Schwarzschild Radius Calculator & Formula
Calculate the Schwarzschild radius rₛ = 2GM/c² of any black hole. The Sun would be 2.95 km, Earth 8.87 mm, Sagittarius A* about 12.7 million km.
The idea behind it
The event horizon is a boundary in spacetime, not a material surface. For a non-rotating, uncharged black hole, its radius grows linearly with mass.
The relationship to remember
rₛ = 2GM/c² ≈ 2.95334 km × 10 solar masses = 29.53 km.
Make your own discovery
Double the mass. Unlike the radius of an ordinary star, this horizon radius also doubles.
Open the Black Hole Event Horizon Simulator ↗Key formulas
| Quantity | Formula | Note or example |
|---|---|---|
| Schwarzschild radius | rₛ = 2GM / c² | G = 6.674 × 10⁻¹¹ m³ kg⁻¹ s⁻², c = 299,792,458 m/s |
| Quick estimate | rₛ ≈ 2.95 km × (M / M☉) | Grows in proportion to mass |
| Event horizon diameter | D = 2rₛ | Black hole “size” |
Worked examples
Each row uses one of this lab’s presets and the same model as the interactive tool.
| Example | Horizon radius | Horizon diameter | Mass |
|---|---|---|---|
| Sun’s mass | 2.95 km | 5.91 km | 1 Sun |
| Stellar mass | 29.53 km | 59.07 km | 10 Suns |
| Sagittarius A* | 12.7 million km (0.085 AU) | 25.4 million km (0.17 AU) | 4,300,000 Suns |
| M87* | 19.2 billion km (128 AU) | 38.4 billion km (257 AU) | 6,500,000,000 Suns |
What this model leaves out
The Schwarzschild solution: no rotation or electric charge. The glowing ring is an explanatory illustration, not an image prediction. It is not the size of an observed black hole shadow.
Check your understanding
Would a black hole with the Sun’s mass pull Earth in?
At Earth’s distance it would have the same gravitational pull as the Sun, neglecting other differences. Earth’s orbit would not suddenly collapse.
Is the bright ring the event horizon?
No. Glowing material and bent light can appear around a black hole; the horizon itself does not emit light that escapes.
What is the formula for the Schwarzschild radius?
rₛ = 2GM/c², where G is the gravitational constant, M the mass and c the speed of light. It is the radius at which the escape speed would equal the speed of light; for one solar mass it is about 2.95 km.
How big would a black hole with Earth’s mass be?
Its Schwarzschild radius would be about 8.87 millimeters, so the event horizon would be roughly 1.8 cm across — about the size of a marble.
Continue with the formula reference or test yourself in space practice.