What happens to the mass when two black holes collide?

When two black holes merge, the total mass of the merged object is always less than the sum of the two original masses. The missing mass is converted directly into gravitational wave energy via Einstein's E=mc². For a pair of roughly equal-mass stellar black holes, about 5% of the total mass is radiated away as gravitational waves in the final moments of inspiral and merger. For the LIGO event GW150914, a 36 and a 29 solar mass black hole produced a 62 solar mass merger product, with approximately 3 solar masses converted into gravitational wave energy — more than the entire Sun would radiate in its full 10-billion-year lifetime, released in a fraction of a second.

How was the first black hole merger detected?

The first confirmed black hole merger was detected on 14 September 2015 by the LIGO (Laser Interferometer Gravitational-Wave Observatory) detectors at Hanford, Washington and Livingston, Louisiana. The signal, designated GW150914, lasted about 0.2 seconds and swept from about 35 Hz up to 150 Hz as the two black holes spiralled inward. The peak strain on Earth's detectors was roughly 10⁻²¹, meaning each 4-kilometre LIGO arm changed in length by about one-thousandth the diameter of a proton. The detection confirmed a major prediction of Einstein's general relativity that had gone untested for 100 years.

Why do black hole mergers radiate gravitational waves instead of light?

Black holes do not radiate light during merger because they have no surface, no atmosphere, and no charged matter being accelerated in the conventional electromagnetic sense. The only emission mechanism available is the spacetime curvature itself. Gravitational waves are ripples in the fabric of spacetime produced whenever any massive object accelerates asymmetrically. During a binary black hole inspiral, the two masses orbit each other at increasing speed, generating a gravitational wave signal that strengthens as they approach. The merger and ringdown phases emit a brief burst as the newly formed black hole vibrates like a struck bell before settling into a stationary Kerr configuration.

What is the Schwarzschild radius?

The Schwarzschild radius is the critical radius at which the escape velocity from a mass equals the speed of light. For a non-rotating black hole, it defines the event horizon: any matter or light that crosses inside this radius cannot escape. The formula is rs = 2GM/c², where G is the gravitational constant, M is the mass, and c is the speed of light. For the Sun (2 × 10³⁰ kg), the Schwarzschild radius is approximately 2.95 km. For a 10 solar mass black hole, it scales linearly to 29.5 km. Earth's Schwarzschild radius is about 8.9 mm.

Can a black hole collision destroy the solar system?

No. Black hole mergers produce gravitational waves, not jets, shockwaves, or projectiles of matter. Even at close astronomical distances, gravitational waves cause strain — a fractional change in length — that falls off as 1/r. The LIGO detection of GW150914 came from a merger 1.3 billion light-years away, and the strain at Earth was less than 10⁻²¹. A merger in the Milky Way, which has never been observed, would produce a much stronger signal but would still pose no physical threat to planets or star systems. The merged black hole itself remains a gravitationally bound object and does not emit radiation that would affect distant systems.

What does 'forbidden' mean in the context of intermediate-mass black hole mergers?

The term 'forbidden' in media coverage of events like GW190521 refers to the pair-instability supernova gap: the theoretical mass range (roughly 55 to 130 solar masses) where a single stellar collapse is believed to produce no remnant black hole. Stars in this range are disrupted by pair production before collapse. Black holes in this range therefore cannot form from direct stellar evolution — they would have to be the products of earlier mergers (second or third generation). As a comment on Reddit's r/astrophysics noted, 'forbidden' is a sensationalised headline: nothing stops a merger product from having a mass in this range. The physics just means such objects could not form by a single star dying.

How accurate is this calculator?

This calculator uses the post-Newtonian symmetric mass ratio approximation for gravitational wave radiation efficiency. The formula η = 0.05 × 4q/(1+q)² gives the approximate fraction of total mass radiated as gravitational waves, peaking at about 5% for equal-mass systems and decreasing as the mass ratio diverges from unity. Full numerical relativity simulations, which require supercomputing resources to solve Einstein's field equations, give efficiencies that match this approximation within 10 to 20% for most astrophysically relevant mass ratios. The Schwarzschild radius formula rs = 2GM/c² is exact for non-rotating (Schwarzschild) black holes. For spinning (Kerr) black holes, the ergosphere and photon sphere differ, but the event horizon radius at the poles is still rs.

