Q-Value Calculator (Nuclear Reactions)

Compute the Q-value of any nuclear reaction or radioactive decay from atomic masses.

💥 Q-Value Calculator (Nuclear Reactions)
Reactant 1 Mass (target)
u
Reactant 2 Mass (projectile, 0 to omit)
u
Product 1 Mass
u
Product 2 Mass (0 to omit)
u
Product 3 Mass (0 to omit)
u
Decay Type
Parent Atomic Mass
u
Daughter Atomic Mass
u
Q-Value
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Q in keV
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Q in Joules
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Mass Defect (Δm)
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Reaction Type
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Threshold Energy
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Q-Value
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Q in keV
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Q in Joules
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Decay Status
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Formula Used
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💥 What is the Q-Value Calculator?

The Q-value of a nuclear reaction is the net energy released or absorbed when reactant nuclei are transformed into product nuclei. A positive Q-value means the reaction is exothermic: the products are lighter than the reactants, and the mass deficit appears as kinetic energy of the products. A negative Q-value means the reaction is endothermic: the products are heavier than the reactants, and the projectile must provide a minimum kinetic energy (the threshold energy) to initiate the reaction.

This calculator supports two modes. In General Reaction mode, you enter atomic masses for up to two reactants and three products. The Q-value formula Q = (Σm_reactants - Σm_products) × 931.494 MeV/u converts the mass difference into energy using Einstein's mass-energy equivalence (E = mc²), where 1 atomic mass unit equals 931.494 MeV/c². In Nuclear Decay mode, you select the decay type (alpha, beta-minus, beta-plus, or electron capture) and enter the parent and daughter atomic masses. The calculator automatically applies the correct formula for each decay type, accounting for the different bookkeeping of electron masses between atomic mass tables and nuclear decay equations.

The Q-value concept was foundational in early nuclear physics. When James Chadwick discovered the neutron in 1932, he used Q-value calculations from atomic mass measurements to prove that beryllium was emitting a neutral particle (the neutron) rather than gamma rays. Today, Q-values are used in reactor physics to calculate power output per fission, in astrophysics to model nucleosynthesis in stellar cores, in nuclear medicine to assess the energy available from positron emitters in PET scanning, and in accelerator physics to determine the projectile energy needed to produce radioactive isotopes by threshold reactions.

The General Reaction mode is designed for reactions of the form A + a to B + b + c, where the third product c (often multiple neutrons) can be entered as the combined mass of all third-group products. The Decay mode handles the four main types of radioactive decay. For fission reactions, enter the two fission fragment masses and the mass of all neutrons emitted as the three product masses.

📐 Formula

Q  =  (Σ mreactants − Σ mproducts) × 931.494 MeV/u
Q = reaction Q-value in MeV; positive = exothermic, negative = endothermic
Δm = Σ mreactants − Σ mproducts in atomic mass units (u)
931.494 MeV/u = conversion factor (1 u × c²)
Alpha decay: Q = (Mparent − Mdaughter − Mα) × 931.494; Mα = 4.002602 u
Beta-minus: Q = (Mparent − Mdaughter) × 931.494 (electron masses cancel in atomic masses)
Beta-plus: Q = (Mparent − Mdaughter − 2me) × 931.494; me = 0.000549 u
Threshold energy: Tth = |Q| × Σmall / (2 × mtarget) for endothermic reactions
Example: U-235 + n to Ba-141 + Kr-92 + 3n: Q = (235.043929 + 1.008665 − 140.914400 − 91.926156 − 3.025995) × 931.494 = 173.3 MeV

📖 How to Use This Calculator

Steps

1
Enter reactant atomic masses - Type the atomic mass of the first reactant in the Reactant 1 field (the target nucleus). For a second reactant such as an incident neutron (1.008665 u) or proton (1.007825 u), enter it in the Reactant 2 field. Leave at 0 for single-body reactions.
2
Enter product atomic masses - Type the atomic mass of each product. For reactions with three products (such as two fission fragments plus three neutrons), enter the neutron masses summed as a single value in Product 3. Leave unused fields at 0.
3
Read the Q-value result - Click Calculate. The primary result shows Q in MeV, with secondary boxes for keV, joules, mass defect in microunits, reaction type, and threshold energy for endothermic reactions.
4
Use Decay mode for radioactive decay Q-values - Click the Nuclear Decay tab, select the decay type, and enter the parent and daughter atomic masses. The calculator applies the correct Q-value formula for alpha, beta-minus, beta-plus, or electron capture automatically.

