What is a Black Hole?
You may think that black holes are mysterious objects that keep physicists up at night, but we actually know quite a lot about them. With this calculator we hope to teach you what the event horizon is, what happens when black holes collide, and how to calculate the properties of the resulting merged black hole.
In general terms, black holes are one of the simplest objects to work with in the Universe. When a star is running out of fuel to burn, it undergoes a series of processes that ends in the formation of one of three interstellar objects: a white dwarf, a neutron star, or a black hole — each denser than the previous one.
For a star to become a black hole after its "death," it needs to be at least 2–3 times the mass of our Sun. If this is the case, the gravitational pull of the star overwhelms all other forces, and the remnant ends up collapsing into a singularity — a point of theoretically infinite density. This singularity is surrounded by the event horizon.
The Event Horizon and the Schwarzschild Radius
Anything that enters the event horizon is trapped forever by the singularity's gravity — not even light can escape. This is why black holes appear truly black: no photons can escape from within the event horizon to reach our eyes or telescopes.
The radius of the event horizon is called the Schwarzschild radius, calculated by:
rs = 2GM / c²
where G is the gravitational constant (6.674 × 10⁻¹¹ m³/kg·s²), M is the black hole mass, and c is the speed of light. For reference, the Schwarzschild radius is approximately 2.95 km per solar mass.
How Do We See Black Holes?
Since black holes emit no light, we detect them indirectly through several methods:
- Gravitational waves — ripples in spacetime produced when massive objects accelerate. The LIGO and Virgo observatories detected the first black hole merger (GW150914) in 2015.
- Accretion disks — gas spiraling into a black hole heats up to millions of degrees and emits X-rays.
- Gravitational lensing — a black hole bends light from objects behind it, creating distinctive arc-shaped images.
- Event Horizon Telescope — in 2019, the first direct image of a black hole's shadow was captured (M87*).
Tidal Disruption and Objects Eaten by Black Holes
When a star passes too close to a black hole, the tidal forces — the difference in gravitational pull between the near and far sides of the star — can exceed the star's own self-gravity. This causes a tidal disruption event (TDE): the star is literally torn apart. About half the stellar material falls into the black hole, producing a bright flare, while the rest is flung away.
How to Use the Black Hole Collision Calculator
Enter the masses of two black holes in solar masses (M☉, where 1 M☉ ≈ 2 × 10³⁰ kg) and select your preferred unit system for the results. The calculator computes:
- Chirp mass — the key parameter controlling the gravitational wave signal: Mc = (m₁m₂)³/⁵ / (m₁+m₂)¹/⁵
- Symmetric mass ratio η — measures how "equal" the masses are; η = 0.25 for equal masses
- Mass radiated as gravitational waves — estimated using the NR approximation ΔM ≈ 0.2η × Mtotal
- Final black hole mass — Mf = Mtotal − ΔM
- Final Schwarzschild radius — the event horizon size of the merged black hole
- Gravitational wave energy — E = ΔM × c²
- Peak GW frequency at ISCO — the innermost stable circular orbit sets the merger frequency
- Ringdown frequency — the quasi-normal mode frequency of the final ringing black hole
Try the preset buttons to reproduce famous LIGO events like GW150914 (36 + 29 M☉ → final 62 M☉, 3 M☉ radiated as GW energy).
Approximations and Simplifications
This calculator uses several approximations:
- The radiated energy formula ΔM ≈ 0.2η × Mtotal is a fit to numerical relativity results for quasi-circular, non-spinning (Schwarzschild) mergers.
- GW frequencies assume non-spinning black holes. Spin (Kerr parameter) shifts these values.
- The Schwarzschild radius formula applies to the final black hole assuming it settles to a Schwarzschild (non-rotating) state. In reality, merged black holes have spin (they are Kerr black holes).
- Actual gravitational wave observations include higher-order effects not captured by these simple approximations.
Despite these simplifications, the results are accurate to within ~10–20% for typical astrophysical merger parameters.
Unit Systems
Metric System
Schwarzschild radius in kilometers (km); gravitational wave energy in Joules (J). The metric system is the international standard in scientific research.
American (Imperial) System
Schwarzschild radius in miles (mi); gravitational wave energy in British Thermal Units (BTU). For context, 1 BTU ≈ 1055 J and 1 mile ≈ 1.609 km.