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Hawking Temperature Calculator

Black holes aren't perfectly black — they glow faintly with a temperature inversely proportional to their mass.

Black hole mass (kg)

Hawking temperature (K)

T = ℏc³ / (8πGMkB)

Schwarzschild radius (m): 2,953.994
Evaporation lifetime (years): 20,971,700,545,783,242,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

What you entered

Black hole mass (kg): 1.989e+30

1
T = ℏc³ ÷ (8πGMkB)
Hawking formula for M = 1.989e+30 kg= 6.1687e-8 K
2
Schwarzschild radius Rs = 2GM/c²
2 × 6.674e-11 × 1.989e+30 ÷ c²= 2953.9938 m
3
Evaporation lifetime ∝ M³
τ for 1.989e+30 kg= 2.0972e+67 years

Result

Hawking temperature (K): 0

A black hole of mass 1.989e+30 kg has a Hawking temperature of 6.1687e-8 K and would evaporate in ~2.0972e+67 years.

Hawking temperature and lifetime of black holes

Temperature is inversely proportional to mass, so smaller black holes are hotter and evaporate faster.

Mass (kg)	Temperature (K)	Schwarzschild radius (m)	Lifetime (years)
1e6	1.2270e+17	1.4852e-21	2.6652e-6
1e12	1.2270e+11	1.4852e-15	2.6652e+12
1e15	1.2270e+8	1.4852e-12	2.6652e+21
5.972e24	2.0545e-2	8.8694e-3	5.6766e+50
1.989e30	6.1687e-8	2.9540e+3	2.0972e+67

The relationship is inverse, which produces the counterintuitive result that black holes get hotter as they shrink and therefore evaporate faster and faster - the last moments are explosive. A solar-mass black hole sits at 6e-8 K, far colder than the 2.7 K cosmic microwave background, so it absorbs more than it radiates and grows rather than evaporating. Its lifetime of 2e67 years is unimaginably longer than the current age of the universe. Row four is the Earth compressed to a black hole, with a radius of under 9 mm.

Smaller black holes are hotter

Counter-intuitively, a less massive black hole has a higher Hawking temperature — a solar-mass black hole radiates at ~60 nanokelvin (far colder than the cosmic microwave background), while a hypothetical mountain-mass black hole would glow white-hot and evaporate in seconds.

Evaporation takes forever (usually)

A solar-mass black hole would take ~10⁶⁷ years to evaporate — vastly longer than the current age of the universe (1.4 × 10¹⁰ years). Only primordial micro black holes (if they exist) would be small enough to be evaporating observably today.

Frequently asked questions

What is the Hawking temperature of a black hole with 10 solar masses?

T = ℏc³/(8πGMk_B). For 10 solar masses (M = 1.989×10³¹ kg): T ≈ 6.2 nanokelvin — about a billion times colder than the cosmic microwave background (2.7 K). It would take roughly 10⁶⁹ years to evaporate.

Could a tiny black hole created in a particle accelerator destroy Earth?

No — even if micro black holes formed (which LHC has never observed), they would have temperatures of ~10²⁶ K and evaporate in ~10⁻²⁶ seconds via Hawking radiation. Smaller = hotter = faster evaporation. A truly dangerous black hole would need far more mass than any accelerator can concentrate.

Has Hawking radiation ever been observed?

Not directly from a black hole — the radiation from stellar-mass black holes is far too faint to detect against the cosmic microwave background. Analog experiments in labs (using sound waves in flowing fluids that mimic event horizons) have confirmed the theoretical predictions, lending strong indirect support.