Schwarzschild Radius Calculator

The Schwarzschild radius calculator lets you obtain the gravitational acceleration on the surface of a black hole, also called the event horizon. Due to the nature of black holes, we can calculate the event horizon (also called Schwarzschild radius) and the black hole gravity from just the mass of the black hole. Below, we will explain what the Schwarzschild radius is and what the black hole equation means.

Put simply, a black hole is what happens to a star when its mass is so big that nothing can stop its internal gravity from compressing all the materials that make up the star. When this happens, the mass density and gravitational force inside the black hole are so strong that the laws of physics, as we know them, cannot explain what happens there anymore. The gravitational field inside a black hole is so strong that not even light can escape from it (hence the 'black' in "black hole"). The separation between the region where we know how things work and the region where we don't is called the event horizon, and in a black hole, it is also known as the Schwarzschild radius.

Despite all this, a black hole behaves like any other massive object when seen from far away. A black hole attracts other objects with mass with a force that can be calculated using our gravitational force calculator just like any other object with mass. Another useful quantity for studying massive objects is the gravitational field or gravitational acceleration, which is the acceleration that any object would experience due to the presence of other massive objects, in this case, a black hole.

In a general situation, you can easily calculate the gravitational acceleration by simply using the gravitational force calculator and setting one of the masses to 1 kg. This is the valid approach to calculating the gravity of a normal object or even the black hole's gravity at a point far away from the surface of the black hole. However, there is a point of special interest for black holes called the event horizon or Schwarzschild radius (that we understand as the surface of the black hole), which is exactly where this calculator becomes the most useful for calculating the black hole gravity.

Let's now see what the importance of these points is and how this black hole Schwarzschild radius calculator works.

The event horizon is a very important concept when talking about black holes. In this Schwarzschild radius calculator, we can easily compute where it is located. The event horizon is the point (or a collection of points) in space that divides two areas that cannot communicate back and forth. In the case of a black hole, it is the point where the escape velocity is the same as the speed of light c.

To learn more about escape velocity, you can check the escape velocity calculator, but put simply, it is the speed required to get away from the gravitational pull of an object. The event horizon of a black hole divides the points in the region of space in which light can still escape the attraction of such a massive object from the points in which nothing, not even light, can resist the pull of the black hole. This means that effectively everything that falls inside the event horizon is "lost forever," and we can never recover it (though some research suggests there might be exceptions to this rule).

Because of this effect, the event horizon is usually considered informally as the surface of a black hole. The event horizon in a black hole is also called the Schwarzschild radius, after the physicist who first introduced this concept. For a non-rotating black hole, it depends only on the mass of the black hole, which makes this black hole event horizon/ Schwarzschild radius calculator very easy to use as it only needs one input parameter.

This black hole gravity calculator is composed of three different parameters that are related in such a way that only one is needed to calculate the rest of them. The typical scenario would be to input the mass of the black hole and get the radius of the event horizon (Schwarzschild radius) and the black hole gravity at such point as the results.

Other behaviors are also allowed, so you can have the Schwarzschild radius or the black hole gravity at the surface as an input value and get the other two parameters from the Schwarzschild radius calculator. Let's look now at the black hole equation:

g = G × M / r²

The parameters of the black hole equation are:

1. M — Mass of the black hole. Typically a very big number, expressed in thousands of solar masses (at least).

2. r — Schwarzschild radius / event horizon / black hole radius. This parameter is calculated using the same equation as in the escape velocity calculator using the speed of light in vacuum and the aforementioned mass to obtain the distance at which the escape velocity is exactly c.

3. g — Black hole gravity at the surface. This is the value of the gravitational field at the event horizon. It is calculated by the same equation as in the gravitational force calculator, setting one of the masses to 1 kg and the other being the mass of the black hole and taking the distance r to be the Schwarzschild radius of this black hole.

4. G — Gravitational constant (6.67430×10⁻¹¹ N⋅m²⋅kg⁻²).

We can also determine the Schwarzschild radius through the following equation:

‌r = 2 × G × M/c²

where c is the speed of light in vacuum (≈ 2.99×10⁸ m/s).

If you would like to learn more about black holes, check out our black hole temperature calculator.

To calculate the Schwarzschild radius r_s of an object, follow these steps:

1. Multiply the mass of the object M with the gravitational constant G (6.67430×10⁻¹¹ N⋅m²⋅kg⁻²).

2. Divide the result by the square of speed of light c (≈ 2.99×10⁸ m/s).

3. Multiply this by 2 to get the Schwarzschild radius r_s = 2⋅G⋅M/c².

4. Verify the result with our Schwarzschild radius calculator.

The Schwarzschild radius of a star with a mass of 10 Solar masses is 29.54 km. To get this result, follow these steps:

1. Multiply the star's mass (M) with the gravitational constant (G):

   M⋅G = 10 ⋅ 1.989×10³⁰ kg ⋅ 6.67430×10⁻¹¹ N⋅m²⋅kg⁻² ≈ 13.275×10²⁰N⋅m²⋅kg⁻¹

2. Divide the result by the square of speed of light (c):

   13.275×10²⁰N⋅m²⋅kg⁻¹/(2.99×10⁸ m/s)² ≈ 14.77×10³ m

3. Multiply this with 2 to get the Schwarzschild radius (r_s):

   r_s = 2⋅14.77×10³ = 29540 m = 29.54 km

4. Verify the result with our Schwarzschild radius calculator.

The Earth's Schwarzchild radius is approximately 8.87 mm or 0.887 cm. This means that the Earth would have to be squeezed to a size over 700 million times smaller than its current size to become a black hole!

Yes, the Schwarzschild radius describes the event horizon around a black hole, the region of space beyond which light itself cannot escape. So, the black hole itself is smaller than the Schwarzschild radius.