Stephen Hawking showed in 1974 that black holes are not completely black: quantum effects make them glow faintly. The smaller the black hole, the hotter it is. A solar-mass black hole is colder than the cosmic microwave background, so it grows rather than evaporates.
How to use the Black Hole Temperature Calculator
- Black hole mass M
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter the black hole mass.
What each result means
- Hawking temperature = 1.054571817e-34×299792458^3÷(8×pi×6.6743e-11×[Black hole mass M]×1.380649e-23)
- Radiated power = 1.054571817e-34×299792458^6÷(15360×pi×6.6743e-11^2×[Black hole mass M]^2)
- Evaporation time = 5120×pi×6.6743e-11^2×[Black hole mass M]^3÷(1.054571817e-34×299792458^4)
- Schwarzschild radius = 2×6.6743e-11×[Black hole mass M]÷299792458^2
Example values
How the main result changes when Black hole mass M changes and everything else stays at the example values above:
| Black hole mass M (M☉) | Hawking temperature (K) |
|---|---|
| 0.5 | 1.2340e-7 |
| 0.75 | 8.2268e-8 |
| 1 | 6.1701e-8 |
| 1.25 | 4.9361e-8 |
| 1.5 | 4.1134e-8 |
| 2 | 3.0850e-8 |
Formula
T = ħc³ / (8πGMk_B), P = ħc⁶ / (15360πG²M²), t_evap = 5120πG²M³ / (ħc⁴)
Worked example
Inputs — Black hole mass M: 1 M☉.
Results — Hawking temperature = 6.1701e-8 K; Radiated power = 9.0076e-29 W; Evaporation time = 2.0957e67 years; Schwarzschild radius = 2.95334 km.
Key terms
- Hawking radiation
- Thermal radiation predicted from black holes by quantum theory.
Frequently asked questions
How hot is a solar-mass black hole?
About 6 × 10⁻⁸ K – far colder than space.
Do black holes evaporate?
In theory, very slowly; small ones would end in a burst.
Has Hawking radiation been observed?
Not yet – it is far too faint for known black holes.
Why are smaller black holes hotter?
Temperature is inversely proportional to mass.