What is the temperature of a black hole?

Most black holes have a Hawking temperature far colder than anything measurable. A stellar black hole with 10 solar masses has a Hawking temperature of about 6.2 x 10^-9 K, which is more than a billion times colder than the cosmic microwave background at 2.725 K. Temperature is inversely proportional to mass: T = hbar x c^3 / (8 x pi x G x M x k_B). The Hawking temperature of Sagittarius A* is approximately 1.5 x 10^-14 K, essentially indistinguishable from absolute zero. Only micro black holes with mass below about 4.5 x 10^22 kg (roughly 24 Jupiter masses) are hotter than the CMB and therefore currently evaporating.

What is the temperature of a black hole in Celsius?

For stellar and supermassive black holes, the Hawking temperature is between -273.149999... and -273.15 degrees Celsius, essentially indistinguishable from absolute zero (-273.15 C). A 10 solar mass black hole has a Hawking temperature of 6.2 x 10^-9 K, which is -273.149999994 degrees Celsius. This extreme cold explains why current black holes in the universe are growing rather than shrinking: they absorb cosmic microwave background radiation at 2.725 K faster than they emit Hawking radiation.

Why is a smaller black hole hotter than a larger one?

This is one of the most counterintuitive results in modern physics. As mass increases, the Schwarzschild radius grows and the curvature of spacetime at the event horizon becomes gentler. Hawking radiation arises from quantum field effects near the event horizon: the gentler the spacetime curvature, the lower the characteristic temperature. Mathematically, T = hbar x c^3 / (8 x pi x G x M x k_B) is directly proportional to 1/M. Doubling the mass halves the temperature. A black hole with the mass of a car would have a Hawking temperature of around 10^23 K, while a stellar black hole of 10 solar masses sits near 6 x 10^-9 K.

Can Hawking radiation from a black hole ever be detected?

No Hawking radiation from any known or hypothetical astronomical black hole has been detected, and current instruments have no prospect of measuring it. A 10 solar mass stellar black hole emits only about 9 x 10^-29 watts of Hawking radiation, a power level trillions of times below any existing detector threshold. Detection would theoretically require a black hole small enough to radiate at above roughly 100 K, and no such objects are known to exist. Analogue systems in condensed matter physics, such as Bose-Einstein condensates, have produced Hawking-like signatures, but these are not gravitational black holes.

Could a micro black hole produced at the Large Hadron Collider be dangerous?

No. Even if the LHC could produce micro black holes at 14 TeV collision energies (which current physics does not require), any such object would evaporate almost instantly due to Hawking radiation. At energies near 14 TeV the equivalent mass is about 2.5 x 10^-23 kg, giving a Hawking temperature of approximately 5 x 10^45 K and an evaporation time of around 10^-88 seconds. Multiple independent safety assessments, including the 2008 CERN safety study reviewed by international physicists, concluded that LHC-produced black holes pose no risk whatsoever. The review is available on the CERN website.

What happens to a black hole as it evaporates -- does it cool down or heat up?

A black hole heats up as it evaporates. As mass decreases, Hawking temperature increases (T is proportional to 1/M), which increases radiation power (P is proportional to 1/M^2), which further accelerates mass loss. This runaway feedback means evaporation accelerates continuously. In the final stages, the black hole emits radiation at astronomical temperatures and explodes in a burst of high-energy particles and gamma rays. This theoretical endpoint has never been observed because no black hole small enough to be near the end of its life has been identified.

What is the Hawking temperature of Sagittarius A*, the black hole at the centre of the Milky Way?

Sagittarius A* has a mass of approximately 4 million solar masses (8 x 10^36 kg), giving a Hawking temperature of about 1.54 x 10^-14 K. This is more than 100 billion times colder than the cosmic microwave background at 2.725 K. At this temperature, Sgr A* is absorbing CMB radiation far faster than it emits Hawking radiation, so it is currently growing. Its evaporation time is approximately 8.7 x 10^90 years, a figure that dwarfs the expected timescale of proton decay by dozens of orders of magnitude.

