Schwarzschild Radius Calculator
Enter the mass of the object. Default unit is solar masses (M☉).
Enter the object's actual radius (in km) to check whether it qualifies as a black hole.
Formula: r_s = 2GM / c²
r_s = 2GM / c²
G = 6.674 × 10⁻¹¹ N·m²/kg²
c = 2.998 × 10⁸ m/s
Enter a Mass to Begin
Select a preset object (Earth, Sun, Sagittarius A*) or enter any mass value. The calculator will instantly show the Schwarzschild radius, surface gravity, density, photon sphere, ISCO, and more.
How to Use the Schwarzschild Radius Calculator
Select Calculation Mode
Choose 'Mass to Radius' to compute the Schwarzschild radius from a known mass, or 'Radius to Mass' to find the mass corresponding to a given event horizon radius. Most users will start with Mass to Radius mode.
Enter a Mass or Use a Preset
Type any mass value and select your unit (kg, solar masses, Earth masses, Jupiter masses, or moon masses). Or click one of the quick preset buttons — Moon, Earth, Sun, Stellar BH, Sagittarius A*, M87*, Neutron Star, or Jupiter — to instantly load a real-world example.
Review All Output Values
The results show the Schwarzschild radius in the most readable unit, along with surface gravity at the event horizon, average density, Hawking temperature, photon sphere radius, and ISCO radius. Toggle 'Show Advanced Outputs' for Hawking temperature and orbital radii.
Check Black Hole Status (Optional)
To determine if an object is currently a black hole, enter its actual physical radius in the optional field. The calculator will compare it to the Schwarzschild radius and tell you whether the object is already a black hole or how much it would need to be compressed.
Frequently Asked Questions
What is the Schwarzschild radius of the Sun?
The Sun's Schwarzschild radius is approximately 2.953 kilometers — about the size of a small city. This means if you could compress the entire mass of the Sun (1.989 × 10³⁰ kg) into a sphere just under 3 kilometers in radius, it would become a black hole. In reality, the Sun is far too small and cool to collapse this way; it will eventually become a white dwarf. However, stars with masses above roughly 20-25 solar masses can undergo core collapse and form stellar black holes after supernova explosions.
What is the Schwarzschild radius of Earth?
Earth's Schwarzschild radius is approximately 8.87 millimeters — about the size of a marble or a small grape. The entire mass of Earth (5.972 × 10²⁴ kg) would need to be compressed into a sphere smaller than a centimeter to become a black hole. Earth is nowhere near dense enough to collapse gravitationally; its actual radius of 6,371 kilometers is about 719 million times larger than its Schwarzschild radius. Compressing Earth to a black hole would require energy vastly beyond any naturally occurring process on Earth.
Do supermassive black holes have lower density than water?
Yes — this is one of the most counterintuitive facts in black hole physics. The average density of a black hole is calculated as mass divided by the volume of a sphere with the Schwarzschild radius. Because the Schwarzschild radius scales linearly with mass but volume scales as radius cubed, average density decreases as mass squared. A black hole of about 10 million solar masses has an average density roughly equal to that of water (1,000 kg/m³). Sagittarius A* at 4.15 million solar masses is slightly denser than water on average, while M87* at 6.5 billion solar masses has an average density hundreds of thousands of times lower than air.
What is the photon sphere and why does it matter?
The photon sphere is a spherical region at a radius of 1.5 times the Schwarzschild radius where photons can travel in unstable circular orbits. If a photon is placed at exactly this radius with the right direction, it will orbit indefinitely — but any perturbation causes it to either spiral inward to the event horizon or escape to infinity. The photon sphere is what gives black holes their distinctive 'shadow' seen in Event Horizon Telescope images of M87* and Sagittarius A*. The bright ring of light surrounding the dark shadow corresponds to photons that have orbited the black hole multiple times before escaping toward the observer.
What is Hawking radiation and is it detectable?
Hawking radiation is a theoretical quantum mechanical process by which black holes slowly emit thermal radiation due to quantum effects near the event horizon. Stephen Hawking predicted this in 1974. The temperature of this radiation is inversely proportional to the mass: T_H = ℏc³ / (8πGMk_B). For stellar-mass black holes (~3-10 solar masses), this temperature is roughly 6 × 10⁻⁸ to 2 × 10⁻⁸ kelvin — far colder than the cosmic microwave background at 2.725 K. This means stellar and supermassive black holes are currently absorbing CMB radiation faster than they emit Hawking radiation. Detection is currently impossible; only primordial black holes of asteroid mass or less could be warm enough to detect.
What is the ISCO and why is it important in astrophysics?
The Innermost Stable Circular Orbit (ISCO) is the smallest circular orbit in which a test particle can stably orbit a black hole without spiraling in. For a non-rotating Schwarzschild black hole, the ISCO occurs at 3 times the Schwarzschild radius, or 6GM/c². Inside the ISCO, there are no stable circular orbits; matter falling within this radius spirals rapidly inward. The ISCO is critical in accretion disk physics — the inner edge of the accretion disk that makes black holes shine in X-rays corresponds approximately to the ISCO. For rotating (Kerr) black holes, the ISCO shrinks toward the event horizon as spin increases, which affects how efficiently accreting matter radiates energy before plunging in.