Schwarzschild Radius Calculator
Find the event-horizon radius for any mass. Enter a mass in solar masses (default), Earth masses, Jupiter masses, or kilograms, and get the Schwarzschild radius rs = 2GM/c² — the size an object must be squeezed below to become a black hole — plus the mean density inside that horizon.
Example: with Mass 1 · Mass unit Solar masses (M☉ = 1.98847×10³⁰ kg) → Schwarzschild radius: 2.953 km.
- Mass in kilograms1.9885e+30 kg
- Mean density inside the horizon1.84e+19 kg/m³ — beyond atomic-nucleus density
Computed by the calculator below using its default values. Change any input to see your own numbers.
rs = 2GM/c², from Karl Schwarzschild's 1916 exact solution to Einstein's field equations. The Sun's rs is about 2.95 km; Earth's is 8.9 mm.
What the Schwarzschild radius means
Every mass has a Schwarzschild radius: compress the object inside that radius and its escape velocity reaches the speed of light, so nothing — light included — can climb back out. The boundary is the event horizon. The formula rs = 2GM/c² falls out of Karl Schwarzschild's 1916 solution to general relativity, found within weeks of Einstein publishing the field equations. It scales strictly linearly with mass: double the mass, double the radius.
The numbers are what make it vivid. The Sun's 1.989×10³⁰ kg would need to fit inside a 2.95 km sphere — a small town. Earth's horizon is 8.9 mm, about peanut-sized. Nothing short of the runaway collapse of a star's core actually achieves these compressions.
Why big black holes are 'thin'
Because rs grows linearly with mass while volume grows with radius cubed, the mean density inside the horizon falls as 1/M². A stellar black hole is denser than an atomic nucleus, but Sagittarius A*, the 4.3-million-solar-mass hole at the Milky Way's center, averages about the density of water — and the biggest known holes average less than air. Crossing the horizon of a supermassive black hole would be locally unremarkable; the density figure this tool reports is the cleanest way to see it. (It is an average over the horizon volume, not a claim about what is inside.)
How it’s calculated
rs = 2GM/c², with G = 6.6743×10⁻¹¹ m³/(kg·s²) (CODATA 2018) and c = 299,792,458 m/s exactly, so c² = 8.98755178737×10¹⁶ m²/s². Mass presets: 1 M☉ = 1.98847×10³⁰ kg (IAU nominal), 1 Earth mass = 5.9722×10²⁴ kg, 1 Jupiter mass = 1.89813×10²⁷ kg. Mean density = M ÷ (4/3)πrs³.
Assumes a non-rotating, uncharged mass — real astrophysical black holes spin, which shrinks the horizon by up to a factor of 2 (Kerr geometry).
Schwarzschild radii of real objects
| Object | Mass | rs |
|---|---|---|
| Earth | 5.97×10²⁴ kg | 8.9 mm |
| Jupiter | 1.90×10²⁷ kg | 2.82 m |
| The Sun | 1 M☉ | 2.95 km |
| Cygnus X-1 (stellar black hole) | 21.2 M☉ | 62.6 km |
| Sagittarius A* (Milky Way center) | 4.30×10⁶ M☉ | 12.7 million km |
| M87* (imaged by EHT, 2019) | 6.5×10⁹ M☉ | ≈ 128 AU |
Computed with rs = 2GM/c² from published masses (mass values: NASA/IAU; Cygnus X-1 and M87* from the discovery/EHT papers); rounded.
Common mistakes
- Reading rs as the size of the object today — it is the radius the mass must be squeezed below, not a property visible from outside collapse.
- Confusing radius with diameter when comparing to familiar objects; the horizon's diameter is 2rs.
- Treating the mean density as the actual interior density — general relativity does not describe the interior as uniform matter at all.
- Applying the non-rotating formula to a rapidly spinning hole and expecting exact agreement — spin changes horizon geometry.
Frequently asked questions
What is the Schwarzschild radius formula?
rs = 2GM/c²: twice the gravitational constant times the mass, divided by the speed of light squared. In convenient terms, rs ≈ 2.95 km for every solar mass.
What is the Schwarzschild radius of the Sun?
About 2.95 km. The Sun would need to collapse from its 696,000 km radius to under 3 km to become a black hole — which cannot happen naturally, since it is far below the stellar-collapse mass threshold.
Does the Earth have a Schwarzschild radius?
Yes — every mass does. Earth's is 8.9 mm. Nothing about Earth is close to becoming a black hole; the number just says how absurdly compressed it would need to be.
Is the event horizon a physical surface?
No. It is a boundary in spacetime where escape requires faster-than-light travel. An infalling observer crosses it without hitting anything — a common confusion the mean-density output helps dispel for large holes.
Why does this calculator ignore spin?
The Schwarzschild solution assumes no rotation or charge. Spinning (Kerr) black holes have a smaller, more complicated horizon — down to half the Schwarzschild value at maximal spin — so treat these results as the non-rotating baseline.