Black Hole Temperature Calculator (Hawking temperature from mass)

Understanding the black hole temperature calculator — concept and principle

Stephen Hawking showed in 1974 that black holes are not completely black: quantum effects make them emit thermal radiation as if they had a temperature. This calculator finds that Hawking temperature from the black hole's mass and shows its Schwarzschild radius for scale.

Hawking temperature is inversely proportional to mass, so a 10 M☉ hole sits at only 6.17 billionths of a kelvin.

How it is calculated

Hawking temperature TH = ħc³ ÷ (8π G M kB).
ħ = h ÷ 2π with h = 6.62607015 × 10⁻³⁴ J·s; kB = 1.380649 × 10⁻²³ J/K; c = 299,792,458 m/s (exact SI values); G = 6.67430 × 10⁻¹¹ m³/(kg·s²).
Mass in solar masses uses GM☉ = 1.3271244 × 10²⁰ m³/s².
Schwarzschild radius rs = 2GM ÷ c².

The principle

Near the event horizon, quantum fluctuations produce pairs of particles; one can escape while the other falls in, so the black hole appears to radiate. The emitted spectrum is that of a black body with a temperature inversely proportional to mass: bigger black holes are colder. A one-solar-mass black hole is about 6.2 × 10⁻⁸ K, far colder than the 2.7 K cosmic microwave background, so real astrophysical black holes absorb more radiation than they emit. Only very small black holes would be hot and evaporate quickly.

Worked example

Default input: 10 solar masses.

Mass = 10 × 1.988 × 10³⁰ kg ≈ 1.988 × 10³¹ kg.
TH = ħc³ ÷ (8π G M kB) ≈ 6.17 × 10⁻⁹ K, one tenth of the one-solar-mass value.
Schwarzschild radius = 2GM ÷ c² ≈ 29.53 km.

Each point is the calculator re-run with only “Black hole mass” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Black hole mass	Hawking temperature (K)
2.5	2.468e-8
5	1.234e-8
7.5	8.227e-9
10	6.17e-9
12.5	4.936e-9
15	4.114e-9
20	3.085e-9

How to read the result

A stellar black hole's Hawking temperature is billions of times colder than the cosmic background, so its radiation is undetectable and it grows by absorbing background photons. Supermassive black holes are colder still. The concept matters for theory: it links gravity, quantum mechanics and thermodynamics, and implies that black holes have entropy.

Common mistakes

Thinking larger black holes are hotter; it is the opposite.
Expecting Hawking radiation from astrophysical black holes to be observable.
Mixing solar masses and kilograms.
Confusing the Schwarzschild radius with the size of the accretion disk.

Keep in mind: Hawking radiation has not been observed directly from any astrophysical black hole. The result is a theoretical value.

Frequently asked questions

What is the temperature of a black hole?

TH = ħc³ ÷ (8πGMkB); about 6.2 × 10⁻⁸ K for one solar mass.

Do black holes evaporate?

In theory yes, by Hawking radiation, but for stellar masses it would take vastly longer than the age of the universe.

Why are smaller black holes hotter?

The temperature is inversely proportional to mass, so halving the mass doubles the temperature.

Sources: Hawking, S. W. (1974). Black hole explosions? Nature, 248, 30–31. · BIPM, SI Brochure 9th ed. (2019) and CODATA 2018 value of G

Checked 9 Nov 2026. Observatoire de Paris, “An Etymological Dictionary of Astronomy and Astrophysics”, entry “Hawking temperature”: T_H = ħc³/(8πGMk) ≈ 6.2 × 10⁻⁸ (M☉/M) K; SI defining constants h, k, c (2019 SI); CODATA 2018 G; IAU 2015 Resolution B3 nominal GM☉.

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