Black Hole Temperature Calculator

Use the black hole temperature calculator to learn the black body temperature of a black hole from just its mass.

Hawking temperature6.1687e-9 KINVERSELY proportional to mass: bigger holes are colder. This one is far below the 2.7 K microwave background, so it absorbs more than it radiates and is currently growing, not evaporating

Schwarzschild radius29.54 km2GM/c² — proportional to mass, so a hole of twice the mass is twice as wide, not eight times

Event horizon area1.0966e+10 m²goes as the SQUARE of the mass, and never decreases in any classical process — that monotonicity is what ties horizon area to entropy

Mean density inside the horizon1.842e+17 kg/m³falls as the square of the mass — a supermassive hole is less dense than water, so crossing its horizon would not feel like anything at all

Evaporation time2.097e+70 yearsgoes as the CUBE of the mass, and only once the universe has cooled below the hole's own temperature

Surface gravity at the horizon1.5212e+12 m/s²

Photon sphere44.31 km1.5 r_s — where light itself orbits

Innermost stable circular orbit88.62 km3 r_s — inside this nothing can orbit, it can only fall. This is what sets the inner edge of an accretion disc

Time dilation at that radius0.816497×a clock there runs at this rate against one far away — √(1 − r_s/r), which reaches zero AT the horizon

A year there is447.338 days out herethe further in, the more extreme

The formula

r_s = 2GM/c²; T_H = ħc³/(8πGMk_B)

Bigger holes are colder and less dense

The Schwarzschild radius is proportional to mass, so the volume inside the horizon goes as the cube while the mass goes as the first power. Mean density therefore falls as the square of the mass. A stellar-mass black hole is unimaginably dense; a supermassive one at a few billion solar masses is less dense than water, and an infalling observer would cross its horizon without noticing anything locally unusual.

Hawking temperature is inversely proportional to mass, so large black holes are colder than the 2.7 K microwave background. They absorb more than they radiate and are currently growing. Evaporation is not something any stellar-mass hole is doing today — it can only begin once the universe itself has cooled below the hole's own temperature, and the evaporation time then scales as the cube of the mass.

Area never decreases

When two black holes merge, several percent of the total mass leaves as gravitational waves — briefly outshining every star in the observable universe. Yet the merged horizon area still exceeds the sum of the two original areas. Area goes as mass squared, so it grows even as mass is lost. That monotonic increase is Hawking's area theorem, and its resemblance to the second law of thermodynamics is what first suggested horizon area is entropy.