Black Hole Temperature Calculator

Hawking radiation is thermal radiation theoretically predicted to be emitted by black holes due to quantum effects near the event horizon. Stephen Hawking showed in 1974 that black holes are not completely black — they slowly radiate energy as a blackbody at a specific temperature inversely proportional to their mass. This means smaller black holes are hotter than larger ones.

The calculator uses the Hawking temperature formula: T = ℏc³ / (8πGMk_B), where ℏ is the reduced Planck constant (1.0546 × 10⁻³⁴ J·s), c is the speed of light (2.998 × 10⁸ m/s), G is the gravitational constant (6.674 × 10⁻¹¹ m³/(kg·s²)), M is the black hole mass in kilograms, and k_B is Boltzmann's constant (1.381 × 10⁻²³ J/K).

Temperature is inversely proportional to mass in the Hawking formula (T ∝ 1/M). A more massive black hole has a larger event horizon and weaker tidal forces at the horizon, leading to lower Hawking temperature. A stellar-mass black hole has a temperature far below the cosmic microwave background, while a microscopic primordial black hole could be extremely hot.

The Schwarzschild radius is the radius of the event horizon — the boundary beyond which nothing, not even light, can escape. It is calculated as r_s = 2GM/c². For a black hole with one solar mass (~1.989 × 10³⁰ kg), the Schwarzschild radius is approximately 2.95 km.

A black hole with one solar mass (about 1.989 × 10³⁰ kg) has a Hawking temperature of approximately 6.17 × 10⁻⁸ K — far colder than the cosmic microwave background temperature of ~2.725 K. This means stellar-mass black holes are actually absorbing more radiation from the universe than they emit.

A black body is a theoretical object that absorbs all electromagnetic radiation incident upon it and emits radiation based solely on its temperature. A black hole absorbs all radiation that crosses its event horizon and emits Hawking radiation thermally, making it very nearly a perfect black body — the closest known physical approximation to this theoretical concept.

Hawking radiation from astrophysical black holes is extraordinarily faint — far below any current or near-future detection capability. For stellar-mass black holes the temperature is billionths of a Kelvin, making direct detection practically impossible. However, analogues of Hawking radiation have been observed in laboratory setups using sonic black holes (dumb holes) in Bose-Einstein condensates.

As a black hole radiates energy, it loses mass. Because temperature increases as mass decreases, the process accelerates — the black hole gets hotter and radiates faster. This runaway evaporation ends in a final explosion when the black hole reaches a very small mass. For a stellar-mass black hole, the evaporation timescale is astronomically longer than the current age of the universe.