Gravitational radius
Enter a positive mass and choose kilograms, solar masses, or Earth masses.
About the Schwarzschild radius
The Schwarzschild radius is the characteristic event-horizon radius associated with a given mass in the simplest black-hole solution of general relativity. If a spherically symmetric, nonrotating, electrically neutral mass were compressed inside this radius, the resulting spacetime would contain a black hole. The radius is not the present physical size of an ordinary object. Earth and the Sun, for example, are vastly larger than their Schwarzschild radii and therefore are not black holes.
This calculator uses Rs = 2GM/c². Here G is the Newtonian gravitational constant, 6.67430 × 10⁻¹¹ cubic meters per kilogram per second squared; M is mass in kilograms; and c is the exact speed of light, 299,792,458 meters per second. The result is reported in meters and kilometers. For convenience, one solar mass is converted as 1.98847 × 10³⁰ kilograms and one Earth mass as 5.9722 × 10²⁴ kilograms.
Radius scales directly with mass. One solar mass corresponds to approximately 2.953 kilometers, while one Earth mass corresponds to only about 8.87 millimeters. A ten-solar-mass ideal Schwarzschild black hole has a radius near 29.5 kilometers. This linear scaling makes quick estimates straightforward: doubling mass doubles the horizon radius. Density required to fit within that radius, however, does not scale in the same way, because volume grows with the cube of radius.
The Schwarzschild solution makes important assumptions. Real astrophysical black holes usually rotate, and rotating objects are described more accurately by the Kerr geometry. Electric charge is expected to be negligible for most astronomical black holes, but charged theoretical solutions have different horizons. The calculation also treats the specified mass as the spacetime's isolated total mass and does not model accretion disks, companions, cosmological effects, or tidal forces.
An event horizon is not a material surface. It is a causal boundary beyond which outward-directed light cannot reach distant observers. The familiar statement that escape velocity reaches the speed of light at the Schwarzschild radius gives the same algebraic expression, but a complete interpretation belongs to general relativity rather than Newtonian mechanics. Use this calculator for accurate scale estimates, educational comparisons, and checks of mass-radius relationships. Detailed modeling of rotating horizons, observations, mergers, or strong-field trajectories requires relativistic methods tailored to the physical system.
Schwarzschild radius FAQ
Does every object have a Schwarzschild radius?
A Schwarzschild radius can be calculated for any positive mass as a characteristic gravitational scale. The object is a black hole only if that mass is confined appropriately within its horizon.
Is the Schwarzschild radius a diameter?
No, it is the radial distance from the center to the ideal event horizon. The corresponding horizon diameter is twice the displayed value.
Why is the result about 3 km per solar mass?
Substituting one solar mass into 2GM/c² gives approximately 2.953 kilometers. Direct proportionality means each additional solar mass contributes the same radius in this ideal model.
Does this calculator handle rotating black holes?
No, it uses the nonrotating Schwarzschild solution. A rotating Kerr black hole has spin-dependent horizon geometry and requires additional information.
Is an event horizon a solid surface?
No, it is a boundary in spacetime rather than material matter. Crossing it need not resemble striking a physical shell, although tidal effects depend strongly on mass and location.