The boundary beyond which future-directed light cannot escape.
Relativity Scale LabWebGL ray marching · Schwarzschild geodesics
Black Hole Simulator
Light rays are traced through curved spacetime on your GPU, so the accretion disk wraps over and under the shadow exactly as general relativity predicts. Orbit the camera, switch relativistic beaming on and off, then set a mass to turn the picture into real kilometres.
Calculating the black hole scale.
One more perspective
Keep exploring the scale
Every toy changes one assumption. Try another and see what moves.
Black hole simulator
A ray-traced black hole you can orbit
Every frame traces one light ray per pixel backwards from the camera and integrates it through curved spacetime. Rays that fall inside the horizon make the black shadow, rays that skim the photon sphere wrap all the way around, and rays that cross the accretion disk pick up its light. Set the mass in Suns to turn the same picture into physical kilometres, then switch to the scale view to compare the horizon with familiar objects and orbits.
How to use the simulator
- Drag the render to orbit the black hole; scroll or pinch to zoom.
- Lower the viewing angle to see the disk fold over the shadow; raise it for a face-on view.
- Toggle Doppler beaming to compare the relativistic image with a naive one.
- Choose a measured example or enter a mass to read real distances on the scale bar.
- Move the stationary probe to see idealized gravitational time dilation.
- Open Scale to compare the horizon with the nearest familiar length.
The Schwarzschild radius formula
Rs = 2GM / c2
Here G is the gravitational constant, M is mass, andc is the speed of light. One solar mass gives an event horizon radius of about 2.95 kilometres.
What the three radii mean
The unstable circular path for light in the idealized metric.
The innermost stable circular orbit for a massive test particle.
The probe uses dτ/dt = √(1 − Rs/r), the clock-rate factor for a stationary observer outside a Schwarzschild black hole. Holding position requires ever more acceleration near the horizon and is impossible at it.
How the render works
Light follows null geodesics. In Schwarzschild spacetime the shape of every such path obeys u″ + u = (3/2) Rs u², where u = 1/r. The shader rewrites this as an effective force, a = −(3/2) h² r/ r⁵ with h the ray's conserved angular momentum, and integrates it with a leapfrog scheme in units where Rs = 1. Rays that dip below r = 1 are captured and painted black. Rays that cross the disk plane between the ISCO and the outer edge sample a thin-disk temperature profile, T ∝ [r⁻³ (1 − √(rin/r))]1/4, shifted by the combined Doppler and gravitational factor and brightened by its cube. Rays that escape sample a procedural star field, which is why background stars smear into arcs near the photon ring.
The apparent shadow is larger than the horizon: its radius is (3√3 / 2) Rs ≈ 2.6 Rs, the impact parameter below which incoming light is captured. That value is what the Event Horizon Telescope compares its M87* and Sagittarius A* images against.
What this model leaves out
The model assumes an isolated black hole with no spin and no electric charge. Real black holes rotate, which drags spacetime, moves the ISCO inward, and makes the shadow slightly asymmetric; that requires a Kerr metric. The accretion disk is infinitely thin, optically simplified, and textured procedurally rather than simulated as plasma, and the render skips the small redshift between the camera's own position and infinity.
Examples and constants
The Sagittarius A* preset uses NASA's 4.3-million-solar-mass estimate. The M87* preset uses the 6.5-billion-solar-mass estimate published with the Event Horizon Telescope's 2019 image. Constants follow the 2022 CODATA values.
More interactive astronomy tools
Black hole simulator FAQ
What does this black hole simulator show?
It renders a non-rotating black hole in real time by tracing light rays backwards through Schwarzschild spacetime on your GPU, and it calculates the Schwarzschild radius, shadow diameter, photon-sphere radius, innermost stable circular orbit, light-crossing time, and Hawking temperature from the mass you choose.
How is the Schwarzschild radius calculated?
For a non-rotating, uncharged black hole, the Schwarzschild radius is two times the gravitational constant times mass, divided by the speed of light squared: Rs = 2GM/c².
Is the image a realistic view of a black hole?
The bending of light is computed from the Schwarzschild metric, so the shadow, photon ring, and the disk wrapping over and under the black hole are geometrically faithful. The disk itself is a simplified thin-disk model with a procedural texture; it does not simulate plasma or radiative transfer, and the black hole does not spin.
Why is one side of the accretion disk brighter?
Gas near the inner edge orbits at about half the speed of light. Relativistic beaming makes the side moving toward you brighter and bluer and the receding side dimmer and redder. Turn off Doppler beaming in the controls to see the disk without this effect.
Does the picture change with mass?
No. In Schwarzschild spacetime every length scales with the Schwarzschild radius, so a stellar-mass and a supermassive black hole look identical when viewed from the same number of Schwarzschild radii. Only the physical size on the scale bar changes.
Why does the event horizon grow with mass?
The Schwarzschild formula makes the radius directly proportional to mass. Doubling the mass doubles the event horizon radius and its light-crossing time.
Educational Schwarzschild model: a non-rotating, uncharged black hole with a thin, procedurally textured accretion disk. Lensing geometry is computed; the disk's plasma is not.