Black Hole Event Horizon Radius Calculator

Estimate the event horizon radius of a non-rotating black hole based on its mass in solar masses (M☉).

Formulas Used

The Schwarzschild radius is calculated for a non-rotating black hole, with results in kilometers and astronomical units (AU).

  1. Schwarzschild Radius (km):

    \[ r_s = \frac{2GM}{c^2} \]

    Where \( G \) is the gravitational constant (\( 6.67430 \times 10^{-11} \, \text{m}^3 \text{kg}^{-1} \text{s}^{-2} \)), \( c \) is the speed of light (\( 2.99792458 \times 10^8 \, \text{m/s} \)), and \( M \) is the mass in kilograms. For mass in solar masses (\( M_\odot = 1.98847 \times 10^{30} \, \text{kg} \)), this simplifies to:

    \[ r_s \approx 2.953 \times \text{mass} \, \text{km} \]

  2. Radius in AU:

    \[ r_{\text{AU}} = \frac{r_s}{1.495978707 \times 10^8} \]

    Converts kilometers to AU using 1 AU ≈ 1.495978707 × 10^8 km.

Example Calculations

Example 1: Stellar-Mass Black Hole

Input: Mass = 10 M☉

Calculations:

  • Schwarzschild Radius: \[ 2.953 \times 10 \approx 29.53 \, \text{km} \]
  • Radius in AU: \[ \frac{29.53}{1.495978707 \times 10^8} \approx 0.000000197 \, \text{AU} \]

Result: Event Horizon Radius: 29.53 km (0.000000197 AU)

Example 2: Supermassive Black Hole

Input: Mass = 4,000,000 M☉

Calculations:

  • Schwarzschild Radius: \[ 2.953 \times 4000000 \approx 11812000 \, \text{km} \]
  • Radius in AU: \[ \frac{11812000}{1.495978707 \times 10^8} \approx 0.07896 \, \text{AU} \]

Result: Event Horizon Radius: 11,812,000 km (0.079 AU)

Example 3: Small Black Hole

Input: Mass = 1 M☉

Calculations:

  • Schwarzschild Radius: \[ 2.953 \times 1 \approx 2.95 \, \text{km} \]
  • Radius in AU: \[ \frac{2.95}{1.495978707 \times 10^8} \approx 0.0000000197 \, \text{AU} \]

Result: Event Horizon Radius: 2.95 km (0.0000000197 AU)

How to Use the Calculator

Follow these steps to estimate the event horizon radius of a black hole:

  1. Enter Mass: Input the black hole’s mass in solar masses (e.g., 10 for a stellar-mass black hole).
  2. Calculate: Click “Calculate Event Horizon Radius” to see the result.
  3. Interpret Result: The result shows the Schwarzschild radius in kilometers and AU. If you see “Please enter a valid positive mass,” ensure the mass is provided and positive.
  4. Share or Embed: Use the share buttons to post results on social media, copy the result, or get an embed code for the calculator.

Note: This calculator assumes a non-rotating (Schwarzschild) black hole. Actual event horizons may vary for rotating or charged black holes.

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