Black Hole Collision Calculator
Enter the masses of two colliding black holes to find the merger outcome. The calculator gives you the combined final black hole mass, both Schwarzschild radii before and after collision, the chirp mass detected by gravitational-wave observatories, the ISCO gravitational-wave frequency where the inspiral peaks, the total energy radiated as gravitational waves, and the ringdown frequency of the newly formed black hole. All results update instantly as you type.
What happens when two black holes collide?
When two black holes spiral toward each other, they pass through three phases. During the inspiral, they orbit at increasing speeds, shedding energy as gravitational waves. At the merger, the two event horizons meet and the objects become one highly distorted black hole in a fraction of a millisecond. During the ringdown, the new black hole vibrates and radiates its distortions as a decaying burst of gravitational waves at a characteristic frequency, settling into a stable Schwarzschild (or Kerr) black hole. The total energy released can exceed the combined luminosity of all stars in the observable universe for the brief instant of coalescence. The first direct detection of this process was made by LIGO on September 14, 2015 (GW150914), confirming a century-old prediction of general relativity.
What is the chirp mass and why does it matter?
The chirp mass Mc = (m1 m2)^(3/5) / (m1 + m2)^(1/5) is the single combination of the two masses that most strongly determines how the gravitational-wave frequency evolves during the inspiral. It is called the chirp mass because, when the signal is converted to audio, the rising frequency produces a chirping sound. LIGO can measure the chirp mass more precisely than the individual masses, because the waveform phase encodes it directly. For an equal-mass 30+30 solar-mass binary, the chirp mass is about 26 solar masses. A higher chirp mass means slower frequency evolution and lower peak frequencies.
Schwarzschild radius and the event horizon
Every black hole has an event horizon - the boundary beyond which nothing, not even light, can escape. For a non-rotating (Schwarzschild) black hole, this radius is Rs = 2GM/c^2. Because G/c^2 is a small number, one solar mass corresponds to just Rs = 2.953 km. The event horizon grows linearly with mass, so a 10 solar-mass black hole has Rs ~ 29.5 km and a million solar-mass black hole has Rs ~ 2.95 million km. After a merger, the combined event horizon is always larger than the sum of the two original ones, consistent with the second law of black hole thermodynamics: the total horizon area cannot decrease.
ISCO, ringdown frequency, and LIGO detectability
The innermost stable circular orbit (ISCO) marks the point where orbital inspiral transitions to plunge and merger. The gravitational-wave frequency at the ISCO is f_ISCO = c^3 / (6^(3/2) pi G M_total), which scales as 4400 Hz divided by the total mass in solar masses. For a 65 solar-mass binary this gives about 68 Hz, well inside LIGO's sensitive band of roughly 10-2000 Hz. After the merger, the remnant rings down at a higher characteristic frequency f_ring, which depends on the final mass and spin. For non-spinning remnants the leading quasinormal mode frequency is approximately 12000 / M_final Hz. Both frequencies appear in the matched-filter templates that LIGO uses to detect signals buried in detector noise.
Notable real-world black hole mergers detected by LIGO/Virgo
| Event | BH 1 (M☉) | BH 2 (M☉) | Final mass (M☉) | Energy radiated (M☉) | ISCO freq (Hz) |
|---|---|---|---|---|---|
| GW150914 (2015) | 35.6 | 30.6 | 63.1 | 3.1 | ~75 |
| GW170104 (2017) | 31.2 | 19.4 | 48.7 | 1.9 | ~90 |
| GW170814 (2017) | 30.5 | 25.3 | 53.2 | 2.7 | ~83 |
| GW190521 (2019) | 95 | 69 | 150 | 14 | ~29 |
| GW200225 (2020) | 19.3 | 8 | 25.8 | 1.5 | ~170 |
Source: LIGO Scientific Collaboration. Masses in solar masses. Energy radiated includes measurement uncertainty.
Frequently asked questions
How much energy is released in a black hole collision?
For a typical equal-mass merger of stellar-mass black holes, roughly 5 percent of the total mass-energy is radiated as gravitational waves. For two 30 solar-mass black holes (total mass ~60 M☉), that is about 3 solar masses worth of energy, or about 5.4 x 10^47 joules, released in a fraction of a second. This is equivalent to several billion times the total energy the Sun will radiate over its entire 10-billion-year lifetime.
Does the final black hole weigh less than the two original ones combined?
Yes. Conservation of energy means the mass-energy carried away by gravitational waves must come from somewhere. The final black hole mass equals the total pre-merger mass minus the energy radiated divided by c^2. For the first LIGO detection GW150914, two black holes of roughly 36 and 29 solar masses merged and left a remnant of about 62 solar masses - about 3 solar masses were converted to gravitational-wave energy.
What is the ISCO and why does it determine the peak frequency?
The innermost stable circular orbit (ISCO) is the closest orbit around a black hole at which a test particle can stay in stable circular motion. For a non-spinning black hole it sits at 6 GM/c^2 from the center. As the two black holes spiral inward, they reach the ISCO and then rapidly plunge and merge. At that moment the gravitational-wave frequency, which is twice the orbital frequency, peaks. The formula f_ISCO = 4400 Hz / M_total (in solar masses) lets you predict whether a merger falls in the LIGO band.
What is the ringdown, and how is the ringdown frequency calculated?
After the merger, the newly formed black hole is highly distorted. It radiates this distortion as decaying sinusoidal gravitational waves - the ringdown - at a set of quasinormal mode (QNM) frequencies determined solely by the final mass and spin. For a non-spinning (Schwarzschild) remnant the dominant l=2,m=2 mode has a frequency of roughly 12000 Hz divided by the final mass in solar masses. Measuring both the frequency and the decay time allows physicists to test whether the remnant is consistent with general relativity's prediction for a Kerr black hole.
Can LIGO detect all black hole mergers?
LIGO is most sensitive to mergers whose ISCO frequency falls in the 10-2000 Hz range, which corresponds to total masses of roughly 2 to 440 solar masses. Very massive mergers (intermediate-mass and supermassive black holes) radiate at millihertz or lower frequencies and will be detected by the planned space-based LISA detector instead. Very light mergers (sub-solar mass) radiate at kilohertz frequencies above LIGO's sensitive band.
Why does the event horizon grow larger than the sum of the two originals?
This follows from the area theorem of general relativity (Hawking 1971): in classical gravity, the total event-horizon area can never decrease. The area of a Schwarzschild black hole goes as the square of its mass, so two black holes of mass m each have total area proportional to 2m^2, but the merged black hole of mass 2m (minus radiated energy) has area proportional to (2m - delta)^2, which is less than 4m^2 but the combined area still satisfies the constraint once you account for the geometry.