About the Schwarzschild Radius Calculator
This Schwarzschild radius calculator finds the radius of the event horizon of a non-rotating black hole with a given mass — the size to which that mass would have to be compressed for not even light to escape. Enter a mass in solar masses, Earth masses, Jupiter masses or kilograms and it returns the radius in readable units, along with the photon sphere, the innermost stable circular orbit (ISCO) and the average density inside the horizon.
It is built for physics and astronomy students, science writers and anyone curious about black holes: how big would the Sun be as a black hole (about 3 km), or Earth (about the size of a marble)? It also shows the Hawking radiation temperature and the time such a black hole would take to evaporate, which reveal why only microscopic black holes would evaporate on any human timescale.
The results use the Schwarzschild solution of general relativity for a non-rotating, uncharged black hole. Real astrophysical black holes spin, which shrinks the horizon and ISCO somewhat, and the evaporation time is the idealised photon-only estimate that ignores the cosmic microwave background.
How to use the schwarzschild radius calculator
- 1Enter the mass of the object or black hole.
- 2Choose the unit — solar masses for stars and black holes, Earth or Jupiter masses for planets.
- 3Read the Schwarzschild radius in the most readable unit.
- 4Check the photon sphere and ISCO distances.
- 5Compare density, Hawking temperature and evaporation time, and the reference table.
Formula and method
The Schwarzschild radius comes from Karl Schwarzschild’s 1916 solution of Einstein’s field equations: at rₛ = 2GM/c² the escape velocity equals the speed of light, defining the event horizon. It is directly proportional to mass — about 2.95 km per solar mass. The photon sphere, where light can orbit, lies at 1.5 rₛ, and the innermost stable circular orbit for matter at 3 rₛ.
Mean density is the mass divided by the volume of a sphere of radius rₛ, which falls as 1/M². The Hawking temperature and the photon-only evaporation time follow Hawking’s 1974 result. Constants: G = 6.6743 × 10⁻¹¹, c = 299,792,458 m/s, ħ and k_B from CODATA 2018; M☉ = 1.98847 × 10³⁰ kg.
- rₛ
- Schwarzschild (event horizon) radius
- G
- Gravitational constant, 6.6743 × 10⁻¹¹ m³·kg⁻¹·s⁻²
- M
- Mass of the black hole (kg)
- c
- Speed of light in vacuum
- ħ, k_B
- Reduced Planck constant and Boltzmann constant
Worked examples
The Sun as a black hole
rₛ = 2 × 6.6743e-11 × 1.98847e30 ÷ (299,792,458)² ≈ 2,953 m. The Sun would have to shrink from 696,000 km to under 3 km in radius to become a black hole.
Earth compressed to a black hole
Earth’s 5.97 × 10²⁴ kg gives rₛ ≈ 8.87 mm — a black hole about the size of a marble (17.7 mm across).
Sagittarius A*, the Milky Way’s central black hole
4.3 million solar masses × 2.953 km ≈ 12.7 million km, or 0.085 AU — about a fifth of Mercury’s distance from the Sun.
M87*, the first black hole imaged
At 6.5 billion solar masses the horizon is about 1.92 × 10¹⁰ km — 128 AU, more than three times Pluto’s distance from the Sun. Its average density is under 0.5 kg/m³.
Frequently asked questions
What is the Schwarzschild radius?+
It is the radius of the event horizon of a non-rotating black hole: rₛ = 2GM/c². Anything compressed inside its own Schwarzschild radius becomes a black hole, and nothing — not even light — can escape from within it.
What would the Schwarzschild radius of the Sun be?+
About 2.95 km. The Sun will never actually become a black hole; stars need roughly 20 or more solar masses at birth to leave a black hole behind after a supernova.
How big would Earth be as a black hole?+
Earth’s Schwarzschild radius is about 8.9 millimetres, so it would be a black hole roughly the size of a marble while still having Earth’s full mass and gravity at a distance.
Do bigger black holes have higher density?+
No — the opposite. Because the radius grows in proportion to mass while volume grows with the cube of radius, average density falls as 1/M². A supermassive black hole of a few hundred million solar masses has an average density below water.
Does a spinning black hole have the same radius?+
No. A rotating (Kerr) black hole’s outer horizon shrinks toward GM/c², half the Schwarzschild value, as spin approaches the maximum. This calculator assumes no spin, which gives the largest possible horizon for a given mass.