Nuclear Q-Value Calculator

Calculate energy released or absorbed in nuclear reactions using mass-energy equivalence.

Sum of reactant masses (u) (u)

1 u = 931.494 MeV/c²

Sum of product masses (u) (u)

Number of reaction events (for energy scaling)

Please check your inputs and try again.

What Q Tells You

The Q-value is the energy released or absorbed by a nuclear reaction, calculated from the mass difference between reactants and products.

Q = (Σm_reactants − Σm_products) × 931.5 MeV/u

Sign of Q	Name	Meaning
Positive	Exoergic	Energy released; can occur spontaneously if no barrier
Negative	Endoergic	Energy must be supplied — requires a threshold

A positive Q means the products are more tightly bound than the reactants, so mass has been converted to kinetic energy. This is the same logic as chemical thermochemistry, but the energies are millions of times larger because nuclear binding is millions of times stronger.

Reaction	Q value	Per nucleon
D + T → He-4 + n	17.6 MeV	3.5 MeV
D + D → He-3 + n	3.27 MeV	0.8 MeV
U-235 fission	~200 MeV	0.85 MeV
Chemical bond	~4 eV	—

The comparison with chemistry at the bottom is the point worth remembering: a single fusion event releases roughly four million times the energy of a chemical bond. This is why a kilogram of nuclear fuel replaces thousands of tonnes of coal.

Why Positive Q Is Not Enough

D–T fusion has a strongly positive Q, yet requires temperatures above 100 million kelvin. The reason is the Coulomb barrier: both nuclei are positively charged and repel each other, so enormous kinetic energy is needed before the strong force can take over. Q describes the energy balance, not the barrier to reaching it — exactly parallel to thermodynamics versus kinetics in chemistry.

Worked Examples

Example 1: U-235 fission: reactants=235.0439+1.0087, products=~234.9940

Δm≈0.058u

Result: Q=0.058×931.5=54 MeV (rough)

Actual: ~200 MeV per fission including all fragments

Example 2: D+T fusion: reactants=2.0141+3.0160, products=4.0026+1.0087

Δm=0.0188u

Result: Q=17.59 MeV per reaction

DT fusion energy — future reactor fuel

Example 3: Why D–T is the chosen fusion reaction

Q = 17.6 MeV, and the largest cross-section at achievable temperatures

Result: Highest yield at the lowest barrier

D–D fusion has a lower Q and a smaller reaction cross-section, so D–T is the practical target for first-generation reactors despite tritium's scarcity.

Example 4: Endoergic reactions need a threshold

Negative Q reaction

Result: Projectile must supply the deficit plus momentum

Threshold energy exceeds |Q| because momentum conservation means some kinetic energy must remain in the products.

Common Mistakes

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Assuming positive Q means the reaction happens readily

The Coulomb barrier must still be overcome. D–T fusion is strongly exoergic but needs temperatures above 100 million kelvin to proceed.

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Mixing atomic and nuclear masses inconsistently

Atomic masses include electrons. Use one convention throughout, since the electron masses largely cancel only when both sides are treated the same way.

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Forgetting to include emitted particles

Neutrons, alphas and betas carry mass and must appear in the product sum. Omitting them gives a substantially wrong Q.

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Comparing Q values without normalising per nucleon

Fission releases about 200 MeV against fusion's 17.6, but per nucleon fusion releases four times more. Total Q alone is misleading.

Frequently Asked Questions

u (atomic mass unit) vs MeV/c²?

1 u = 1.66054×10⁻²⁷ kg = 931.494 MeV/c². Use u because atomic masses are tabulated precisely. Δm in u × 931.494 = Q in MeV. For example, proton = 1.00728 u, neutron = 1.00866 u.

Binding energy vs Q-value?

Q = energy released in a specific reaction. Binding energy = energy to completely separate a nucleus into protons and neutrons. Average binding energy per nucleon peaks at Fe-56 (~8.8 MeV/nucleon). Fusion of light nuclei and fission of heavy nuclei both release energy.

What does a positive Q-value mean?

Energy is released because the products are more tightly bound than the reactants. Mass has been converted to kinetic energy.

Why does fusion need such high temperatures if Q is positive?

Because of the Coulomb barrier between positively charged nuclei. Q describes the energy balance, not the barrier that must first be overcome.

Why does fission release more total energy than fusion?

Because far more nucleons are involved. Per nucleon, fusion releases about four times more — 3.5 MeV against 0.85.

How does nuclear energy compare to chemical?

A single fusion event releases roughly four million times the energy of a chemical bond, which is why nuclear fuel is so energy dense.

Formula Explorer connections

Interpretation: This relationship connects isotopic composition, decay, radiation, mass defect or nuclear energy to a measurable quantity. Assumption: Use the correct nuclide, decay constant, branching behavior and time units. Radiation estimates also depend on geometry, shielding and detector response.

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