Black Hole Calculator

About the Black Hole Calculator

The **Black Hole Calculator** computes the fundamental properties of a Schwarzschild (non-rotating) black hole from its mass. Enter the mass in solar masses, Earth masses, or kilograms, and obtain the Schwarzschild radius, Hawking temperature, photon sphere, innermost stable circular orbit (ISCO), surface gravity, evaporation time, Hawking luminosity, and gravitational time dilation at an observer distance.

Black holes are among the most extreme objects in the universe. The event horizon — the boundary beyond which nothing escapes — scales linearly with mass. Hawking radiation temperature, however, is inversely proportional to mass, meaning small black holes are incredibly hot while supermassive ones are colder than the cosmic microwave background.

Use the built-in presets for real black holes like Sagittarius A* and M87*, or explore hypothetical Earth-mass and primordial black holes. The reference tables reveal how properties scale with mass and how time dilation varies with distance. It keeps the horizon, orbital radii, and evaporation estimates together so the size and thermodynamic behavior can be compared in the same view.

When This Page Helps

Use this page to connect black hole mass to horizon size, orbital structure, Hawking temperature, and evaporation time without manually carrying the constants through each relation. It is useful whenever you want a non-rotating baseline before comparing different masses or moving on to a more detailed relativistic model. That makes it a compact reference for the most common Schwarzschild relationships.

How to Use the Inputs

1. Select a black hole preset or enter a custom mass.
2. Choose the mass unit: solar masses, Earth masses, or kilograms.
3. Set the observer distance in AU for time dilation calculations.
4. Read the Schwarzschild radius, Hawking temperature, photon sphere, ISCO, and more.
5. Explore the mass comparison and distance tables.
6. Use the spin parameter (future: Kerr effects) to note the distinction from non-rotating.

Example Calculation

Tips & Best Practices

• Schwarzschild radius in km ≈ 3 × M (in solar masses).
• Hawking temperature is only significant for black holes lighter than the Moon.
• The event-horizon area is proportional to entropy (Bekenstein-Hawking).
• Time dilation becomes noticeable only within a few Rs of the event horizon.
• The photon sphere is what creates the bright ring in EHT black hole images.

How The Scaling Works

The Schwarzschild radius grows linearly with mass, which is why supermassive black holes can have event horizons larger than planetary orbits. Hawking temperature scales the opposite way, so smaller black holes are hotter while large astrophysical black holes are effectively cold on cosmological background scales.

Orbital Landmarks

The photon sphere, ISCO, and event horizon are different radii with different meanings. The photon sphere is where light can orbit unstably, the ISCO marks the inner edge of stable circular motion for test particles, and the horizon is the true point of no return. Keeping those radii distinct prevents a lot of common confusion.

Model Scope

These outputs assume a Schwarzschild black hole with no spin or charge. Real astrophysical black holes are expected to rotate, which changes the ISCO, frame dragging, and horizon geometry. Use these results as the non-rotating baseline before moving to Kerr-specific formulas.

Frequently Asked Questions

• What is the Schwarzschild radius?

  It is the radius of the event horizon for a non-rotating black hole. Outside that radius escape is possible in principle; inside it, classical escape is not.

• Can a black hole evaporate?

  Yes. Hawking radiation causes black holes to lose mass, but the evaporation time for stellar and supermassive black holes is incomprehensibly longer than the current age of the universe.

• What is the photon sphere?

  A shell at 1.5 Rs where photons travel in unstable circular orbits. It defines the "shadow" seen in black hole images.

• What is ISCO?

  It is the innermost stable circular orbit, the smallest orbit where a test particle can circle without rapidly plunging inward. Inside that radius, stable circular motion is no longer possible for a Schwarzschild black hole.

• What about rotating (Kerr) black holes?

  Rotation shrinks the ISCO on the prograde side and adds an ergosphere. This calculator focuses on Schwarzschild (non-rotating) results.

• Does time really slow near a black hole?

  Yes. Gravitational time dilation is a confirmed prediction of general relativity, measurable even in Earth's gravity field.