Enter mass, choose units, and compute radius quickly. See diameter, area, and light crossing time. Export clean tables for reports, labs, and classes today.
The Schwarzschild radius is the event-horizon radius for a non-rotating, uncharged mass:
Derived values shown include diameter (2rs), circumference (2πrs), area (4πrs²), and light crossing time (rs/c).
Values are approximate and depend on constants used.
| Object | Mass input | Unit | Schwarzschild radius (km) |
|---|---|---|---|
| Earth | 1 | Earth masses (M⊕) | 8.87010e-6 |
| Jupiter | 1 | Jupiter masses (M_J) | 0.00281916 |
| Sun | 1 | Solar masses (M☉) | 2.95334 |
| Stellar black hole | 10 | Solar masses (M☉) | 29.5334 |
| Sagittarius A* (approx.) | 4.00000e+6 | Solar masses (M☉) | 1.18134e+7 |
The solar-mass result is roughly 2.95 km, a helpful check.
A deeper, data-driven explanation of the Schwarzschild radius and the extra outputs shown above.
The Schwarzschild radius is the theoretical radius of the event horizon for an ideal, non‑rotating, uncharged black hole. It is not a physical surface; it marks the point where escape becomes impossible for light. As a compactness test, it answers: “How small would this mass need to be to form a horizon?”
This calculator uses rₛ = 2GM/c². G is the gravitational constant (m³·kg⁻¹·s⁻²) and c is the speed of light (m/s). Internally the tool converts your input to kilograms and computes rₛ in meters, then converts the display to your chosen unit.
Enter mass in solar masses (M☉), Earth masses (M⊕), Jupiter masses (M_J), kilograms, grams, or pounds. Scientific notation like 6.0e24 is supported for wide ranges. Because rₛ scales directly with mass, even small input changes show up proportionally in the output.
Besides radius, the calculator also reports diameter, circumference, and horizon area, all in meters for consistency. It includes a light‑crossing time estimate (roughly rₛ divided by c) and a mean density inside rₛ using the volume of a sphere. These extras help you compare objects on geometry and timescale, not just size. You can display the radius in kilometers, miles, feet, centimeters, or millimeters, depending on whether you want astrophysical or human‑scale intuition.
Compare rₛ with an object’s real radius. If the real radius is much larger, the object is far from becoming a black hole. If the real radius were forced below rₛ, general relativity predicts horizon formation in this simplified setting. For stars, this comparison explains why only collapsed remnants can approach horizon‑like compactness.
Schwarzschild radius scales linearly: double the mass and you double rₛ. A practical benchmark is 1 M☉ → about 2.95 km, so 10 M☉ → about 29.5 km. This linear rule makes back‑of‑the‑envelope checks easy before running detailed models.
For Earth (1 M⊕), rₛ is about 8.9 mm—smaller than a fingertip width. For Jupiter (1 M_J), rₛ is about 2.8 m. For a million‑solar‑mass object, rₛ is about 2.95 million km, on the order of a few solar radii, which highlights how supermassive horizons can span planetary scales.
This relation assumes a non‑spinning, uncharged mass (the Schwarzschild solution). Real black holes can rotate, altering horizon properties. Also, pressure, rotation, and realistic matter physics are ignored, so treat results as a clean baseline. Use the significant‑digits control for readable rounding, then export CSV for datasets or PDF for sharing and archiving.
Short answers for common questions about interpreting the results.
It’s the radius of the event horizon for an ideal, non‑rotating, uncharged black hole of a given mass. It shows how compact the mass must be before light can no longer escape.
Because rₛ depends on mass, and Earth’s mass is modest on cosmic scales. The resulting radius is only millimeters, far smaller than Earth’s actual radius, so Earth is nowhere near horizon‑forming compactness.
This tool uses the Schwarzschild formula, which assumes no rotation or charge. Rotating black holes follow the Kerr solution, where horizon size and geometry differ. Use this result as a baseline approximation.
It estimates how long light takes to travel one Schwarzschild radius, roughly rₛ/c. It’s a simple timescale used for intuition, not a full simulation of near‑horizon trajectories.
It divides the mass by the volume of a sphere with radius rₛ. This highlights how denser horizons require extreme compression, especially for small masses, and how density drops as mass increases.
Use kilometers for stellar or supermassive masses, and meters or millimeters for planetary masses. Miles and feet can be useful for audience familiarity. The physics is unchanged; only the display unit differs.
They are approximate and depend on the constants used and rounding. If you override G or c, your results will shift slightly. The solar‑mass value near 2.95 km is a good quick check.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.