Schwarzschild radius and black-hole event horizons
The Schwarzschild radius is the event-horizon radius in the Schwarzschild solution for a nonrotating, uncharged black hole.
It scales directly with mass: one solar mass corresponds to a radius of about 2.95 kilometers.
How to calculate Schwarzschild radius
- Choose a preset or enter mass: Use kilograms, solar masses, Earth masses, or pounds.
- Calculate: Generate radius, diameter, and light-crossing time.
- Interpret the model: Remember that rotating black holes require the Kerr solution.
Formula and variables
Multiply mass by twice the Newtonian gravitational constant, then divide by the exact speed of light squared.
rₛ = 2GM/c²- rₛ — Schwarzschild radius
- Event-horizon radius (m)
- G — Gravitational constant
- Newtonian constant of gravitation (m³ kg⁻¹ s⁻²)
- M — Mass
- Mass of the object (kg)
- c — Speed of light
- Speed of light in vacuum (m/s)
One-solar-mass black hole
Find the Schwarzschild radius for one solar mass.
- Mass
- 1 M☉ = 1.98847 × 10³⁰ kg
- rₛ = 2GM/c²
- rₛ ≈ 2,953 m
Result: The Schwarzschild radius is approximately 2.95 km.
The event-horizon diameter is about 5.91 km for this idealized mass.
Understanding your results
Radius grows linearly with mass
Doubling mass doubles the Schwarzschild radius because G and c are constants.
- The radius is not the current physical radius of an ordinary star or planet.
- A body becomes a black hole only if its mass-energy is confined inside the relevant horizon.
Assumptions
- Spherical, nonrotating, uncharged Schwarzschild spacetime.
- Mass is isolated for the purpose of the model.
Limitations
- Does not calculate the horizons of rotating or charged black holes.
- Does not model accretion disks, tidal forces, evaporation, or cosmological effects.
Common mistakes
- Confusing event-horizon radius with diameter.
- Entering solar masses while the selected unit is kilograms.
- Treating the formula as the physical radius of an ordinary object.
Practical use cases
Astronomy education
Compare event-horizon scales for stellar and supermassive black holes.
Relativity exercises
Verify calculations involving the Schwarzschild metric.
Frequently asked questions
Is the Schwarzschild radius the diameter of a black hole?
No. It is a radius; the corresponding horizon diameter is twice rₛ.
Does every mass have a Schwarzschild radius?
The formula assigns a scale to any mass, but an ordinary object is not a black hole unless it is compressed within the applicable horizon.
Sources and review
- General Relativity and Quantum Gravity — OpenStax College Physics 2e. Accessed 2026-07-14.
Reviewed 2026-07-14.