Black Hole Temperature Calculator — Hawking Radiation
Hawking radiation predicts that black holes are not perfectly black — they glow as blackbodies at a temperature inversely proportional to their mass. Enter the mass to see the temperature, luminosity and evaporation timescale.
Mass unit
Temperature at which the black hole radiates as a blackbody — stellar black holes are essentially 0 K
- 1
Mass in kilograms
1 M☉ × 1.989e30 kg/M☉ = 1.989e+30 kg - 2
Hawking prefactor A = ℏc³/(8πGk_B)
1.227e+23 J·K/kgA constant combining ℏ, c, G and k_B; T = A ÷ M. - 3
Hawking temperature T = A ÷ M
1.227e+23 ÷ 1.989e+30 = 0
How does this calculator work?
Hawking temperature T_H = ℏc³/(8πGMk_B) ≈ 1.227×10²³/M K. A solar-mass black hole is ~6×10⁻⁸ K; a 10¹² kg micro black hole is ~10¹¹ K. Luminosity grows as 1/M² and evaporation time as M³ — stellar black holes effectively live forever on any cosmological timescale.
Formula
How this is calculated
Stephen Hawking showed in 1974 that quantum effects near the event horizon cause black holes to emit thermal radiation. The temperature T_H = ℏc³/(8πGMk_B) is inversely proportional to mass — a one-solar-mass black hole radiates at T ≈ 6×10⁻⁸ K (far colder than the cosmic microwave background at 2.7 K, so it absorbs more than it emits and effectively grows). Only micro black holes lighter than about 10¹² kg are hot enough to be observable.
The Hawking luminosity L = ℏc⁶/(15360πG²M²) is the power radiated; it grows as 1/M², so the temperature and luminosity increase as the black hole shrinks. The total evaporation time t = 5120πG²M³/(ℏc⁴) scales as M³ — a solar-mass black hole would take roughly 2×10⁶⁷ years to evaporate, far longer than the age of the universe. A 10¹² kg primordial micro black hole would evaporate in about the current age of the universe.
All formulae use CODATA 2018 physical constants: ℏ = 1.054571817×10⁻³⁴ J·s, c = 2.997924580×10⁸ m/s, G = 6.67430×10⁻¹¹ N·m²/kg², k_B = 1.380649×10⁻²³ J/K. These are theoretical results; Hawking radiation has never been directly observed.
Frequently asked questions
T ∝ 1/M: more massive means cooler. A 10 M☉ black hole has T ≈ 6×10⁻⁹ K, far colder than the 2.7 K cosmic microwave background. Such black holes absorb radiation from the CMB and gain mass over cosmological time — they cannot evaporate until the universe cools below their temperature.
Via Wien's displacement law (λ_max = 2.898×10⁻³ m·K / T), it gives the wavelength at which the black hole emits most strongly. A stellar black hole emits at radio-wave lengths (thousands of km); a hot micro black hole emits gamma rays.
Not directly from a real black hole — stellar black holes are too cold and their Hawking flux is negligible compared to other radiation. Analogue experiments in the laboratory using "sonic" or optical analogues have observed Hawking-like effects, and the theoretical framework is well-supported, but direct astrophysical detection remains an open challenge.
TG we-Calculate Editorial Team. (2026). Black Hole Temperature Calculator — Hawking Radiation [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/black-hole-temperature-calculator
TG we-Calculate Editorial Team. "Black Hole Temperature Calculator — Hawking Radiation." TG we-Calculate. 2026. https://we-calculate.com/calculator/black-hole-temperature-calculator.
TG we-Calculate Editorial Team, "Black Hole Temperature Calculator — Hawking Radiation," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/black-hole-temperature-calculator
@misc{wecalculate_black_hole_temperature_calculator, title = {Black Hole Temperature Calculator — Hawking Radiation}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/black-hole-temperature-calculator}}, year = {2026}, note = {TG we-Calculate} }
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