Black Hole Calculator
Enter a mass and find a black hole's event horizon (Schwarzschild radius), its Hawking temperature, and how long it would take to evaporate.
How to use this calculator
- 1Enter a mass in solar masses, Earth masses, or kilograms.
- 2Read the Schwarzschild radius — the size of the event horizon for that mass.
- 3Explore the extremes: a mountain-mass black hole is microscopic and blazing hot; a galactic one is larger than the solar system and colder than space.
How it works
Black hole properties
Schwarzschild radius: Rs = 2 × G × M ÷ c² Hawking temperature: T = ħc³ ÷ (8π G M k_B) Evaporation time: t ≈ 5120 π G² M³ ÷ (ħ c⁴) G, c, ħ, k_B are fundamental constants everything depends only on the mass M
A non-rotating black hole is defined by one number — its mass. The Schwarzschild radius is the size to which that mass must be compressed for its escape velocity to reach the speed of light, and it is simply proportional to the mass. The Hawking temperature and evaporation time come from quantum field theory near the horizon: smaller black holes are hotter and evaporate faster, so the physics runs in the opposite direction to everyday objects, where bigger things hold more heat.
Worked example
For one solar mass (1.989 × 10³⁰ kg): Rs = 2 × 6.674×10⁻¹¹ × 1.989×10³⁰ ÷ (2.998×10⁸)² ≈ 2,950 m. A black hole the mass of the Sun would be a sphere less than 6 km across — and its Hawking temperature would be a mere 60 billionths of a kelvin.
Black Hole Calculator: the complete guide
The event horizon, from ordinary gravity
The Schwarzschild radius is not exotic mathematics — it falls straight out of the escape-velocity formula. Set the escape velocity equal to the speed of light and solve for radius, and you get Rs = 2GM/c². It is the radius to which you would have to crush a given mass so that nothing, not even light, could escape from its surface.
For the Earth, that radius is about 9 millimetres — squeeze the entire planet to the size of a marble and it becomes a black hole. For the Sun it is under 3 kilometres. Nothing forces ordinary matter to collapse this far, which is why these objects are rare, but the mathematics of the boundary is remarkably simple.
Bigger black holes are less dense than you'd think
Because the radius grows in direct proportion to the mass, but volume grows as the cube of the radius, the mean density inside the event horizon falls as mass rises. A stellar black hole is fantastically dense, but a supermassive one is not. The black hole at the centre of the Milky Way, four million solar masses, has a mean density lower than water.
For the largest known black holes, billions of solar masses, the average density inside the horizon can be less than air. This is deeply counterintuitive — the horizon is not a surface of crushed matter but a region of spacetime, and its 'density' is just mass divided by the volume it encloses, not a description of anything you would find there.
Hawking radiation and the strangest thermodynamics
Stephen Hawking showed in 1974 that black holes are not perfectly black: quantum effects at the horizon make them emit faint thermal radiation and slowly lose mass. The temperature is inversely proportional to mass, so the physics is upside-down — smaller black holes are hotter and evaporate faster, while giant ones are colder and more stable.
The numbers are extreme. A solar-mass black hole has a temperature of about 60 nanokelvin, far colder than the 2.7 K background of empty space, so it absorbs more than it emits and grows rather than shrinks. Its evaporation time, if isolated, would be around 10⁶⁷ years — vastly longer than the current age of the universe. Only tiny, primordial black holes could evaporate within the universe's lifetime, and none has ever been observed.
Frequently asked questions
What is the Schwarzschild radius?
It is the radius of a black hole's event horizon — the boundary from which nothing can escape. It equals 2GM/c², so it depends only on mass. Compress any mass within its Schwarzschild radius and it becomes a black hole; for the Sun that radius is under 3 km.
How big would a black hole with the Sun's mass be?
Its event horizon would be about 3 km in radius, or 6 km across — a sphere smaller than most cities holding the entire mass of the Sun. The Sun does not become a black hole because nothing squeezes it that far; it lacks the mass to collapse.
Do black holes really evaporate?
In theory, yes, through Hawking radiation — but astrophysical black holes evaporate absurdly slowly. A solar-mass black hole would take around 10⁶⁷ years, far longer than the age of the universe, and in practice it absorbs background radiation faster than it emits, so it grows instead. Only hypothetical tiny black holes would evaporate quickly.
Are supermassive black holes extremely dense?
No — surprisingly, the opposite. Since radius scales with mass but volume with radius cubed, the mean density inside the horizon drops as mass rises. The largest known black holes have an average density below that of air, even though a stellar-mass one is fantastically dense.