About the Black Hole Collision Calculator
When two black holes spiral together and merge, the resulting black hole is not simply the sum of the two starting masses. Some of the total mass-energy is carried away as gravitational waves — ripples in spacetime first detected directly by LIGO in 2015. This calculator combines two well-established results, the Schwarzschild radius and mass-energy equivalence, to estimate the merged black hole's mass, the energy radiated, and the size of its event horizon.
Understanding the formula
Enter the masses of the two colliding black holes in solar masses (M☉, where one M☉ ≈ 1.989 × 10^30 kg) and an assumed percentage of the total mass radiated as gravitational waves. The calculator adds the two masses for the pre-merger total, subtracts the radiated fraction for the final mass (M_final = (M1 + M2) × (1 − f)), converts the radiated mass into energy with E = mc², and finds the final event horizon radius with the Schwarzschild formula r = 2GM/c² (G is the gravitational constant, c is the speed of light).
Choosing a radiated-energy percentage
- Comparable-mass, non-spinning binary black holes typically radiate roughly 3-5% of their total mass as gravitational waves during merger.
- The first confirmed detection, GW150914, involved black holes of about 36 M☉ and 29 M☉ merging into a final black hole of about 62 M☉ — around 3 M☉, about 5%, was radiated away.
- The exact fraction depends on the mass ratio and spins of the two black holes and requires full numerical-relativity simulations to pin down precisely; this calculator treats it as an adjustable assumption.
Knowing the limits
This calculator uses the non-rotating (Schwarzschild) approximation and a user-supplied radiated-energy percentage — it does not model spin, orbital dynamics, or the "kick" velocity imparted to the final black hole. Research-grade predictions of final mass and spin rely on numerical-relativity simulations of the full Einstein field equations.