Hawking Temperature Calculator

A black hole isn’t perfectly black. Quantum effects near its event horizon mean it should emit a faint thermal glow — Hawking radiation — at a temperature fixed entirely by its mass. Because the relationship runs backward from intuition (heavier black holes are colder, not hotter), it produces one of the strangest and most illuminating curves in astrophysics.

The formula

Every symbol here is a fixed constant of nature except one: the mass $M$ . Temperature is inversely proportional to mass, so this single relation ranges over dozens of orders of magnitude depending on what kind of black hole you plug in — from imperceptibly cold for anything astrophysical, to blisteringly hot for anything hypothetically tiny.

Why real black holes are almost unimaginably cold

A black hole with the Sun’s mass has a Hawking temperature of only about 6.17 × 10⁻⁸ K — forty million times colder than the cosmic microwave background (CMB), the 2.725 K afterglow of the Big Bang that fills all of space. Sgr A*, the supermassive black hole at the center of the Milky Way (about 4.3 million solar masses), is colder still — its Hawking temperature is roughly 1.4 × 10⁻¹⁴ K, a number with barely any physical meaning left in it except “far colder than anything else in the observable universe.”

This matters for a very concrete reason: the CMB itself has a temperature of 2.725 K, and every black hole we know of has a Hawking temperature dramatically below that. That means every astrophysical black hole is currently bathed in — and absorbing — far more radiation from the CMB than it emits as Hawking radiation. Net evaporation cannot begin for any of them until the universe expands and cools enough that the CMB drops below their (already unimaginably low) Hawking temperature — many trillions of years from now, long after star formation itself has ended.

Why hypothetical tiny black holes are the opposite extreme

Flip the mass around and the picture flips completely. A hypothetical black hole with the mass of a small asteroid — around 10¹² kg — would have a Hawking temperature of roughly 1.2 × 10¹¹ K, far hotter than the core of any star. Such an object would be radiating so intensely that it would be evaporating rapidly, losing mass (and therefore climbing to ever higher temperatures) in a runaway process that ends in a final burst. No black hole this small has ever been observed — this is a regime that would only be populated by “primordial” black holes, if any formed in the extreme densities of the very early universe, or by microscopic black holes under speculative high-energy physics scenarios. The calculator’s mass field accepts values this small specifically so the contrast with a real, astrophysical black hole is visible directly on the same chart.

The one number that separates the two regimes

$T_H$ < 2.725 K (the CMB temperature) is the dividing line. Above it, a black hole is a net emitter and is genuinely evaporating today. Below it, a black hole is a net absorber, gaining more energy from the CMB than it loses to Hawking radiation, no matter how long you wait — until the universe itself cools further. Every known astrophysical black hole, from the smallest confirmed stellar-mass remnants (roughly 3 solar masses) up to the largest supermassive giants, sits enormously far below this line.

Reading the chart

Both axes are logarithmic, which is the only way to fit a relationship spanning roughly fifty orders of magnitude onto one picture. Because $T_H \propto 1/M$ is a pure power law, it appears as a single straight line in log-log space — no curve fitting needed, just the two endpoints of the domain shown. Three fixed reference points mark a Sun-mass black hole, Sgr A*, and the smallest known stellar-mass black holes; a highlighted dot tracks whatever mass you enter; and a dashed horizontal line marks the CMB temperature, the boundary described above.