Calculate the event horizon radius of a black hole from its mass. Includes photon sphere, ISCO, Hawking temperature, and famous black hole comparisons.
The Schwarzschild radius defines the event horizon of a non-rotating black hole — the boundary beyond which nothing, not even light, can escape. First derived by Karl Schwarzschild in 1916 from Einstein's general relativity field equations, this radius is directly proportional to the black hole's mass: Rs = 2GM/c².
Black holes span an enormous range of sizes: stellar-mass black holes from collapsed stars have radii of a few kilometers, supermassive black holes at galaxy centers can be larger than our solar system, and hypothetical primordial micro black holes might be smaller than an atom.
This calculator computes the Schwarzschild radius along with related properties — the photon sphere, the innermost stable circular orbit (ISCO), Hawking radiation temperature, and estimated evaporation time. A comparison mode lets you check whether any given object compressed to its mass would form a black hole, and a reference table of famous black holes provides real-world context.
Black holes are among the most fascinating objects in the universe. This calculator makes their physics accessible by computing key properties from just the mass, comparing them to familiar objects, and illustrating the extreme nature of spacetime near the event horizon. Keep these notes focused on your operational context. Tie the context to the calculator’s intended domain.
Schwarzschild radius: R_s = 2GM/c², where G = 6.674 × 10⁻¹¹ m³/(kg·s²), M is mass (kg), c = 2.998 × 10⁸ m/s. Photon sphere: r_ph = 1.5 R_s. ISCO: r_isco = 3 R_s. Hawking temperature: T = ℏc³/(8πGMk_B).
Result: R_s ≈ 2.953 km
If the Sun were compressed into a black hole, its event horizon would have a radius of about 2.95 km. Its photon sphere would be at 4.43 km and the ISCO at 8.86 km.
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The radius of the event horizon of a non-rotating (Schwarzschild) black hole. Any object compressed within its Schwarzschild radius would become a black hole.
About 8.87 mm — roughly the size of a marble. Earth would need to be compressed to this size to become a black hole.
The Schwarzschild solution applies to non-rotating black holes. Rotating (Kerr) black holes have a more complex horizon structure with an inner and outer horizon.
Theoretical radiation emitted by black holes due to quantum effects near the event horizon. Smaller black holes radiate faster and are hotter. Stellar-mass black holes have temperatures near absolute zero.
At 1.5× the Schwarzschild radius, photons can theoretically orbit the black hole (unstable). This is the closest distance at which light can travel in a circular orbit.
The Innermost Stable Circular Orbit at 3× the Schwarzschild radius is the closest stable orbit for matter. Below this, objects spiral inward. The ISCO determines the inner edge of accretion disks.