Does time stop at the event horizon of a black hole?

From the perspective of a distant observer, an infalling object appears to slow down and freeze asymptotically at the event horizon due to gravitational time dilation — it never appears to cross it. However, from the perspective of the infalling object itself, it passes through the event horizon in finite proper time without any dramatic local event. The apparent freezing is a consequence of the infinite redshift of light emitted near the horizon, not a physical suspension of time. During a black hole merger, both event horizons approach and merge; the mathematics of this process requires numerical relativity because the usual perturbative approximations break down when the spacetime is highly dynamical.

What is the difference between stellar, intermediate, and supermassive black holes?

Stellar-mass black holes form from the gravitational collapse of massive stars and typically range from about 5 to 100 solar masses. Intermediate-mass black holes (IMBHs) span roughly 100 to 100,000 solar masses and are the subject of active research — GW190521 detected a merger product near the lower boundary of this range. Supermassive black holes, like the one at the centre of the Milky Way (Sagittarius A*, approximately 4 million solar masses) or the M87 black hole imaged by the Event Horizon Telescope (6.5 billion solar masses), occupy the cores of most large galaxies. Their formation mechanisms differ, and multi-generation mergers are one candidate pathway for building intermediate and supermassive objects from stellar-mass seeds.

How long does a black hole merger take?

The timescale depends heavily on the masses and initial separation. Two stellar-mass black holes captured into a close binary can take millions to billions of years to inspiral through gravitational wave emission before reaching the merger phase. The actual merger and ringdown — the final orbits, plunge, and settling of the product — lasts milliseconds for stellar-mass systems and up to minutes for supermassive black hole mergers. LIGO's GW150914 signal lasted about 0.2 seconds. The ringdown, where the merged object vibrates quasi-normally before settling, typically damps out within a few light-crossing times of the final object, which for a 62 solar mass black hole (Schwarzschild radius ~183 km) is under a millisecond.

Black Hole Collision Calculator – Merger Mass, GW Energy & Schwarzschild Radius

What Is the Black Hole Collision Calculator?

The Black Hole Collision Calculator computes what happens when two black holes merge, using the physics underlying LIGO's landmark GW150914 detection. Enter the masses of two black holes in solar masses and the calculator returns the Schwarzschild radius of each, the estimated fraction of total mass radiated as gravitational waves, the mass and radius of the merged product, the total gravitational wave energy released, and the peak gravitational wave frequency. The gravitational wave efficiency uses the symmetric mass ratio approximation, which gives approximately 5% mass conversion to gravitational waves for equal-mass mergers and less for unequal pairs.

All black hole masses are in solar masses (M☉ = 1.989 × 10³⁰ kg). The Schwarzschild radius formula rs = 2GM/c² applies to non-rotating (Schwarzschild) black holes. Real astrophysical black holes are thought to be rotating (Kerr black holes), but the event horizon area scales with mass in the same way to within a factor of order unity depending on spin.

The Schwarzschild Radius: How Large Is a Black Hole?

The Schwarzschild radius is the size of a black hole's event horizon, the point of no return beyond which nothing can escape. For a non-rotating black hole, rs = 2GM/c² scales linearly with mass. A solar-mass black hole has a Schwarzschild radius of about 2.95 km. A 10 M☉ black hole is 29.5 km across its event horizon. The 62 M☉ product of GW150914 had an event horizon of approximately 183 km in radius, smaller than the state of Rhode Island. Contrast that with the supermassive black hole at the centre of M87, which the Event Horizon Telescope imaged in 2019: at 6.5 billion solar masses, its event horizon spans roughly 19 billion km, larger than our entire solar system.

The linearity of Schwarzschild radius with mass means that doubling the mass doubles the event horizon radius, not the volume. Volume scales as the cube of radius, so a black hole that is twice as massive has eight times the enclosed volume. Density — if one could meaningfully define it for a black hole — therefore decreases as mass increases. A supermassive black hole at the galactic centre has an average interior density lower than water.

What Happens to the Missing Mass?

