### Schwarzschild Radius Calculator:

The Schwarzschild radius calculator allows you to get the gravitational acceleration at the surface of a black hole, also known as the event horizon.

Due to the nature of black holes, both the event horizon (also known as the Schwarzschild radius) and the black hole’s gravity can be calculated from the black hole’s mass. A black hole is when a star’s mass is so massive that nothing can stop its internal gravity from compressing all the material that makes up that star.

When this happens, the mass density and gravity inside the black hole are so strong that the laws of physics can no longer explain what’s going on there.

The gravitational field inside a black hole is so strong that even light cannot escape hence the ‘blackness’ inside the 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’s called the Schwarzschild radius.

Just like any other object with a force we can calculate it using our gravity calculator. Another useful quantity for studying massive objects is the gravitational field, or gravitational acceleration, It is the acceleration experienced by any object due to the presence of our massive matter in this case of a black hole.

### Schwarzschild Radius Formula:

Schwarzschild radius formula is gravitational radius of the black hole G_{(m/s)} in meter per second is equal to the Schwarzschild radius or event radius or black hole radius r_{(mm)} in millimeter and multiply the square of the c^{2} and divided by the two and multiply the mass of the black hole m_{(g)} in grams.Hence the Schwarzschild radius formula can be written as

G_{(m/s)}= (r_{(mm)} *c^{2} )/2 *m_{(g)}

The black hole equation is along the lines

The gravitational radius of the black hole formula is

R =(2m *G ) /c^{2}

Where

M=is the mass of the black hole

G =is the speed of the light and it is 299.792.458 m/s

R = is the Schwarzschild radius or event radius or black hole radius

### Example:1

Calculate the Schwarzschild radius for earth with mass 6.8 *10^{27} grams?

### Answer:

Given that

Mass of the earth m =6.7 *10^{27} grams=6.7 *10^{30} mg

Schwarzschild radius formula is r =(2m *G )/c^{2}

R = (2*6.7 *10^{30} *9.8) /(299,792,458)^{2}

R=1.3132 *10^{32} / (8.98 *10^{16})

R=14.62 *10^{14}

Therefore, the Schwarzschild radius is 14.62 *10^{14}mm

### Example:2

Calculate the Schwarzschild radius for earth with mass 9.4*10^{27} grams?

### Answer:

Given that

Mass of the earth m =9.8 *10^{27} grams=9.4 *10^{30} mg

Schwarzchild radius formula is r =(2m *G )/c^{2}

R = (2* 9.4*10^{30} *9.8) /(299,792,458)^{2}

R=1.8424 *10^{32} / (8.98 *10^{16})

R=2.05167 *10^{14} mm

Therefore, the Schwarzschild radius is 2.05167 *10^{14}mm