17.5959
MeV
0.01889
u
1
3.5192
MeV/nucleon
17.5959
MeV
0.01889
u
1
3.5192
MeV/nucleon
The Q-Value Nuclear Reaction Calculator determines the energy released or absorbed in a nuclear reaction from the masses of the reactants and products. The Q-value is the most fundamental energy quantity in nuclear physics, dictating whether a reaction is exothermic (energy-releasing) or endothermic (energy-absorbing), and quantifying exactly how much energy is involved.
Defined as the difference in total kinetic energy between products and reactants, the Q-value reflects the conversion of mass to kinetic energy (or vice versa) through $$E = mc^2$$. Positive Q-values indicate exothermic reactions that can occur spontaneously (given sufficient kinetic energy to overcome Coulomb barriers), while negative Q-values require a minimum threshold energy to proceed. This calculator covers any two-body nuclear reaction of the form $$A + B \rightarrow C + D$$.
The Q-value is calculated from conservation of mass-energy:
$$Q = (\Sigma m_{\text{reactants}} - \Sigma m_{\text{products}}) \times 931.494 \text{ MeV/u}$$
For a reaction $$A + B \rightarrow C + D$$:
$$Q = (m_A + m_B - m_C - m_D) \times 931.494$$
Equivalently, using binding energies:
$$Q = BE_{\text{products}} - BE_{\text{reactants}}$$
The sign convention is:
$$Q > 0$$: Exothermic — mass is converted to kinetic energy, products are more tightly bound
$$Q < 0$$: Endothermic — kinetic energy is converted to mass, products are less tightly bound
$$Q = 0$$: Elastic scattering — no nuclear transformation occurs
For endothermic reactions, the minimum kinetic energy (threshold) in the lab frame is: $$T_{\text{th}} = |Q| \cdot (1 + m_a/m_A)$$ where $$m_a$$ is the projectile mass and $$m_A$$ is the target mass.
The Q-Value in MeV is the net energy released (positive) or absorbed (negative). A positive Q means the reaction produces kinetic energy and can power reactors or weapons. The Mass Difference in u shows the raw mass conversion. Reaction Type classifies the reaction: 1 = exothermic, -1 = endothermic, 0 = elastic. The Q per Product Nucleon helps compare the energy efficiency of different reactions on a per-nucleon basis — fusion reactions typically have much higher values than fission.
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The deuterium-tritium fusion reaction (D + T → He-4 + n) releases 17.6 MeV, the highest Q-value of any fusion reaction accessible at practical temperatures.
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The p + Li-7 → 2 He-4 reaction releases 17.35 MeV, used in early nuclear physics experiments and proposed for aneutronic fusion concepts.
The Q-value is the net energy released or absorbed in a nuclear reaction, calculated from the mass difference between reactants and products: $$Q = (m_{\text{reactants}} - m_{\text{products}}) \times 931.494$$ MeV. Positive Q means energy is released; negative Q means energy must be supplied.
Exothermic reactions (Q > 0) release energy because the products are more tightly bound than the reactants. Endothermic reactions (Q < 0) absorb energy, requiring kinetic energy input to overcome the energy deficit. Fission and fusion power rely on exothermic reactions; endothermic reactions occur in cosmic ray spallation and particle physics experiments.
The threshold kinetic energy (in the lab frame) is $$T_{th} = |Q| \cdot (1 + m_{projectile}/m_{target})$$, always greater than |Q| to conserve both energy and momentum. This is the minimum projectile energy needed to make the reaction energetically possible in the center-of-mass frame.
Among commonly discussed reactions, D-T fusion has Q = 17.6 MeV for a 5-nucleon system. However, the fission of U-235 releases about 200 MeV total (including neutron and beta decay energy), though this involves ~236 nucleons. On a per-nucleon basis, fusion reactions are far more energetic.
Q equals the difference in total binding energy between products and reactants: $$Q = BE_{products} - BE_{reactants}$$. Reactions that produce more tightly bound products (higher total BE) have positive Q-values. This is why iron (highest BE/nucleon) cannot release energy by either fusion or fission.
You can use either, as long as you are consistent. If using atomic masses, the electron masses cancel out for reactions conserving charge (which all nuclear reactions do). The calculator works with whatever mass values you provide — just be consistent between reactants and products.
For multi-body final states, add all product masses. This calculator supports two products directly. For three-body reactions (e.g., fission with two fragments plus neutrons), you can sum all product masses into one effective value, or extend the calculation manually.
Q-values are measured by detecting the kinetic energies of reaction products using calibrated detectors (silicon, germanium, scintillation). At known beam energy, conservation of energy and momentum determines Q from the measured product energies and angles. High-precision Q-values come from mass spectrometry of the involved nuclides.
Radioactive decay can be viewed as a nuclear reaction with one reactant and multiple products. The Q-value equals the total kinetic energy of all decay products. For alpha decay of U-238: Q = 4.27 MeV. For beta decay of C-14: Q = 0.156 MeV. Positive Q is required for spontaneous decay.
A positive Q means the products have less total mass-energy than the reactants, so the reaction is energetically favorable. However, the Coulomb barrier between charged nuclei can prevent the reaction even when Q > 0. Sufficient kinetic energy (or quantum tunneling) is needed to bring nuclei close enough for the strong force to act. This is why fusion requires extremely high temperatures.
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