What is the Schwarzschild radius?

It is the radius of the event horizon of a non-rotating, uncharged black hole. If a mass M is compressed into a sphere smaller than its Schwarzschild radius, nothing — not even light — can escape its gravity.

What is the Schwarzschild radius of Earth?

Earth's Schwarzschild radius is about 8.87 mm — roughly the size of a marble. Earth would have to be compressed to that size to become a black hole.

What is the Schwarzschild radius of the Sun?

The Sun's Schwarzschild radius is approximately 2.953 km. The Sun would need to be squeezed into a sphere about 3 km across to form a black hole.

Does the Schwarzschild radius apply to rotating black holes?

The Schwarzschild solution assumes zero rotation and zero charge. Rotating black holes are described by the Kerr metric and have a smaller event horizon (ergosphere structure). Use this calculator as a first-order estimate for any mass.

What formula does this calculator use?

r_s = 2GM / c², where G = 6.67430×10⁻¹¹ m³ kg⁻¹ s⁻², M is mass in kilograms, and c = 2.99792458×10⁸ m/s.

What is the Schwarzschild radius of a proton?

A proton's mass (~1.673×10⁻²⁷ kg) gives a Schwarzschild radius of about 2.49×10⁻⁵⁴ m — far smaller than any known particle, illustrating that quantum effects dominate at those scales.

Schwarzschild Radius Calculator

Enter an object's mass to compute its Schwarzschild radius — the event horizon size if that mass were compressed into a black hole.

Mass Input

Preset Objects

Mass Unit

Mass Value

Scientific notation supported (e.g. 1.5e30)

Formula

r_s = 2GM / c²

G = 6.67430×10⁻¹¹ m³ kg⁻¹ s⁻²

c = 2.99792458×10⁸ m/s

Select a preset or enter a mass to see the event horizon size.

Schwarzschild Radius

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Meters (m)

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Kilometers (km)

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Light-years (ly)

Density Required to Form a Black Hole

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kg/m³

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× nuclear density

Nuclear density ≈ 2.3×10¹⁷ kg/m³. Values below 1× are less dense than a nucleus.

Scale Comparison

Reference	Size	vs r_s

Input: — · r_s = 2 × 6.67430×10⁻¹¹ × M / (2.998×10⁸)²

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Summary

The Schwarzschild radius is the critical radius at which an object's escape velocity equals the speed of light, forming an event horizon. Derived by Karl Schwarzschild in 1916 from Einstein's field equations, it is given by r = 2GM/c², where G is the gravitational constant, M is the mass, and c is the speed of light. Any mass compressed below its Schwarzschild radius becomes a black hole.

How it works

Select your mass input unit (kilograms, solar masses, Earth masses, or a preset object).
Enter the mass value in the input field.
The calculator applies r = 2GM/c² using G = 6.674×10⁻¹¹ N·m²/kg² and c = 2.998×10⁸ m/s.
The Schwarzschild radius is displayed in meters, kilometers, and light-years.
A comparison table shows the result relative to familiar objects like atoms, protons, and the observable universe.

Use cases

Verify textbook examples in general relativity and astrophysics courses.
Compare the event horizon sizes of stellar-mass vs. supermassive black holes.
Illustrate how compressed everyday objects (Earth, Sun) would need to be to form black holes.
Explore the extreme density required for quantum-gravity thought experiments.
Support astronomy outreach and science communication projects.

Frequently Asked Questions

Last updated: 2026-06-15 · Reviewed by Nham Vu