Schwarzschild Radius Calculator — Black Hole Sizes for Any Mass
Calculate the Schwarzschild radius (event horizon) for any mass, from subatomic particles to supermassive black holes. Understand what makes a black hole a black hole.
Every object has a Schwarzschild radius — the theoretical radius at which it would become a black hole if compressed to that size. The Earth's Schwarzschild radius is about 9mm. The Sun's is around 3km. Most objects will never reach that density, but the concept reveals something fundamental about gravity and spacetime.
Calculate Schwarzschild radii for any mass at CalcHub.
The Formula
Karl Schwarzschild derived his famous radius from Einstein's field equations in 1916 — famously, while serving on the Russian front in World War I:
r_s = 2GM / c²
Where:
- G = gravitational constant (6.674 × 10⁻¹¹ m³/kg/s²)
- M = mass in kilograms
- c = speed of light (2.998 × 10⁸ m/s)
The result is the radius of the event horizon — the point of no return beyond which not even light can escape.
Schwarzschild Radii for Common Masses
| Object | Mass | Schwarzschild Radius |
|---|---|---|
| Human (70 kg) | 70 kg | ~1.0 × 10⁻²⁵ m (sub-atomic) |
| Earth | 5.97 × 10²⁴ kg | ~8.87 mm |
| Moon | 7.35 × 10²² kg | ~0.109 mm |
| Sun | 1.99 × 10³⁰ kg | ~2.95 km |
| Stellar black hole (10 M☉) | 1.99 × 10³¹ kg | ~29.5 km |
| M87* (6.5 billion M☉) | ~1.3 × 10⁴⁰ kg | ~19.2 billion km |
| Ton 618 (66 billion M☉) | ~1.3 × 10⁴¹ kg | ~195 billion km |
How to Use the Calculator
- Enter mass in kilograms, solar masses, or Earth masses
- Get Schwarzschild radius in meters, kilometers, or AU
- See how the event horizon compares to real astronomical objects
Density at the Event Horizon
A stellar black hole (10 solar masses) has an event horizon radius of ~30km — nuclear density at the Schwarzschild sphere boundary. But M87*'s event horizon is so large that the average density inside it is about 0.0009 kg/m³ — far less dense than air at sea level. The "point of no return" for supermassive black holes is in a near-vacuum region; you'd cross the event horizon without experiencing anything dramatic locally.
Rotating vs. Non-Rotating Black Holes
The Schwarzschild solution describes non-rotating black holes. Real black holes rotate (described by the Kerr metric), which compresses the effective event horizon somewhat. The Kerr event horizon is smaller than Schwarzschild by a factor that depends on spin. For maximum spin ("extremal" Kerr black hole), the event horizon radius is exactly half the Schwarzschild radius.
What would happen if you fell into a stellar black hole?
Tidal forces — the difference in gravity between your head and feet — would stretch you into a thin strand of atoms before you even reached the event horizon. Physicists call this "spaghettification." For a supermassive black hole, tidal forces at the event horizon are much gentler; you might cross it without noticing, only realizing later that escape is impossible.
Can anything escape from inside the event horizon?
Classically, no. But Stephen Hawking showed in 1974 that quantum effects allow black holes to slowly emit thermal radiation (Hawking radiation), very gradually losing mass. For stellar-mass black holes, this process is astronomically slow — they would take 10⁶⁷ years or longer to evaporate, far longer than the current age of the universe.
What is the smallest theoretical black hole?
A primordial black hole — theoretically formed in the extreme density of the early universe — could have any mass. The minimum mass for a "stable" primordial black hole (one that hasn't evaporated via Hawking radiation) is around 10¹¹ kg — roughly the mass of a mountain, with a Schwarzschild radius of ~10⁻¹⁶ m. Whether such objects exist is an open question in cosmology.
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