Hawking Temperature Calculator
In 1974, Stephen Hawking derived that black holes emit thermal radiation at a temperature inversely proportional to their mass. The Hawking temperature is given by T = hbar c cubed divided by (8 pi G M kB), where hbar is the reduced Planck constant, c is the speed of light, G is Newton's gravitational constant, M is the black hole mass, and kB is the Boltzmann constant. Stellar-mass black holes have temperatures of fractions of a nanokelvin, far colder than the cosmic microwave background. Only hypothetical primordial micro-black holes with masses of kilograms or less would be warm enough to observe. Enter a mass below to explore these remarkable predictions of quantum gravity.
Hawking temperature formula
T = (hbar * c^3) / (8 * π * G * M * kB)
Physical constants used: hbar = 1.054571817e-34 J s; c = 299,792,458 m/s; G = 6.67430e-11 m^3 kg^-1 s^-2; kB = 1.380649e-23 J/K. The Schwarzschild radius is rs = 2GM/c squared. These constants are from NIST CODATA 2018.
Temperature reference values
A 1 kg micro-black hole would have a Hawking temperature of approximately 1.227 x 10 to the 23rd kelvin, hotter than any known stellar core. A solar-mass black hole (1.989 x 10 to the 30th kg) has a temperature of about 6.2 x 10 to the -8th kelvin (62 nanokelvin). The CMB temperature is 2.725 K, meaning all known astrophysical black holes are far too cold to detect through Hawking radiation with current instruments.
Hawking temperature: frequently asked questions
What is Hawking radiation?
Hawking radiation is thermal radiation theoretically emitted by black holes due to quantum effects near the event horizon. Stephen Hawking predicted in 1974 that black holes are not perfectly black but radiate energy at a characteristic temperature inversely proportional to their mass.
Why does a more massive black hole have a lower temperature?
Hawking temperature is inversely proportional to mass: T = hbar c cubed / (8 pi G M kB). A stellar-mass black hole has a temperature far below even the cosmic microwave background (2.7 K), while a primordial mini black hole with mass of a kilogram would be extremely hot.
Can we observe Hawking radiation?
Not yet. The Hawking temperature of a solar-mass black hole is approximately 62 nanokelvins, far below the 2.7 K CMB. We would need to detect radiation 40 million times colder than the coldest natural background, which is far beyond current technology.
What are the physical constants used?
The formula uses: hbar (reduced Planck constant) = 1.054571817 x 10 to the -34th J s; c (speed of light) = 299,792,458 m/s; G (gravitational constant) = 6.67430 x 10 to the -11th m cubed kg to the -1 s to the -2; kB (Boltzmann constant) = 1.380649 x 10 to the -23rd J/K. These are the 2018 CODATA values.
What is the Schwarzschild radius, and how does it relate to Hawking temperature?
The Schwarzschild radius is rs = 2GM/c squared. Hawking temperature can also be written as T = hbar c / (4 pi rs kB). A larger black hole has a larger Schwarzschild radius and therefore a lower temperature.
Official sources
- NIST CODATA 2018 physical constants: physics.nist.gov/cuu/Constants/.
- NASA Goddard: Black hole basics: imagine.gsfc.nasa.gov.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.