Black Hole Temperature Calculator
Calculate Hawking radiation temperature, power output, and Schwarzschild radius using quantum physics.
Enter a black hole mass and choose the unit to instantly compute the Hawking temperature, thermal radiation power, Schwarzschild radius, and estimated evaporation time.
Black Hole Temperature Calculator
Calculate Hawking radiation temperature, power output, and Schwarzschild radius using quantum physics.
About the Black Hole Temperature Calculator
In 1974, Stephen Hawking made one of the most startling predictions in theoretical physics: black holes are not entirely black. Through a quantum mechanical process now called Hawking radiation, black holes slowly emit thermal radiation with a temperature inversely proportional to their mass. This discovery unified quantum mechanics, general relativity, and thermodynamics in a single formula and remains one of the greatest theoretical results of the twentieth century.
The Hawking temperature of a non-rotating, uncharged (Schwarzschild) black hole is T_H = ℏc³/(8πGMk_B), where ℏ is the reduced Planck constant (1.055 × 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⁻¹ s⁻²), M is the black hole mass, and k_B is Boltzmann's constant (1.381 × 10⁻²³ J/K). For a solar-mass black hole (~2 × 10³⁰ kg), this gives a temperature of approximately 6 × 10⁻⁸ K — far colder than the cosmic microwave background (~2.7 K), which means all known astrophysical black holes are absorbing far more radiation than they emit and are effectively growing rather than evaporating.
The Schwarzschild radius, r_s = 2GM/c², marks the event horizon — the boundary inside which nothing, not even light, can escape. For a solar-mass black hole, the event horizon lies at about 2.95 km; for the Earth (~6 × 10²⁴ kg), it would be just 9 mm. The size of the event horizon sets the effective blackbody radiating area, which feeds directly into the total Hawking radiation power.
The total power radiated by a Schwarzschild black hole is given by the Stefan–Boltzmann law applied to its event horizon: P = ℏc⁶/(15360πG²M²). Because power scales as 1/M², smaller black holes radiate enormously more power. A hypothetical micro black hole of mass 10¹⁰ kg (about the mass of a mountain) would have a Hawking temperature of ~10¹³ K and radiate with a power of ~10²⁴ W — comparable to the total power of millions of suns.
As a black hole radiates, it loses mass and heats up, which increases the power, which removes mass faster, in a runaway process. The evaporation time is approximately t_evap = 5120πG²M³/(ℏc⁴). For a solar-mass black hole this gives around 2 × 10⁶⁷ years — many orders of magnitude longer than the current age of the universe (1.38 × 10¹⁰ years). Only extremely small primordial black holes formed in the early universe could possibly be evaporating today. A black hole with mass ~5 × 10¹¹ kg would have been evaporating since the Big Bang and would be exploding in a burst of gamma rays right now.
The black hole temperature calculator lets you explore these relationships across many orders of magnitude — from micro black holes (grams) to the supermassive monsters at galactic centres (billions of solar masses). The results highlight the extraordinary contrast between the macroscopic silence of stellar black holes and the violent quantum evaporation of microscopic ones.
Black Hole Temperature Examples
The table below shows Hawking temperatures and Schwarzschild radii for black holes spanning many orders of magnitude in mass.
| Mass | Key results | Type / context |
|---|---|---|
| 10 M☉ (1.989 × 10³¹ kg) | T_H ≈ 6.17 × 10⁻⁹ K, r_s ≈ 29.5 km, t_evap ≈ 2.1 × 10⁷⁰ yr | Typical stellar black hole |
| 1 × 10¹⁵ kg (primordial) | T_H ≈ 1.23 × 10⁸ K, r_s ≈ 1.49 × 10⁻¹² m, P ≈ 356 W | Primordial BH evaporating today |
| 4 × 10⁶ M☉ (Sgr A*) | T_H ≈ 1.54 × 10⁻¹⁴ K, r_s ≈ 1.18 × 10⁷ km | Milky Way galactic centre |
How to Use the Black Hole Temperature Calculator
- Enter the mass of the black hole in the input field.
- Choose the mass unit: solar masses (M☉) for astrophysical objects, kilograms for smaller bodies, or grams for micro black holes.
- Click Calculate to compute the Hawking temperature, Schwarzschild radius, radiation power, and evaporation time.
- Compare the Hawking temperature with 2.7 K (CMB temperature) to see whether the black hole is net-absorbing or net-evaporating radiation.
- Use the Reset button to clear the fields and try a different mass.
Frequently Asked Questions
Has Hawking radiation ever been detected?
As of 2024, Hawking radiation from astrophysical black holes has never been directly detected. The temperatures involved (~10⁻⁸ K or colder) are completely swamped by the 2.7 K cosmic microwave background. However, analogue Hawking radiation has been observed in condensed-matter laboratory systems (sonic black holes), providing strong indirect confirmation of the quantum mechanism.
Why is a smaller black hole hotter?
The Hawking temperature is inversely proportional to mass: T ∝ 1/M. A smaller black hole has a higher surface gravity at its event horizon, which amplifies the quantum vacuum fluctuations responsible for particle creation. As a black hole loses mass it gets hotter, emits more power, and shrinks even faster — a self-reinforcing cycle that ends in a final explosive evaporation.
What is the Schwarzschild radius?
The Schwarzschild radius r_s = 2GM/c² is the radius of the event horizon for a non-rotating black hole. Any mass compressed below this radius collapses into a black hole from which nothing can escape. For the Earth this is 9 mm; for the Sun it is about 3 km; for a 10-solar-mass black hole it is roughly 30 km.
How long does it take for a black hole to evaporate?
The evaporation time scales as M³: t_evap ≈ 5120πG²M³/(ℏc⁴). A solar-mass black hole would take about 2 × 10⁶⁷ years — vastly longer than the current age of the universe. Only primordial black holes with masses below about 5 × 10¹¹ kg could have evaporated since the Big Bang.
Does the result change for a spinning or charged black hole?
Yes. A Kerr (spinning) black hole emits more radiation than a Schwarzschild black hole of the same mass, because the ergosphere provides extra energy to the Hawking process. A Reissner–Nordström (charged) black hole radiates less. This calculator uses the simpler Schwarzschild formula and is most accurate for slowly rotating, uncharged black holes.
What would a micro black hole look like?
A micro black hole small enough to evaporate quickly would be an extraordinarily intense source of high-energy gamma rays, with a temperature of billions of Kelvin or more. Its final milliseconds of evaporation would release energy comparable to a nuclear weapon. No such objects have been observed, and any that formed at the LHC would have been far too tiny to produce a hazardous effect.