To calculate the **Schwarzschild radius** of a black hole, use the formula **R = 2GM / c²**, where **G** is the gravitational constant, **M** is the mass of the black hole, and **c** is the speed of light. For example, a black hole with the mass of the Sun has a Schwarzschild radius of **2.95 km**.

## Black Hole Radius Calculator

Enter any 1 value to calculate the missing variable

A **Black Hole Radius Calculator** helps determine the Schwarzschild radius, the point at which an object collapses into a black hole. Enter the mass to calculate the radius, providing insight into the size of a black hole’s event horizon.

**Formula:**

$R = \frac{2GM}{c^2}$

Where:

Variable |
Meaning |
---|---|

R | Schwarzschild radius (in meters) |

G | Gravitational constant $6.67430 \times 10^{-11} \, \text{m}^3\text{kg}^{-1}\text{s}^{-2}$ |

M | Mass of the black hole (in kilograms) |

c | Speed of light $3 \times 10^8 \, \text{m/s}$ |

**Example Calculation:**

Let’s calculate the Schwarzschild radius for a black hole with the mass of the **Sun**:

- Mass of the Sun,
**M**: $1.989 \times 10^{30} \, \text{kg}$

Using the formula:

$R = \frac{2 \times 6.67430 \times 10^{-11} \times 1.989 \times 10^{30}}{(3 \times 10^8)^2} = 2.95 \, \text{km}$

Step |
Calculation |
---|---|

Mass of the Sun (M) | $1.989 \times 10^{30} \, \text{kg}$ |

Schwarzschild radius (R) | 2.95 km |

**Answer**: The Schwarzschild radius for a black hole with the mass of the Sun is **2.95 km**.

**What is Black Hole Radius Calculator ?**

A **black hole radius calculator** typically uses the **Schwarzschild radius** formula to determine the radius at which an object becomes a black hole.

For example, to calculate the Schwarzschild radius of a 10 solar mass black hole, you would enter in the mass of the object and calculate the radius. This radius determines the point at which the escape velocity equals the speed of light, effectively forming a black hole.

Using a **black hole radius calculator with steps** simplifies the process of calculating the size of a black hole based on its mass. It is also used to compute the **Schwarzschild radius of Earth**, the **Sun**, or even a human.

Moreover, advanced calculators can factor in concepts like **Hawking radiation** and rotating black holes for a more detailed analysis of black hole properties.

Understanding the **Schwarzschild radius** is essential in astrophysics for determining the boundary of a black hole, beyond which not even light can escape.