Case 1
- Mass
- 198900010²⁴ kg
2,954.13m
Open with these valuesSchwarzschild Radius Calculator
2,954.13m
Result: 2,954.13 mCompress the Sun to a radius of 2954 metres, about 2.95 km, and it becomes a black hole. The Schwarzschild radius scales straight with mass: r = 2GM/c². Enter the mass in units of 10²⁴ kg — the Sun is 1989000, Earth is 5.972 and lands at just under 9 mm.
The numbers at a glance
| Mass (10²⁴ kg) | Result (m) |
|---|---|
| 500,000.000000 | 742.62 |
| 1,000,000.000000 | 1,485.23 |
| 1,500,000.000000 | 2,227.85 |
| 1,989,000.000000Your value | 2,954.13 |
| 2,000,000.000000 | 2,970.46 |
| 2,500,000.000000 | 3,713.08 |
| 3,000,000.000000 | 4,455.70 |
| 3,500,000.000000 | 5,198.31 |
Worked examples
Case 2
- Mass
- 5.97210²⁴ kg
0.01m
Open with these valuesCase 3
- Mass
- 1989000010²⁴ kg
29,541.27m
Open with these valuesHow it's calculated
r = 2 × G × M ÷ c²
- StepEnter the mass in units of 10²⁴ kg — the Sun is 1989000.
- StepThe calculator divides 2GM by c², with c = 299792458 m/s exactly.
- ResultRead the event-horizon radius in metres; divide by 1000 for km.
Reference table
| Mass | What that is | Schwarzschild radius (m) |
|---|---|---|
| 5.972 | Earth, an event horizon under a centimetre | 0.008870 |
| 1898 | Jupiter, a little under three metres | 2.818970 |
| 1989000 | The Sun, 2.95 km | 2954.13 |
| 19890000 | A ten-solar-mass stellar black hole | 29541.27 |
| 8540000000000 | Sagittarius A*, the black hole at the Milky Way's centre | 12683881739.65 |
Questions
How do I calculate the Schwarzschild radius?
Multiply the mass by twice the gravitational constant and divide by the speed of light squared: r = 2 × G × M / c², with G = 6.6743e-11 and c = 299792458 m/s. The mass box counts in units of 10²⁴ kg, so the Sun is 1989000 and the radius comes back as about 2954 m.
What is the Schwarzschild radius?
It is the size of the event horizon a mass would have if it collapsed into a non-rotating black hole. It is the radius to which the mass must be squeezed so that nothing, not even light, can escape from inside. It depends on nothing but the mass.
What is the Schwarzschild radius of the Sun?
Using the Sun's mass of 1.989e30 kg, it is about 2954 metres, roughly 2.95 km. The Sun is vastly larger than that and will never become a black hole; its core is simply not massive enough to collapse that far.
Does every object have one?
Mathematically yes, any mass has one. Earth's is about 8.87 mm and a person's is far smaller than a proton. It only becomes physically meaningful once an object is actually compressed inside that radius, which in nature happens only to very massive collapsing stars.
Is this the real size of a black hole?
It is the horizon radius of the simplest case, a non-rotating and uncharged black hole, which is the Schwarzschild solution. Real black holes usually spin, and rotation changes the horizon geometry, described instead by the Kerr solution. Treat this value as the classic baseline rather than an exact size.
Why does the display show 0.00 for small masses?
The readout carries two decimals, and Earth's horizon of 0.00887 m falls below that. The calculation itself is exact — the reference table shows the same value to six decimals. Two decimals are what the largest reference case, Sagittarius A*, allows.
Sources and last check
Information, not professional advice.