At what mass does a black hole become hotter than the cosmic microwave background?

A black hole becomes hotter than the CMB (2.725 K) when its mass drops below approximately 4.5 x 10^22 kg, which is roughly 24 Jupiter masses or 0.023 solar masses. Below this threshold, Hawking radiation exceeds CMB absorption and the black hole undergoes net evaporation. No known black hole has been confirmed in this mass range. The smallest confirmed black holes from X-ray binary observations have masses of about 5 solar masses, more than a billion times above the CMB threshold mass.

How long does it take a stellar black hole to fully evaporate?

For a 10 solar mass stellar black hole, the evaporation time is approximately 2 x 10^70 years. This is vastly longer than the current age of the universe (1.38 x 10^10 years) and far beyond the expected timescale of proton decay (10^34 to 10^45 years). The only black holes that would have evaporated by now are primordial black holes formed in the early universe with initial masses below about 1.7 x 10^11 kg. Any such objects evaporating today would appear as gamma-ray bursts, but no confirmed primordial black hole has been observed.

Black Hole Temperature Calculator - Hawking Radiation & Evaporation Time

What Is the Black Hole Temperature Calculator?

This calculator computes the Hawking temperature of any black hole from its mass using the theoretical relationship first derived by Stephen Hawking in 1974. Enter a mass in solar masses, Earth masses, or kilograms and the calculator returns the Hawking temperature in kelvin and Celsius, the Schwarzschild radius, the total evaporation time, the instantaneous radiation power in watts, the Wien peak wavelength of the emitted radiation, and the corresponding electromagnetic band. A bidirectional mode lets you work in reverse: enter a Hawking temperature to find the corresponding mass.

The tool covers black holes across more than 50 orders of magnitude in mass, from a micro black hole with the mass of a mountain to a supermassive black hole like M87* with 6.5 billion solar masses. Four preset configurations allow instant calculation for the most studied examples: a typical stellar black hole, Sagittarius A* at the centre of the Milky Way, M87* (the first black hole ever directly imaged), and a primordial micro black hole near the end of its evaporation lifetime. A status banner shows whether the selected black hole is currently hotter or colder than the cosmic microwave background at 2.725 K, which determines whether it is currently gaining or losing mass.

Hawking Radiation: How Black Holes Emit Thermal Energy

In 1974, Stephen Hawking combined quantum mechanics with general relativity to show that black holes are not perfectly black. Virtual particle pairs are created continuously near the event horizon through quantum fluctuations. When a pair forms just outside the Schwarzschild radius, one particle can fall inward while the other escapes as real radiation. This process causes the black hole to lose mass over time through what is now called Hawking radiation.

The temperature of this radiation depends entirely on the surface gravity at the event horizon, which for a non-rotating black hole is set entirely by mass. The governing formula is:

T = hbar x c^3 / (8 x pi x G x M x k_B)

where hbar is the reduced Planck constant (1.055 x 10^-34 J s), c is the speed of light, G is Newton's gravitational constant, M is the black hole mass, and k_B is the Boltzmann constant. Temperature is inversely proportional to mass: the heavier the black hole, the colder its Hawking radiation. A 10 solar mass stellar black hole radiates at 6.2 x 10^-9 K. A micro black hole with the mass of a car would radiate at around 10^23 K.

How Black Hole Temperature Varies with Mass

The inverse relationship between mass and temperature produces a vast range of physical regimes. The table below shows five key examples spanning from primordial micro black holes to the largest supermassive black holes in the observable universe.

Black Hole	Mass	Hawking Temperature	CMB Status	Evaporation Time
Primordial micro (~1.7x10^11 kg)	1.7x10^11 kg	~7.2x10^11 K	Evaporating now	~13.8 billion years
CMB threshold mass	4.5x10^22 kg	2.725 K	Exact boundary	2.4x10^44 years
Stellar BH (10 M☉)	2.0x10^31 kg	6.2x10^-9 K	Growing	2.1x10^70 years
Sagittarius A* (4x10^6 M☉)	8.0x10^36 kg	1.5x10^-14 K	Growing	8.7x10^90 years
M87* (6.5x10^9 M☉)	1.3x10^40 kg	9.5x10^-18 K	Growing	3.7x10^100 years

The CMB threshold at 4.5 x 10^22 kg is particularly meaningful. The cosmic microwave background fills the universe uniformly at 2.725 K. Any black hole colder than this absorbs more thermal radiation from the CMB than it emits via Hawking radiation, so it is currently gaining mass. Every confirmed stellar and supermassive black hole in the universe is a net CMB absorber, not a net emitter.

