What this calculator does
Black holes are not entirely black. Hawking showed that quantum effects at the event horizon cause them to radiate, with a temperature inversely proportional to mass. A one-solar-mass black hole has a temperature of about 6×10⁻⁸ kelvin, far colder than empty space.
That coldness is why the process is unobservable. A stellar black hole absorbs far more from the cosmic microwave background than it radiates, and its evaporation timescale of 2×10⁶⁷ years dwarfs the current age of the universe by more than fifty orders of magnitude.
The formula
Hawking temperature is set by the reduced Planck constant and the speed of light cubed, divided by the mass, gravitational constant and Boltzmann constant. Evaporation time scales with mass cubed, so larger black holes last vastly longer.
| Term | Meaning |
|---|---|
| Hawking temperature | The effective thermal temperature of radiation escaping the horizon. |
| Schwarzschild radius | The event horizon radius, proportional to mass. |
| Evaporation timescale | How long the black hole would take to radiate away entirely, ignoring anything falling in. |
The inputs explained
| Field | What to enter |
|---|---|
| Black hole mass (solar masses) | The black hole mass in solar masses. Stellar black holes run from about 3 to 100; the one at the centre of our galaxy is around 4.3 million. |
When to use it
Understanding why Hawking radiation is unobservable
Stellar black holes are colder than the cosmic microwave background, so they grow rather than shrink.
Comparing black hole scales
Temperature falls and lifetime rises steeply with mass, which separates stellar and supermassive holes enormously.
Finding an event horizon size
The Schwarzschild radius scales linearly with mass and is the one intuitive figure here.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How do temperature and lifetime scale with mass?
From a stellar remnant to the supermassive hole at the galactic centre.
| Mass | Hawking temperature (T) | Evaporation timescale |
|---|---|---|
| 1 M☉ | 6.1701e-8 K | 2.0957e+67 years |
| 10 M☉ | 6.1701e-9 K | 2.0957e+70 years |
| 4.3 million M☉ | 1.4349e-14 K | 1.6662e+87 years |
Questions
How can a black hole radiate if nothing escapes?
The radiation originates from quantum effects just outside the horizon, not from inside it. Nothing crosses back out; the energy carried away nonetheless reduces the black hole's mass.
Why are bigger black holes colder?
Temperature is inversely proportional to mass. A larger horizon has weaker tidal gradients across it, and the resulting radiation spectrum is correspondingly colder.
Will black holes actually evaporate?
Not while the universe remains as it is. Any stellar black hole is far colder than the 2.7 K cosmic microwave background, so it absorbs more than it emits and grows. Evaporation only begins once the background cools below the hole's own temperature, in the extremely distant future.
Why does lifetime scale so steeply?
Because evaporation time goes as mass cubed, combining more mass to shed with a lower rate of shedding it. Ten times the mass gives a thousand times the lifetime.
For the event horizon radius on its own, see the Schwarzschild radius calculator. For the escape speed that defines it, see the escape velocity calculator.