Schwarzschild Radius Calculator

About the Schwarzschild Radius Calculator

The Schwarzschild radius defines the event horizon of a non-rotating black hole — the boundary beyond which nothing, not even light, can escape. First derived by Karl Schwarzschild in 1916 from Einstein's general relativity field equations, this radius is directly proportional to the black hole's mass: Rs = 2GM/c².

Black holes span an enormous range of sizes: stellar-mass black holes from collapsed stars have radii of a few kilometers, supermassive black holes at galaxy centers can be larger than our solar system, and hypothetical primordial micro black holes might be smaller than an atom.

This calculator computes the Schwarzschild radius along with related properties — the photon sphere, the innermost stable circular orbit (ISCO), Hawking radiation temperature, and estimated evaporation time. A comparison mode lets you check whether any given object compressed to its mass would form a black hole, and a reference table of famous black holes provides real-world context.

When This Page Helps

This calculator helps you move from a black-hole mass to the key scales that matter near the horizon. It is useful when comparing stellar-mass and supermassive black holes, checking whether an object would collapse into a black hole at a given radius, or building intuition for how quickly black-hole size grows with mass.

How to Use the Inputs

1. Enter the mass of the object in kilograms, solar masses, Earth masses, or Jupiter masses.
2. Use preset buttons for the Sun, Earth, or famous black holes like Sagittarius A*.
3. Switch to "Compare to Object Size" mode to check if an object would become a black hole at its current mass.
4. Enter the object's actual radius in meters for the comparison.
5. Review all outputs: Schwarzschild radius, photon sphere, ISCO, Hawking temperature.
6. Explore the famous black holes table for real-world comparisons.

Example Calculation

Tips & Best Practices

• The Schwarzschild radius scales linearly with mass — 10× the mass gives 10× the radius.
• Sagittarius A* (4 million M☉) has R_s ≈ 12 million km — about 17 solar radii.
• Hawking evaporation time for stellar-mass BHs far exceeds the age of the universe.
• An object is a black hole if its actual radius is smaller than its Schwarzschild radius.
• The density required for a BH decreases as mass increases — supermassive BHs can be less dense than water.

Event Horizon Scale

The Schwarzschild radius grows linearly with mass. That makes it a clean way to compare compact objects, from stellar remnants to galaxy-center black holes, without needing a more complex rotating solution.

Nearby Radii

The photon sphere and ISCO show where light and matter can still orbit before becoming unstable. Those values are useful for thinking about accretion disks, lensing, and the appearance of the shadow around a non-rotating black hole.

Physical Limits

Hawking temperature and evaporation time are included for context, not for everyday engineering use. For stellar and supermassive black holes, the evaporation time is far longer than the age of the universe, so the practical takeaway is usually the horizon scale and orbital distances.

Frequently Asked Questions

• What is the Schwarzschild radius?

  The radius of the event horizon of a non-rotating (Schwarzschild) black hole. Any object compressed within its Schwarzschild radius would become a black hole.

• What is the Schwarzschild radius of Earth?

  About 8.87 mm — roughly the size of a marble. Earth would need to be compressed to this size to become a black hole.

• Does the Schwarzschild radius change for rotating black holes?

  The Schwarzschild solution applies to non-rotating black holes. Rotating (Kerr) black holes have a more complex horizon structure with an inner and outer horizon.

• What is Hawking radiation?

  Theoretical radiation emitted by black holes due to quantum effects near the event horizon. Smaller black holes radiate faster and are hotter. Stellar-mass black holes have temperatures near absolute zero.

• What is the photon sphere?

  At 1.5× the Schwarzschild radius, photons can theoretically orbit the black hole (unstable). This is the closest distance at which light can travel in a circular orbit.

• What is the ISCO?

  The Innermost Stable Circular Orbit at 3× the Schwarzschild radius is the closest stable orbit for matter. Below this, objects spiral inward. The ISCO determines the inner edge of accretion disks.