a black hole.