Hawking Radiation Temperature Calculator

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 ≈ 6.17 × 10⁻⁸ K, virtually undetectable, 44 million times colder than the CMB (Cosmic Microwave Background) at 2.725 K
• A stellar-mass black hole (10 M☉): T ≈ 6.17 × 10⁻⁹ K
• Every astrophysical black hole is colder than the CMB, so all of them absorb more than they emit. They are growing, not evaporating, and will keep growing until the universe cools below their temperature

Evaporation timescale:

t ≈ 5120 π G² M³ / (ħ c⁴)

t ≈ 8.41 × 10⁻¹⁷ × (M/kg)³ seconds

Or, with the mass in solar masses and the answer in years, t ≈ 2.10 × 10⁶⁷ × (M/M☉)³ years. Those two coefficients get mixed up a lot, so watch which units a source is using before borrowing its number.

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 finish evaporating within 13.8 billion years it would need a starting mass below about 1.7 × 10¹¹ kg, roughly 170 million tonnes, or a mountain squeezed into something smaller than a proton. Those are the hypothetical primordial black holes, and they would be exploding in gamma rays right now, which is one of the things gamma-ray observatories quietly look for.

Peak emission wavelength (Wien’s law): λ_max = 2898 μm·K / T

At such low temperatures, Hawking radiation peaks in the radio/microwave range.