When two black holes merge, the total mass of the product is always less than the sum of the components. The deficit appears as gravitational wave energy: pure spacetime ripples propagating outward at the speed of light. For GW150914, approximately 3 solar masses of material — more energy than the Sun will emit across its entire 10-billion-year main-sequence lifetime — was converted to gravitational waves in about 0.2 seconds. The luminosity at peak was roughly 3.6 × 10⁴⁹ watts, temporarily outshining every star in the observable universe combined.

The efficiency of this conversion depends on the mass ratio of the two merging black holes. Equal-mass mergers are the most efficient, radiating about 5% of total mass as gravitational waves. Highly unequal-mass mergers are less efficient because the smaller object contributes less to the orbital dynamics. This is captured in the symmetric mass ratio η = m₁m₂/(m₁+m₂)², which ranges from 0 (extreme mass ratio) to 0.25 (equal masses). Our calculator uses GW efficiency = 0.05 × 4η, giving the full 5% only at equal mass. For a system like a stellar-mass black hole merging with a supermassive one, efficiency can fall below 0.1%.

LIGO and the Detection of Gravitational Waves

Before 2015, gravitational waves had never been directly observed, though their existence had been inferred from binary pulsar timing since 1974 (work that won the Nobel Prize in 1993). The LIGO detectors use laser interferometry across 4-kilometre arms to measure changes in length far smaller than an atomic nucleus. GW150914 produced a strain of roughly 10⁻²¹ — meaning each 4 km arm changed by about 4 × 10⁻¹⁸ m at peak. Isolating this signal from seismic noise, thermal noise, and quantum shot noise required decades of engineering and is among the most precise measurements ever made.

Since GW150914, LIGO and its European partner Virgo have catalogued dozens of binary black hole mergers, a binary neutron star merger (GW170817), and a neutron star-black hole merger. GW190521, detected in 2019, produced a merged black hole of approximately 150 M☉, placing it in the intermediate-mass range. As a thread on Reddit's r/astrophysics noted about this event, reaching this mass via a single stellar collapse is not physically possible in current models. A third or fourth generation of mergers, accumulating mass over multiple events in dense star clusters, is the most likely explanation.

The Peak Gravitational Wave Frequency and LIGO's Window

Gravitational waves from a binary black hole inspiral sweep upward in frequency as the orbit tightens, a phenomenon called a chirp. The peak frequency at merger corresponds approximately to twice the orbital frequency at the innermost stable circular orbit (ISCO) of the final merged black hole. For a non-spinning black hole, this is f ≈ c³/(6^(3/2) × π × G × M). For GW150914's 62 M☉ product, this gives about 71 Hz, consistent with the observed peak of the chirp.

LIGO is sensitive across roughly 10 to 2000 Hz. Stellar-mass black hole mergers of 5 to 100 M☉ fall comfortably within this band. Very massive mergers (supermassive black holes) produce signals at millihertz frequencies far below LIGO's reach, which is why the planned space-based LISA mission will target that lower-frequency regime. Our calculator flags whether your chosen masses produce a peak frequency within LIGO's band or whether a different detector would be required. You can also compare merger results with the Schwarzschild Radius Calculator for deeper analysis of the event horizon geometry.

The Most Common Misunderstanding About Black Hole Collisions

The most persistent misconception about black hole mergers is that they are explosive events comparable to a supernova or nuclear detonation — that nearby matter is blasted away, and that a merger in our galaxy would be catastrophic for Earth. This conflates two different phenomena. The energy output of a merger is enormous in absolute terms, but it is radiated entirely as gravitational waves, which interact with matter extraordinarily weakly. The strain from GW150914, originating 1.3 billion light-years away, was 10⁻²¹. A merger in the Milky Way would produce a strain several orders of magnitude larger and would be a transformative scientific event, but the gravitational tidal forces on Earth would still be completely harmless.

A related misconception is that merging black holes grow by absorbing each other's mass cleanly, with nothing lost. In reality, the merger deficit is unavoidable: it is a consequence of the non-linearity of Einstein's equations and the fact that gravitational binding energy cannot be stored inside the event horizon but must be emitted as radiation. The exact amount lost depends on the mass ratio and spin alignment of the merging objects, which is why numerical relativity simulations are needed for precision values beyond the approximation used here. For deeper context on gravitational forces at the scale of astrophysical objects, see our Escape Velocity Calculator and the Schwarzschild Radius Calculator.

Black Hole Collision Calculator