Black Hole Size to Mass Calculator

Calculator Inputs

Input Size Value

Input Type

Length Unit

Display Precision

Comparison Mass

Comparison Mass Unit

Chart Sample Points

Formula Used

Schwarzschild radius: R_s = 2GM / c²

Mass from radius: M = R_sc² / 2G

Here, R_s is the event-horizon radius, G is the gravitational constant, and c is the speed of light. The calculator converts diameter, circumference, or area back into radius before solving for mass.

How to Use This Calculator

Enter a black hole size value.
Select whether the value is radius, diameter, circumference, or area.
Choose the size unit, such as kilometers or meters.
Set display precision and optional comparison mass values.
Click Calculate Mass to show results above the form.
Review the numeric outputs, Plotly chart, and comparison note.
Export the current result as CSV or PDF if needed.

Example Data Table

Black Hole Radius	Radius Unit	Approximate Mass	Solar Masses	Notes
3	km	1.99 × 10³⁰ kg	≈ 1.00	Close to one solar mass.
30	km	1.99 × 10³¹ kg	≈ 10.00	Typical stellar-mass example.
3000	km	1.99 × 10³³ kg	≈ 1000.00	Intermediate-mass scale.
30000000	km	1.99 × 10³⁷ kg	≈ 10000000.00	Supermassive regime example.

FAQs

1. What does this calculator estimate?

It estimates black hole mass from event-horizon size using the Schwarzschild relation. You can start from radius, diameter, circumference, or surface area.

2. Does this work for rotating black holes?

This page uses the non-rotating Schwarzschild model. Real rotating black holes need Kerr geometry, so the result is a simplified baseline.

3. Why does mass increase linearly with radius?

In the Schwarzschild formula, radius is directly proportional to mass. Doubling the event-horizon radius doubles the inferred mass.

4. Can I enter diameter instead of radius?

Yes. The calculator converts diameter, circumference, or area into an equivalent Schwarzschild radius before computing mass.

5. What is the average density output?

It is the mass divided by the sphere volume enclosed by the Schwarzschild radius. It is a comparison aid, not a literal interior structure model.

6. Why compare solar and Earth masses?

Those reference scales make very large values easier to read. Stellar black holes are often discussed in solar masses, while smaller comparisons may use Earth masses.

7. What units are supported?

You can enter meters, kilometers, centimeters, millimeters, miles, or feet. The calculator converts everything internally into SI units.

8. Are the CSV and PDF exports dynamic?

Yes. After a successful calculation, the export buttons package the current on-screen result values into downloadable CSV and PDF files.