Schwarzschild Radius Calculator
Computes the Schwarzschild radius — the critical size at which any mass becomes a black hole. Use it to find the event horizon of stars, planets, or any object undergoing hypothetical gravitational collapse.
About this calculator
The Schwarzschild radius r_s is the radius of the event horizon of a non-rotating black hole, defined as the distance from the singularity at which escape velocity equals the speed of light. It is derived from general relativity and given by: r_s = 2GM / c², where G = 6.674×10⁻¹¹ m³ kg⁻¹ s⁻² is the gravitational constant, M is the mass in kilograms, and c = 299,792,458 m/s is the speed of light. With unit conversion factors the formula becomes r_s = (2 × 6.674×10⁻¹¹ × M × massUnitFactor) / (c² × outputUnitFactor). Any object compressed below its Schwarzschild radius will collapse into a black hole. For the Sun (M ≈ 1.989×10³⁰ kg), r_s ≈ 2,953 meters — just under 3 km. For Earth, it is only about 8.87 mm.
How to use
Find the Schwarzschild radius of a 10-solar-mass black hole. Step 1: M = 10 × 1.989×10³⁰ kg = 1.989×10³¹ kg. Step 2: r_s = 2 × 6.674×10⁻¹¹ × 1.989×10³¹ / (299,792,458)². Step 3: Numerator = 2 × 6.674×10⁻¹¹ × 1.989×10³¹ = 2.655×10²¹. Step 4: Denominator = c² = 8.988×10¹⁶. Step 5: r_s = 2.655×10²¹ / 8.988×10¹⁶ ≈ 29,540 meters ≈ 29.5 km. Enter 10 solar masses in the mass field and select meters as the output unit to verify.
Frequently asked questions
What happens physically at the Schwarzschild radius of a black hole?
The Schwarzschild radius marks the event horizon — the boundary beyond which nothing, not even light, can escape the gravitational pull. An outside observer never sees an object cross this boundary; instead, it appears to freeze and fade due to extreme gravitational time dilation and redshift. For the infalling observer, however, crossing the event horizon is not locally dramatic for large black holes; tidal forces at the horizon of a stellar-mass black hole are lethal, but for a supermassive black hole they can be mild at the horizon. Once inside, all paths in spacetime lead inevitably to the central singularity.
How is the Schwarzschild radius different for stellar-mass versus supermassive black holes?
The Schwarzschild radius scales linearly with mass: doubling the mass doubles the radius. A stellar-mass black hole of 10 solar masses has r_s ≈ 29.5 km, while the supermassive black hole M87* (about 6.5 billion solar masses) has r_s ≈ 19.2 billion km — larger than our entire solar system. Supermassive black holes are less dense at their event horizons because volume grows as r³ while mass only grows as r, meaning density ∝ 1/r². A black hole with the mass of the observable universe would have a Schwarzschild radius comparable to the observable universe itself.
Could the Earth or Sun ever become a black hole?
Only if compressed below their respective Schwarzschild radii — about 8.87 mm for Earth and about 2.95 km for the Sun. No natural process can compress Earth or the Sun that severely. Stars become black holes only if their mass exceeds roughly 20–25 solar masses and they lack the radiation pressure to halt collapse after exhausting nuclear fuel. Our Sun will eventually become a white dwarf, never approaching its Schwarzschild radius. The calculation is a useful thought experiment but requires fantastically extreme compression far beyond any natural stellar process for Earth-like bodies.