# How big would Earth be if it was a black hole?

If the Earth were compressed into a black hole, it would be extremely tiny compared to its current size. This is because black holes are incredibly dense objects that pack an enormous amount of mass into a very small space.

## What is a black hole?

A black hole is a region of spacetime that has such an intense gravitational field that nothing, not even light, can escape from it. Black holes form when very massive stars collapse at the end of their life cycles. This collapse crushes the mass of the star into an extremely small space, creating a black hole.

### Key properties of black holes:

• Incredibly massive – Black holes pack a huge amount of mass into a very small space.
• Extremely dense – The density of a black hole is unlike anything else in the universe. Mass is compressed to near infinity.
• Inescapable gravitational field – The gravitational field of a black hole is so strong that nothing can escape once it crosses the event horizon.
• Singularities – At the center of a black hole is thought to be a gravitational singularity, a point where density and gravity become infinite.

## How are black hole sizes calculated?

The sizes of black holes can be estimated based on just a few key characteristics:

The size of a non-rotating black hole is given by its Schwarzschild radius. This is calculated using the mass of the black hole:

Where:

• G is the gravitational constant
• M is the mass of the black hole
• c is the speed of light in a vacuum

This gives the radius of the event horizon, which is the boundary around the black hole where escape becomes impossible.

### Mass and density

The enormous mass of a black hole is compressed into an extremely small volume, leading to virtually infinite density at the singularity. The density increases as you approach the center.

### Escape velocity

The escape velocity at the event horizon is equal to the speed of light. This means nothing can break free of the gravitational grip of the black hole.

## What would be the size of Earth as a black hole?

Based on the mass of the Earth, we can calculate its Schwarzschild radius if compressed into a black hole:

• Mass of Earth = 5.972 × 1024 kg
• G (gravitational constant) = 6.673 × 10-11 m3 kg-1 s-2
• c (speed of light) = 299,792,458 m/s

Plugging these values into the Schwarzschild radius formula:

Schwarzschild radius = 2 x (6.673 × 10-11 m3 kg-1 s-2) x (5.972 × 1024 kg) / (299,792,458 m/s)2

= 8.870 mm

Therefore, if the Earth were a black hole, its radius would be about 9 millimeters.

Property Earth as a planet Earth as a black hole
Diameter 12,742 km 18 mm
Circumference 40,075 km 57 mm
Surface area 510.1 million km2 1.02 x 10-5 km2
Volume 1.08321 trillion km3 3.14 x 10-17 km3
Density 5.514 g/cm3 5 x 1030 g/cm3

This table helps visualize just how incredibly compact Earth would be as a black hole. The diameter would shrink from almost 13,000 km to just 18 millimeters. The density would be greater than the density of an atomic nucleus by many orders of magnitude.

## How does this compact size come about?

Earth gets compressed into such a minuscule size as a black hole because of the incredible gravitational forces at play. At the point where Earth would theoretically collapse into a black hole, some key things would happen:

• Gravity would overwhelm the other fundamental forces of nature, such as electromagnetism.
• Matter would be crushed into a tiny volume, likely forming a singularity.
• Spacetime itself would be stretched and warped.

This extreme process would compact the Earth’s mass down to a region smaller than an atom’s nucleus. The Schwarzschild radius describes the tiny event horizon surrounding this central singularity.

### Forces at play

Here’s a more detailed look at how the forces play out:

• Gravity – Gravity is by far the strongest force during black hole formation. It crushes matter down forcefully and dominates the other fundamental interactions.
• Electromagnetism – Electromagnetic forces try to resist the compression, but gravity overwhelms EM once densities get high enough.
• Weak and strong nuclear – These forces control nuclear processes and particle decays. They play a minor role in black hole collapse.

Gravity is king when a black hole forms. The extreme warping of spacetime allows an incredible concentration of mass in a tiny region.

## How dense would the Earth be as a black hole?

The density of the Earth as a black hole would be astronomical. Estimates based on the Schwarzschild radius give:

• Density = Mass / Volume
• Mass of Earth = 5.972 × 1024 kg
• Volume = 4/3 π r3 = 3.14 × 10-17 km3

Plugging this in gives an estimated density of:

Density = Mass / Volume
= 5.972 × 1024 kg / 3.14 × 10-17 km3

= 1.9 x 1041 kg/km3

5 x 1030 g/cm3

This is far beyond any normal matter densities we encounter on Earth. For comparison:

• Density of water = 1 g/cm3
• Density of osmium (most dense element) = 22.6 g/cm3
• Density of a neutron star = 1017 to 1020 g/cm3

So Earth compressed into a black hole would be incredibly dense – significantly denser than the densest normal matter and approaching the densities found within other black holes and neutron stars.

## Conclusion

If the Earth were somehow compressed into a black hole, it would become an astonishingly tiny object. Instead of its current diameter of about 13,000 km, it would shrink down to a Schwarzchild radius of only about 9 millimeters. This is because the mass of the Earth would be compressed into an incredibly dense state, with virtually infinite density at the singularity. This thought experiment shows just how extremely compact objects black holes really are, with unimaginable mass crammed into a space smaller than an atom. The immense gravitational forces present in black holes warp spacetime enough to make this extreme compression possible when massive stars die.