Evaporation Time, Radiation Power, and Peak Wavelength

Three derived quantities translate Hawking temperature into physical observables that are easier to reason about.

Evaporation time scales as the cube of mass: t = (5120 pi G^2 / (hbar x c^4)) x M^3. This extreme sensitivity means that doubling the mass increases the evaporation time by a factor of eight. A 10 solar mass stellar black hole has an evaporation time of about 2 x 10^70 years, far outlasting proton decay. Primordial black holes that began evaporating at the Big Bang with initial masses below roughly 1.7 x 10^11 kg would be finishing their evaporation around the present day, appearing as gamma-ray bursts. The Fermi Gamma-ray Space Telescope has searched for this signature, but no confirmed primordial black hole evaporation event has been detected.

Radiation power follows P = (hbar x c^6) / (15360 x pi x G^2 x M^2), scaling as the inverse square of mass. For a 10 solar mass stellar black hole, this gives roughly 9 x 10^-29 watts, far below any detectable threshold. A primordial micro black hole at 10^12 kg emits about 3.6 x 10^8 watts, comparable to a small power station.

The Wien peak wavelength lambda = 2.898 x 10^-3 / T places the thermal emission peak in the electromagnetic spectrum. A stellar black hole at 10^-9 K radiates peak power at wavelengths on the order of millions of kilometres, deep in the radio band. A primordial micro black hole at 10^11 K has a Wien peak in the gamma-ray regime around 10^-14 metres. For a complementary view of black hole geometry and how the event horizon relates to mass, see our Schwarzschild radius calculator.

Accuracy and Limitations

This calculator uses the Hawking temperature formula for a Schwarzschild (non-rotating, uncharged) black hole. Real astrophysical black holes are rotating (described by the Kerr metric) and may carry charge. Rotation reduces the effective surface gravity at the event horizon, which lowers the Hawking temperature slightly relative to the non-rotating prediction. For stellar and supermassive black holes, the correction is small enough that the qualitative conclusions remain unchanged.

The formula also assumes the black hole exists in isolation without ongoing accretion. In practice, every known stellar and supermassive black hole is currently accreting matter at a rate that vastly exceeds Hawking radiation mass loss. Hawking radiation itself has never been directly detected in a gravitational context. The prediction follows from well-tested quantum field theory in curved spacetime, and laboratory analogues in Bose-Einstein condensates and optical systems have produced Hawking-like signatures, but the gravitational effect remains a theoretical prediction awaiting direct observation. Results from this calculator should be read as physically grounded theoretical values, not empirically measured quantities.

The Most Common Mistake: Confusing Hawking Temperature with Accretion Disk Temperature

The most frequently encountered error when reading about black hole temperatures is conflating two completely different physical processes. Hawking temperature is the quantum radiation temperature of the event horizon itself, typically between 10^-18 K and 10^-9 K for any known astrophysical black hole. Accretion disk temperature is the temperature of infalling gas heated by friction and compression before crossing the event horizon, which reaches 10^7 K for stellar black holes and up to 10^9 K in active galactic nuclei.

When astronomers describe a hot black hole, they invariably mean a hot accretion disk. The X-ray emissions captured by the Event Horizon Telescope collaboration and detected by observatories such as Chandra originate in the accretion disk, not from Hawking radiation. The two phenomena differ by more than 20 orders of magnitude in temperature and are produced by completely different physical mechanisms. For a broader look at black hole physics, including the energy and gravitational wave output of merging black holes, see our black hole collision calculator.

Black Hole Temperature Calculator