How To Calculate Black Hole Mass

Black Hole Mass Formula:

\[ M = \frac{c^3 \times r_s}{2G} \]

Speed of Light (c):

m/s

Schwarzschild Radius (r_s):

Gravitational Constant (G):

m³ kg⁻¹ s⁻²

Black Hole Mass (M):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Black Hole Mass Calculation?

The black hole mass calculation using Schwarzschild radius is a fundamental equation in general relativity that relates the mass of a black hole to its event horizon size. This formula is derived from Karl Schwarzschild's solution to Einstein's field equations.

2. How Does the Calculator Work?

The calculator uses the Schwarzschild radius formula:

\[ M = \frac{c^3 \times r_s}{2G} \]

Where:

\( M \) — Black hole mass (solar masses)
\( c \) — Speed of light (3 × 10⁸ m/s)
\( r_s \) — Schwarzschild radius (km)
\( G \) — Gravitational constant (6.674 × 10⁻¹¹ m³ kg⁻¹ s⁻²)

Explanation: The Schwarzschild radius represents the radius of the event horizon, beyond which nothing can escape the black hole's gravitational pull. The mass is directly proportional to this radius.

3. Importance of Black Hole Mass Calculation

Details: Calculating black hole mass is essential for understanding black hole properties, studying gravitational effects, and analyzing astronomical observations. It helps determine the black hole's gravitational influence on surrounding matter and its role in galaxy formation.

4. Using the Calculator

Tips: Enter the speed of light in m/s, Schwarzschild radius in kilometers, and gravitational constant in m³ kg⁻¹ s⁻². Default values are provided for constants, but you can adjust them if needed for specific calculations.

5. Frequently Asked Questions (FAQ)

Q1: What is the Schwarzschild radius?
A: The Schwarzschild radius is the radius of the event horizon of a non-rotating black hole, representing the point of no return for matter and light.

Q2: How is this formula derived?
A: The formula comes from solving Einstein's field equations for a spherically symmetric, non-rotating mass in vacuum, first done by Karl Schwarzschild in 1916.

Q3: What are typical black hole masses?
A: Stellar black holes: 3-20 solar masses; Supermassive black holes: millions to billions of solar masses; Intermediate black holes: hundreds to thousands of solar masses.

Q4: Does this work for rotating black holes?
A: No, this formula is for non-rotating (Schwarzschild) black holes. Rotating black holes require the Kerr metric and are more complex.

Q5: How is Schwarzschild radius measured in practice?
A: Through various astronomical methods including gravitational lensing effects, orbital dynamics of nearby stars, and accretion disk observations.