Schwarzschild Radius Calculator

Estimate black hole radius from mass inputs fast. Explore solar, planetary, stellar, and custom scenarios. See steps, charts, units, exports, and practical examples clearly.

Calculator Input

Use preset masses or enter a custom value. The calculator handles kilograms, grams, solar masses, Earth masses, Jupiter masses, and pounds.

Plotly Graph

The chart shows Schwarzschild radius versus mass on logarithmic axes, plus your selected point when a calculation is available.

Graph updates using the latest submitted mass.

Example Data Table

These reference values help compare familiar masses with their corresponding event horizon scales.

Object Mass Mass in kg Schwarzschild radius Diameter
Earth 1 Earth masses 5.972200e+24 kg 8.870103 mm 17.740206 mm
Sun 1 Solar masses 1.988470e+30 kg 2.953339 km 5.906679 km
Jupiter 1 Jupiter masses 1.898130e+27 kg 2.819164 m 5.638327 m
10-solar-mass object 10 Solar masses 1.988470e+31 kg 29.533394 km 59.066788 km
Sagittarius A* scale 4.300000e+6 Solar masses 8.550421e+36 kg 0.08489 AU 0.16978 AU

Formula Used

Schwarzschild radius: Rs = 2GM / c²
Diameter: D = 2Rs
Circumference: C = 2πRs
Surface area: A = 4πRs²
Volume of equivalent sphere: V = (4/3)πRs³
Average density inside Rs: ρ = M / V
Light crossing time: t = Rs / c
Photon sphere radius: rph = 1.5Rs
Innermost stable circular orbit for a non-rotating case: risco = 3Rs
Gravitational time factor at radius r: √(1 - Rs / r), valid only when r > Rs

Here, G is the gravitational constant, M is mass, and c is the speed of light. The calculator assumes a non-rotating, uncharged object, matching the standard Schwarzschild solution.

How to Use This Calculator

  1. Choose a preset object or enter your own object label.
  2. Enter the mass value using standard or scientific notation.
  3. Select the correct mass unit from the dropdown.
  4. Optionally enter an observation radius to test time dilation outside the horizon.
  5. Click the calculate button to show the result above the form.
  6. Review the table, summary cards, and graph for quick interpretation.
  7. Use the CSV button for spreadsheet-ready export.
  8. Use the PDF button to save a clean calculation report.

Frequently Asked Questions

1) What is the Schwarzschild radius?

It is the radius of the event horizon for a non-rotating, uncharged mass. If all mass fits inside that radius, light cannot escape to distant observers.

2) Does a larger mass always give a larger radius?

Yes. Schwarzschild radius increases linearly with mass. Doubling the mass doubles the event horizon radius, provided the same non-rotating Schwarzschild assumptions remain valid.

3) Can Earth become a black hole naturally?

Not under normal conditions. Earth would need to be compressed inside a Schwarzschild radius of only a few millimeters, which is far beyond natural planetary behavior.

4) Why does the calculator include photon sphere and ISCO?

They provide extra physical context. The photon sphere marks unstable light orbits, while ISCO gives the smallest stable circular orbit for matter around a non-rotating black hole.

5) What does the average density result mean?

It is the mass divided by the volume of a sphere with radius Rs. It helps compare how compact an object must be to form an event horizon.

6) Is the time dilation factor valid everywhere?

No. This simple factor applies only outside the event horizon for a stationary observer. At or below the horizon, a stationary position is not physically possible.

7) Does this calculator handle spinning black holes?

No. It uses the Schwarzschild model only. Rotating black holes follow the Kerr solution, which changes horizon properties and orbit locations.

8) Why is Hawking temperature included?

It adds an advanced thermodynamic estimate. The temperature is extremely tiny for stellar and supermassive black holes, but it is useful for theory comparisons.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.