Black Hole Event Horizon Radius Calculator

Black Hole Event Horizon Radius Calculator computes Schwarzschild radius in meters and km from mass for non-rotating black holes in astronomical studies.

Black Hole Mass (kg):

Formulas Used in Black Hole Event Horizon Radius Calculator

The calculator uses the following formula to estimate the Schwarzschild radius:

Schwarzschild Radius:

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

Where:

\\( r_s \\): Schwarzschild radius (m)
\\( G \\): Gravitational constant (\\( 6.67430 \times 10^{-11} \, \text{m}^3 \text{kg}^{-1} \text{s}^{-2} \\))
\\( M \\): Black hole mass (kg)
\\( c \\): Speed of light (\\( 2.99792458 \times 10^8 \, \text{m/s} \\))

Example Calculations

Example 1: Stellar-Mass Black Hole (~1 Solar Mass)

Input: Mass = \\( 1.989 \times 10^{30} \\) kg

\\[ r_s = \frac{2 \cdot 6.67430 \times 10^{-11} \cdot 1.989 \times 10^{30}}{(2.99792458 \times 10^8)^2} \approx 2953.97 \ \text{m} \\] \\[ \text{Converted} = \frac{2953.97}{1000} \approx 2.95 \ \text{km} \\]

Result: Schwarzschild Radius = 2953.97 m (2.95 km)

Example 2: Intermediate-Mass Black Hole (~1000 Solar Masses)

Input: Mass = \\( 1.989 \times 10^{33} \\) kg

\\[ r_s = \frac{2 \cdot 6.67430 \times 10^{-11} \cdot 1.989 \times 10^{33}}{(2.99792458 \times 10^8)^2} \approx 2953966.93 \ \text{m} \\] \\[ \text{Converted} = \frac{2953966.93}{1000} \approx 2953.97 \ \text{km} \\]

Result: Schwarzschild Radius = 2953966.93 m (2953.97 km)

Example 3: Supermassive Black Hole (~4 Million Solar Masses)

Input: Mass = \\( 7.956 \times 10^{36} \\) kg

\\[ r_s = \frac{2 \cdot 6.67430 \times 10^{-11} \cdot 7.956 \times 10^{36}}{(2.99792458 \times 10^8)^2} \approx 1.1816 \times 10^{10} \ \text{m} \\] \\[ \text{Converted} = \frac{1.1816 \times 10^{10}}{1000} \approx 1.1816 \times 10^7 \ \text{km} \\]

Result: Schwarzschild Radius = \\( 1.1816 \times 10^{10} \\) m (\\( 1.1816 \times 10^7 \\) km)

Formulas Used in Black Hole Event Horizon Radius Calculator

Example Calculations

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