Schwarzschild Radius Calculator

Why a Black Hole Sun Wouldn't Suck Earth In

The single most persistent black hole misunderstanding is that they suck in everything around them. They do not. If the Sun were replaced by a black hole of identical mass, its horizon would shrink to a 2.95 kilometre sphere, but the gravity felt by Earth, 150 million kilometres away, would not change in the slightest, since gravity depends on mass and distance, not on size. The planets would keep orbiting exactly as before. The danger of a black hole is purely local, it comes from getting close to that tiny horizon, where the field becomes extreme. A black hole is not a drain in the fabric of space, it is a very compact mass, and at a distance it pulls no harder than the star it replaced. The NASA Imagine the Universe guide to black holes sets out this point explicitly, covering why the Schwarzschild radius is a one-way surface rather than an inward force.

What the Schwarzschild Radius Calculator Actually Does

This tool works out the size of the event horizon any mass would have if it collapsed into a black hole, using r_s = 2GM/c². Enter a mass in kilograms, Earth masses, Jupiter masses, solar masses, or billions of solar masses, and it returns the Schwarzschild radius along with the photon sphere, innermost stable orbit, surface gravity, and average density inside the horizon. Named after Karl Schwarzschild, who solved Einstein's field equations in 1916 while serving on the First World War front, this radius marks the boundary beyond which nothing, not even light, escapes, the NASA black hole overview describes it as a black hole's defining feature. This calculator carries out a full survival analysis, figuring out whether a person could cross a given horizon intact, comparing average density against everyday materials, and showing how far an object needs compressing to become a black hole, across presets from a single proton to the ultramassive quasar TON 618.

The Formula and What It Means

r_s = 2GM/c², one of general relativity's most important results, reads off in a single line: horizon radius is directly proportional to mass, double the mass and you double the radius. Because the speed of light squared sits in the denominator, the radius is tiny for ordinary masses, the Sun's is just 2.95 kilometres, Earth's a mere 8.87 millimetres, a human body's smaller than a single atomic nucleus, which is why everyday matter never collapses on its own. This linear scaling has a striking consequence: the compression needed to form a black hole is almost unimaginable for small objects but far gentler for large ones. Turning Earth into a black hole requires crushing its entire mass into a marble; turning a supermassive cloud of millions of solar masses into one only needs a density comparable to water. The same geometry underlies the merged horizons computed by our Black Hole Collision Calculator.

Average Density: Why Bigger Black Holes Are Emptier

One of astrophysics' most surprising facts is that supermassive black holes are not especially dense on average. Average density is mass divided by the volume of a sphere with the Schwarzschild radius, and because radius grows linearly with mass while volume grows as its cube, density falls as one over mass squared. A small black hole is extraordinarily dense; a giant one can be more diffuse than the air you breathe.

This is why calling a black hole simply "a region of extreme density" misleads for the largest ones, the mass is thought to collapse to a central singularity, but averaged over a supermassive black hole's vast horizon volume, the figure is laughably low. The JPL account of imaging M87* notes its event horizon is larger than our entire solar system, a scale this calculator reproduces directly.

Tidal Forces and the Survival Question

What would happen if you fell in is the opposite of most people's intuition. Tidal force, the difference in gravitational pull between head and feet, stretches an infalling body into a thin stream, spaghettification. Crucially, tidal force at the horizon scales as one over mass squared, most violent for the smallest black holes. For a stellar-mass black hole, the tidal difference across a human body reaches billions of times Earth gravity, tearing you apart thousands of kilometres before the horizon; for Sagittarius A*, the same calculation gives a tidal difference under a thousandth of a g, utterly imperceptible, you would sail across the horizon without feeling a thing. As the spaghettification reference explains, the event horizon is not a physical surface but a feature of global geometry, locally entirely unremarkable. The photon sphere at 1.5 times the Schwarzschild radius and the innermost stable orbit at 3 times it round out the geometry; our Black Hole Temperature Calculator covers the thermal side of the same story.

Accuracy and Limitations

This calculator uses the exact Schwarzschild solution for a non-rotating, uncharged black hole, so radius, photon sphere, and ISCO are precise for that idealised case, with exact analytic expressions for average density, tidal force, and gravitational time dilation via the Schwarzschild metric. For most astrophysical purposes these values are reliable, since charge is negligible for real black holes and corrections from modest spin are small. Real black holes generally rotate, described by the Kerr solution, where the event horizon is smaller than the Schwarzschild radius and additional structure like the ergosphere appears. The tidal-force figure is a Newtonian approximation capturing the right magnitude and scaling but not the full relativistic tidal tensor near the horizon, and reported average density is a useful comparison figure rather than a literal description of mass distribution. For the deep interior, classical general relativity predicts a singularity where the theory itself breaks down, the LIGO guide to what black holes are provides observational context for what the Schwarzschild radius means in terms of observable effects.