Black Hole Size Calculator: Find the Schwarzschild Radius from Mass

A tool to calculate the size of a non-rotating black hole’s event horizon based on its mass.

Please enter a valid, positive number for the mass.

What is the Schwarzschild Radius?

The Schwarzschild radius is the radius of the event horizon of a non-rotating, uncharged black hole. It represents the “point of no return”; once matter or light crosses this boundary, it cannot escape the black hole’s gravitational pull. Any object can theoretically become a black hole if you compress its mass into a volume smaller than its Schwarzschild radius. This calculator helps you find this critical size. The ability to calculate the size of a black hole using mass is fundamental to understanding these cosmic giants. The size is directly proportional to the mass—the more massive the black hole, the larger its event horizon.

The Formula to Calculate a Black Hole’s Size

The size of a black hole, its Schwarzschild radius (Rₛ), is calculated using a surprisingly simple formula derived from Einstein’s theory of general relativity. It connects the object’s mass directly to its gravitational influence.

Rₛ = 2GM / c²

This formula allows you to calculate the size of a black hole using mass and two fundamental physical constants.

Formula Variables

Variables used in the Schwarzschild radius calculation.

Variable	Meaning	Unit	Typical Value
Rₛ	Schwarzschild Radius	Meters (m)	Varies based on mass
G	Gravitational Constant	m³·kg⁻¹·s⁻²	6.67430 × 10⁻¹¹
M	Mass of the object	Kilograms (kg)	From stellar to billions of solar masses
c	Speed of Light in a vacuum	m/s	299,792,458

Practical Examples

Example 1: Our Sun

If you were to compress the Sun into a black hole, what would its size be?

• Input Mass: 1 Solar Mass
• Calculation: Rₛ = 2 * (6.674e-11) * (1.989e30) / (299792458)²
• Result: The Sun’s Schwarzschild radius is approximately 2.95 kilometers. For context, the Sun’s actual radius is about 696,000 kilometers.

Example 2: The Earth

What if you wanted to turn Earth into a black hole?

• Input Mass: 1 Earth Mass (5.972 × 10²⁴ kg)
• Calculation: Rₛ = 2 * (6.674e-11) * (5.972e24) / (299792458)²
• Result: Earth would need to be compressed to a radius of about 8.87 millimeters—smaller than a marble.

These examples illustrate the immense density required to form a black hole and show how an understanding of general relativity is key to these calculations.

How to Use This Black Hole Size Calculator

1. Enter the Mass: Input the mass of the object you want to analyze.
2. Select the Unit: Choose the appropriate unit for your mass—Kilograms, Solar Masses (the mass of our sun), or Earth Masses. Our calculator handles the conversion automatically. This is a common feature in an escape velocity formula calculator as well.
3. View the Result: The calculator instantly provides the Schwarzschild radius. This is the size the object would need to be compressed to in order to become a black hole.
4. Interpret the Results: The primary result shows the calculated radius in an appropriate unit (e.g., millimeters, kilometers, or AU). Intermediate values show the mass in kilograms and the constants used.

Key Factors That Affect a Black Hole’s Size

• Mass: This is the single most important factor. The Schwarzschild radius is directly proportional to the mass. Doubling the mass doubles the radius.
• Rotation (Spin): This calculator is for non-rotating (Schwarzschild) black holes. Rotating (Kerr) black holes are more complex; their event horizons are distorted and they have a region called the ergosphere.
• Electric Charge: Like spin, charge can affect a black hole’s structure, but most astrophysical black holes are expected to have negligible charge.
• The Gravitational Constant (G): A fundamental constant of nature, its value determines the strength of gravity itself. A different ‘G’ would change every calculation.
• The Speed of Light (c): The universal speed limit. It appears squared in the denominator, showing how immense it is and why the resulting radius is often so small.
• Density Prerequisite: While not in the formula, an object must achieve a critical density to collapse. The forces within a star normally prevent this until it runs out of fuel. For more on this, see our article about the types of black holes.

Frequently Asked Questions (FAQ)

1. What is an event horizon?

The event horizon is the boundary around a black hole beyond which nothing, not even light, can escape. It is the “surface” we calculate with the Schwarzschild radius.

2. Can anything become a black hole?

Theoretically, yes. Any object with mass has a Schwarzschild radius. However, only the most massive stars have enough gravity to overcome the forces that support them and collapse naturally into a black hole.

3. Is the Sun massive enough to become a black hole?

No. When the Sun runs out of fuel, it will become a white dwarf. It lacks the sufficient mass (generally over 20 solar masses) to trigger the supernova explosion that leads to a stellar-mass black hole.

4. What is a singularity?

At the center of a black hole, general relativity predicts a point of infinite density called a singularity, where the known laws of physics break down.

5. Why do I need to select different mass units?

Astronomers use different units for convenience. Solar masses are standard for stars and black holes, while Earth masses are useful for planets. Kilograms are the base scientific unit. The calculator simplifies how you can calculate the size of a black hole using mass from any of these common starting points.

6. Does the calculator work for rotating black holes?

No, this is specifically an event horizon calculator for non-rotating (Schwarzschild) black holes. Rotating (Kerr) black holes have a more complex geometry.

7. Is the universe itself a black hole?

This is a fascinating question. While you can calculate a Schwarzschild radius for the mass of the observable universe, the universe is expanding, not collapsing. The standard cosmological model does not describe the universe as a black hole.

8. What happens if I fall into a black hole?

As you approach the event horizon, you would experience extreme tidal forces—a process called “spaghettification.” From an outside observer’s perspective, your approach would appear to slow down infinitely due to gravitational time dilation. You might be interested in our time dilation calculator for more on this effect.