What happens at the Schwarzschild radius?
It is the event horizon — the boundary from which nothing, not even light, can escape. Time appears to stop there from an outside observer.
Schwarzschild Radius Calculator
r_s = 2GM/c²
Calculate the Schwarzschild radius (event horizon) of a black hole. r_s = 2GM/c².
Calculate
Enter values above to calculate
How it calculates
1
G = 6.674×10⁻¹¹ N·m²/kg²; c = 2.998×10⁸ m/s
2
r_s = 2GM/c²
3
Result in metres
Formula
r_s = 2GM/c²
Variable Table
| Symbol | Quantity | SI Unit |
|---|---|---|
| r_s | Schwarzschild radius | m |
| G | Gravitational constant = 6.674×10⁻¹¹ | N·m²/kg² |
| M | Mass | kg |
| c | Speed of light = 2.998×10⁸ | m/s |
How to Use This Calculator
This schwarzschild radius calculator is built for quick physics checks and worked-problem review. Enter values in the units shown beside each input, then compare the result with the formula and variable table before using it in a longer solution. The calculator does the arithmetic, but the physics still depends on choosing a model that matches the situation.
Start by identifying the system, the known quantities, and the quantity you want to find. If a value is given in a non-SI unit, convert it before substitution. A correct numerical answer with mixed units can still be physically wrong, especially when squared units, inverse seconds, charges, temperatures, or distances are involved.
Assumptions and Limits
The formula r_s = 2GM/c² is a model, not a universal description of every possible case. It assumes the quantities in the variable table are the relevant quantities for the problem and that hidden effects are either negligible or already included in the inputs. If friction, drag, relativistic speeds, changing fields, non-constant temperature, or geometry-specific effects matter, check whether a more complete model is needed.
Use the result as a magnitude and units check. Ask whether the answer has the right sign, whether it grows or shrinks when an input changes, and whether the limiting cases make sense. Setting an input to zero, doubling a quantity, or using a very large value is often enough to catch a formula choice or unit mistake before it reaches a final answer.
Worked Example
Find the Schwarzschild radius of the Sun (M = 1.989×10³⁰ kg).
Step 1: r_s = 2 × 6.674×10⁻¹¹ × 1.989×10³⁰ / (2.998×10⁸)²
Step 2: r_s = 2.654×10²⁰ / 8.988×10¹⁶
Answer: r_s ≈ 2,953 m ≈ 3 km (the Sun as a black hole would be ≈ 6 km across)
Common Mistakes
- The Schwarzschild radius is a property of mass, not an actual physical surface (unless the mass is compressed inside it)
- For Earth: r_s ≈ 9 mm — Earth would need to be compressed to a sphere smaller than a marble
- r_s ∝ M — double the mass doubles the event horizon radius
Related
Frequently Asked Questions
Does the Sun have a Schwarzschild radius?
Yes, ≈ 3 km. But the Sun's actual radius is 696,000 km, so it is not a black hole. Only if all its mass were inside 3 km would an event horizon form.