How big is a black hole of a given mass?
Any mass becomes a black hole if it is squeezed inside its Schwarzschild radius, rs = 2GM ÷ c². That is the radius of the event horizon, the surface from which not even light can leave. This black hole calculator takes a mass in solar masses, Earth masses, Moon masses, Jupiter masses or kilograms, or works backwards from a horizon radius, and returns the radius and diameter, the photon sphere, the mean density, the surface gravity, the Hawking temperature, the radiated power and the time Hawking radiation would take to evaporate it.
It is aimed at physics students and curious readers. Every formula is shown with its numbers, and the answers are computed in your browser.
How to use the Black Hole Calculator
- Choose whether you know the mass or the horizon radius.
- Type the mass, such as 1, 4.3e6 or 10, and pick the unit. Or type the radius in kilometres.
- Read the Schwarzschild radius in the large result and the other quantities below it.
- Open the working to see each formula with its numbers, and copy the summary line if you need it.
Black Hole Calculator features
Event horizon
Radius and diameter with the unit chosen automatically, from millimetres to light-years.
Photon sphere and last stable orbit
The 1.5 rs and 3 rs radii that matter for light and orbiting matter.
Density and gravity
Mean density inside the horizon and the Newtonian-style value GM ÷ rs².
Hawking temperature and lifetime
Temperature, radiated power and the evaporation time in years, with a comparison to the age of the universe.
Mass from radius
Enter a horizon radius to find the mass that has it.
Formulas and a worked example
With G = 6.6743 × 10−11 m³ kg−1 s−2, c = 299,792,458 m/s, ħ = 1.054572 × 10−34 J s and kB = 1.380649 × 10−23 J/K, the quantities are rs = 2GM ÷ c², mean density ρ = M ÷ (4/3 π rs³), T = ħc³ ÷ (8πGMkB) and t ≈ 5120πG²M³ ÷ (ħc⁴). The radius grows in proportion to the mass, the temperature falls as 1 ÷ M and the lifetime grows as M³.
Example: for one solar mass (1.98841 × 1030 kg), rs = 2 × 6.6743 × 10−11 × 1.98841 × 1030 ÷ c² ≈ 2.953 km. The mean density inside is about 1.8 × 1019 kg/m³, the Hawking temperature is about 6.2 × 10−8 K, and the evaporation time is about 2 × 1067 years. The Earth would have to shrink to about 8.87 mm to become a black hole.
What the numbers mean
A larger black hole is less dense, not more: the density falls as 1 ÷ M², so the largest, billions of solar masses, are less dense than air. The surface gravity quoted here is the Newtonian-style value GM ÷ rs² = c⁴ ÷ 4GM, which equals the horizon surface gravity used in Hawking’s derivation; a stationary observer’s true acceleration at the horizon is infinite. A black hole colder than the 2.725 K microwave background takes in more energy than it gives out, so every stellar-mass or larger black hole is growing, not shrinking, today.
For the speed needed to leave a planet instead, use the escape velocity calculator; setting the escape velocity to the speed of light gives the same rs. For orbits around massive bodies see the orbital period calculator.
Limits of this calculator
- Non-rotating, uncharged (Schwarzschild) black holes only. A spinning black hole has a smaller horizon and different orbits.
- The evaporation time is the textbook photon-only estimate; real black holes would also emit other particles, which shortens the time slightly.
- Hawking radiation has not been observed. Treat the temperature and lifetime as theory, not measurement.
Black Hole Calculator FAQ
What is the Schwarzschild radius of the Sun?
About 2.95 km (2,953 m). The Sun’s actual radius is about 695,700 km, so it is far from being a black hole.
How do you calculate the radius of a black hole?
Multiply the mass by 2G and divide by c squared: r = 2GM ÷ c². It is about 2.95 km for each solar mass.
How long does a black hole last?
By Hawking radiation alone, t ≈ 5120πG²M³ ÷ (ħc⁴), about 2 × 1067 years for a solar-mass black hole. The time grows with the cube of the mass.
What size would the Earth be as a black hole?
Its Schwarzschild radius is about 8.87 mm, roughly the size of a marble.
Why is a big black hole not very dense?
The radius scales with the mass while the volume scales with the cube of the radius, so the mean density falls as 1 ÷ M². Supermassive black holes can be less dense than air.
Which constants does it use?
G, ħ and kB from the 2022 CODATA recommendation (NIST) and the exact SI value of the speed of light.