# Schwarzschild Radius Calculator

URL: https://speedycalculator.com/calculators/physics/schwarzschild-radius/
Last updated: 2026-10-30

> The Schwarzschild radius calculator finds the event horizon radius of a non-rotating black hole of a given mass, along with its surface gravity and the average density inside the horizon.

## Inputs

- Mass M (M☉, M⊕, kg)

## Results

- Schwarzschild radius r_s
- Surface gravity κ
- Average density inside the horizon

## Formula

```
r_s = 2GM/c²,  κ = c⁴/(4GM),  ρ = M / (4/3·π·r_s³)
```

## Explanation

Compress any mass inside its Schwarzschild radius and it becomes a black hole. For the Sun that is about 3 km; for Earth, just 9 mm. Supermassive black holes are so large that their average density can be lower than water's.

### How to use the Schwarzschild Radius Calculator

- **Mass M**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Enter the mass.

### What each result means

- **Schwarzschild radius r_s** = 2×6.6743e-11×[Mass M]÷299792458^2
- **Surface gravity κ** = 299792458^4÷(4×6.6743e-11×[Mass M])
- **Average density inside the horizon** = [Mass M]÷(4÷3×pi×[Schwarzschild radius r_s]^3)

### Example values

How the main result changes when **Mass M** changes and everything else stays at the example values above:

Mass M (M☉)Schwarzschild radius r_s (km)0.51.47670.752.21512.95331.253.69171.54.4325.9067

## Worked example

Inputs — Mass M: 1 M☉.

Results — **Schwarzschild radius r_s = 2.953339 km**; Surface gravity κ = 15,215,914,300,168.049 m/s²; Average density inside the horizon = 1.8429e19 kg/m³.

## Key terms

- **Event horizon**: Boundary beyond which nothing can escape.

## FAQ

**What is the Schwarzschild radius of the Sun?**
About 2.95 km.

**What about Earth?**
About 8.9 mm.

**Can a black hole have low density?**
Yes – density falls as 1/M², so huge black holes are "light".

**Does this apply to spinning black holes?**
No – rotating (Kerr) black holes have smaller horizons.


## Sources

- [OpenStax – University Physics Volume 3](https://openstax.org/details/books/university-physics-volume-3)
- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)