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The Schwarzschild radius (sometimes RS) is the radius of a (simple) black hole's event horizon, according to Karl Schwarzschild's solution to Einstein's field equation. More specifically, his solution yields the radius of the event horizon of an electrically-neutral, non-rotating black hole. The term is also used for other astronomical objects, meaning the radius of the event horizon of a black hole that has the same mass as the object, i.e., that radius of the black hole resulting from the object's collapse, if no mass were lost in the process. The Schwarzschild radius is a function of the object's mass and is directly proportional to it:
RS = 2GM/c²
Some examples:
| Object | approx Schwarzschild radius |
| Large SMBH | ~1013 m or ~100 AU |
| Milky Way SMBH (Sagittarius A*) | ~1.2×1010 m or ~1/10 AU |
| Large stellar-mass BH (e.g., 15 MSun) | ~44 km |
| Sun | ~3 km |
| Jupiter | ~2.8 m |
| Earth | ~9 mm |
| 1 kg object | ~1.4×10-27 m |
| Planck mass (~2.18×10-5g) object | ~3.23×10-35 m |
The Schwarzschild radius places a limit on how small an object of a given mass can be without becoming a black hole, but somewhat larger astronomical objects collapse into black holes if their structure is insufficiently "strong" to support the given mass (i.e., they produce insufficient pressure, which depends on their equations of state, to support the mass). A black hole appears if any spherical sub-portion of an object exceeds that portion's Schwarzschild density, the density that implies a mass is within its corresponding Schwarzschild radius.
The Schwarzschild radius formula (above) appears in various correction factors adapting classical formulas so as to approximately accommodate small general relativistic effects, and often such correction factors are cited incorporating RS.
The term gravitational radius (typically, rg) is also used for the Schwarzschild radius, but also sometimes used for half the above definition, i.e., lacking the factor of two; either of these is a convenient unit because some analysis of observational data yields distances only as multiples of GM/c².
The term Schwarzschild diameter naturally means twice the Schwarzschild radius.