Hawking Radiation Temperature Calculator
Calculate the Hawking radiation temperature of a black hole and its evaporation timescale.
Lighter black holes are hotter and evaporate faster.
Hawking radiation is theoretical thermal radiation emitted by black holes due to quantum effects near the event horizon. It was predicted by Stephen Hawking in 1974 and has yet to be directly observed.
Hawking temperature formula:
T = ħc³ / (8πGMkB)
Simplified for stellar masses:
T ≈ 6.169 × 10⁻⁸ K × (M☉ / M)
Where:
- ħ = 1.055 × 10⁻³⁴ J·s (reduced Planck constant)
- kB = 1.381 × 10⁻²³ J/K (Boltzmann constant)
- M☉ = 1.989 × 10³⁰ kg
The extraordinary numbers:
- A solar-mass black hole: T ≈ 6 × 10⁻⁸ K — virtually undetectable, 45 million times colder than the cosmic microwave background (2.7 K)
- A stellar-mass black hole (10 M☉): T ≈ 6 × 10⁻⁹ K
- The CMB is at 2.7 K — all astrophysical black holes absorb more than they emit
Evaporation timescale:
t ≈ 5120 π G² M³ / (ħ c⁴)
t ≈ 2.099 × 10⁻⁹ × (M/kg)³ seconds
A solar-mass black hole would take ~2 × 10⁶⁷ years to evaporate — far longer than the age of the universe. For a black hole to evaporate within the age of the universe (~13.8 Gyr), it would need to have started with a mass smaller than ~10¹² kg (a billion tonnes) — called a primordial black hole.
Peak emission wavelength (Wien’s law):
λ_max = 2898 μm·K / T
At such low temperatures, Hawking radiation peaks in the radio/microwave range.