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SNR: Fusion Calculation

Energy of fusing hydrogen to helium

Just how much energy is released in a hydrogen fusion reaction? The reaction is:

4(1H) ⇒ 4He + 2 e+ + 2 neutrinos + energy

Energy per fusion reaction

The energy comes from the difference in the mass of the 4 hydrogen atom and the resulting helium atom through Einstein's famous equation: E=mc2.

[Note that the masses of the 2 e+ and the 2 neutrinos are so small compared to the masses of hydrogen and helium that we can neglect them from this simple calculation.]

To make this calculation, you'll need the following:

  • Mass of a hydrogen atom, mH = 1.673 × 10-27 kg
  • Mass of a helium atom, mHe = 6.645 × 10-27 kg
  • Speed of light, c = 2.998 × 108 m/s


Mass difference:

Δ m = (4 × mH) - mHe
  = 4.7 × 10-29 kg

Energy released in each fusion reaction:

E = mc2
  = (Δ m) × c2
  = 4.7 × 10-29 kg × (108 m/s)2
  = 4.224 × 10-12 kg m2/s2
  = 4.224 × 10-12 J

How much energy is that? Let's compare to something familiar – powering a 60-Watt lightbulb for 1 second.

1 Watt = 1 J/s

So, we need 60 Joules to power the bulb for one second:

# reactions = total energy/energy per reaction
  = 60 J/4.224 × 10-12 J
  = 1.4 × 1013 reactions

Or 14,000 billion reactions just to power that light bulb for one second. This would produce 7,000 billion helium atoms. That might sound like a lot of atoms; however, to fill a balloon with the helium that results form these reactions, you need about 1023 helium atoms, or the equivalent number of reactions if you powered the light bulb for 300 years, instead of one second.


A service of the High Energy Astrophysics Science Archive Research Center (HEASARC), Dr. Alan Smale (Director), within the Astrophysics Science Division (ASD) at NASA/GSFC

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