Schwarzschild radius calculator
Enter a mass to see how small it would have to be squeezed to become a black hole, the radius of its event horizon. Or enter a radius to find the mass of the black hole with that horizon. The calculator also shows the diameter, the mean density inside the horizon and the Hawking temperature.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Choose what to find: the radius from a mass, or the mass from a radius.
- Enter the mass in solar masses (1.98847 × 10³⁰ kg), Earth masses (5.9722 × 10²⁴ kg) or kilograms, or the radius in km, m or mm.
- Read the radius or mass, the diameter, the density and the Hawking temperature.
- Schwarzschild radius: r = 2GM ÷ c², with G = 6.6743 × 10⁻¹¹ m³/(kg·s²) and c = 299,792,458 m/s.
- Mass from radius: M = r·c² ÷ (2G).
- Mean density: ρ = M ÷ (4/3 · π · r³). Hawking temperature: T = ħc³ ÷ (8πGMk_B).
Worked example
For the Sun: r = 2 × 6.6743 × 10⁻¹¹ × 1.98847 × 10³⁰ ÷ 299,792,458² = 2.9533 km, a horizon 5.906679 km across. A black hole of 10 solar masses has ten times the radius, 29.5334 km.
A horizon of 1 km belongs to a mass of 1000 × 299,792,458² ÷ (2 × 6.6743 × 10⁻¹¹) = 6.733 × 10²⁹ kg, or 0.3386 solar masses.
Tips
- Rotating black holes have a smaller horizon, down to half of this radius for the fastest spin; the formula here is for no rotation.
- Not a surface. Nothing marks the horizon; it is the point of no return.
- Large values appear in scientific notation, such as 1.84285E19 kg/m³ for the Sun’s density.
Frequently asked questions
What is the Schwarzschild radius?
It is the radius of the event horizon of a non-rotating, uncharged black hole, r = 2GM ÷ c². Anything that gets closer to the centre than this, even light, cannot escape. For the Sun it is about 2.95 km.
How big would the Earth be as a black hole?
The Earth's 5.9722 × 10²⁴ kg would have to fit in a sphere of radius 8.87 mm, smaller than a marble.
Why do big black holes have a low density?
The radius grows in proportion to the mass, while the volume grows with the cube of the radius, so the mean density falls as 1 ÷ M². A black hole of about a hundred million solar masses has a mean density inside its horizon around that of water.
What is the Hawking temperature?
Quantum effects make a black hole radiate as if it had a temperature T = ħc³ ÷ (8πGMk_B). For one solar mass it is about 6.2 × 10⁻⁸ K, far colder than the cosmic microwave background, so real stellar black holes absorb more than they emit.