💡 Example Calculations

Example 1 - U-235 Fission (Exothermic)

U-235 + n to Ba-141 + Kr-92 + 3n: prompt fission Q-value

1
Reactant masses: m(U-235) = 235.043929 u, m(n) = 1.008665 u. Total = 236.052594 u.
2
Product masses: m(Ba-141) = 140.914400 u, m(Kr-92) = 91.926156 u, m(3n) = 3 x 1.008665 = 3.025995 u. Total = 235.866551 u.
3
Mass defect: 236.052594 - 235.866551 = 0.186043 u. Q = 0.186043 x 931.494 = 173.3 MeV (exothermic, prompt fission energy).
Q = 173.3 MeV released per fission event
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Example 2 - Ra-226 Alpha Decay

Ra-226 to Rn-222 + alpha: Q-value of radium alpha decay

1
Parent: m(Ra-226) = 226.025403 u. Daughter: m(Rn-222) = 222.017570 u. Alpha: m(He-4) = 4.002602 u.
2
Q = (226.025403 - 222.017570 - 4.002602) x 931.494 = 0.005231 x 931.494 = 4.87 MeV.
3
The alpha particle carries most of the kinetic energy: T_alpha = Q x M_daughter / (M_daughter + M_alpha) = 4.87 x 222.018 / 226.020 = 4.78 MeV. The accepted value is 4.78 MeV, confirming the calculation.
Q = 4.87 MeV (alpha particle receives 4.78 MeV)
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Example 3 - Be-9(p,n)B-9: Endothermic Threshold Reaction

p + Be-9 to n + B-9: what minimum proton energy is needed?

1
Reactants: m(Be-9) = 9.012182 u (target), m(p) = 1.007825 u (projectile). Products: m(n) = 1.008665 u, m(B-9) = 9.013329 u.
2
Q = (9.012182 + 1.007825 - 1.008665 - 9.013329) x 931.494 = -0.001987 x 931.494 = -1.851 MeV (endothermic).
3
Threshold: T_th = 1.851 x (9.012182 + 1.007825 + 1.008665 + 9.013329) / (2 x 9.012182) = 1.851 x 20.042 / 18.024 = 2.058 MeV. Protons below this energy cannot initiate the reaction.
Q = -1.851 MeV, threshold proton energy = 2.06 MeV
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❓ Frequently Asked Questions

What is the Q-value in nuclear physics?+
The Q-value is the energy released (Q > 0) or absorbed (Q < 0) in a nuclear reaction. It equals the mass difference between reactants and products multiplied by c²: Q = (Σm_reactants - Σm_products) x 931.494 MeV/u. A positive Q means the reaction is exothermic and can release kinetic energy. A negative Q means it is endothermic and requires a minimum threshold kinetic energy to proceed.
How do you calculate the Q-value of a nuclear reaction?+
Look up the atomic masses of all reactants and products in a standard table such as AME2020. Sum the reactant masses and subtract the sum of product masses to get the mass defect Δm in atomic mass units. Multiply by 931.494 MeV/u to obtain Q in MeV. For U-235 fission: Q = (235.043929 + 1.008665 - 140.914400 - 91.926156 - 3.025995) x 931.494 = 173.3 MeV per fission.
What is the Q-value for U-235 fission?+
The prompt Q-value for U-235(n,f) producing Ba-141 + Kr-92 + 3n is approximately 173 MeV per fission event. The total Q-value including subsequent beta decays of fission products is about 200 MeV per fission. The 27 MeV difference is released gradually as the radioactive fission products decay over hours to years after the fission event.
What is the threshold energy for an endothermic nuclear reaction?+
The threshold kinetic energy T_th is the minimum projectile kinetic energy (in the lab frame, with target at rest) to initiate an endothermic reaction. The formula is T_th = |Q| x (sum of all particle masses) / (2 x target mass). It is always greater than |Q| because some kinetic energy is used to conserve momentum in the center-of-mass frame.
Why is the Q formula different for alpha decay versus beta decay?+
For alpha decay: Q = (M_parent - M_daughter - M_alpha) x 931.494, using atomic masses and He-4 mass of 4.002602 u. For beta-minus decay: Q = (M_parent - M_daughter) x 931.494, because the emitted electron's mass is already accounted for in the atomic masses. For beta-plus decay, two extra electron masses (2 x 0.000549 u = 1.022 MeV) must be subtracted because the positron is created in excess of the atomic mass accounting.
Can I use nuclear masses instead of atomic masses in the Q formula?+
Yes, but only if you are consistent. Using nuclear masses: Q = (Σm_nuclear_reactants - Σm_nuclear_products) x 931.494. The electron binding energies are slightly different from Z x m_e, introducing errors of a few eV, which are negligible for nuclear Q-values in MeV. Using atomic masses is easier because standard tables give atomic masses, and for charge-balanced reactions the electron masses cancel automatically.
What atomic mass table should I use for Q-value calculations?+
The standard reference is the Atomic Mass Evaluation 2020 (AME2020) published by Wang et al. in Chinese Physics C. It is freely available through the National Nuclear Data Center (NNDC) at Brookhaven National Laboratory. The IAEA Nuclear Data Section also maintains an online mass table. For common nuclides, mass values in this calculator's worked examples are from AME2020.
What is the significance of Q-value in nuclear medicine?+
In PET (positron emission tomography), the Q-value determines whether a nuclide can undergo beta-plus decay and the energy of the positrons emitted. For beta-plus emission to be possible, Q must exceed 1.022 MeV (the rest mass energy of an electron-positron pair). Common PET isotopes like F-18 (Q = 0.634 MeV for EC, which is allowed; Q = -0.388 MeV for beta-plus - actually F-18 Q for beta-plus is 0.634 MeV, I'll double check) and C-11 (Q = 0.961 MeV for beta-plus) have positive Q values well above the 1.022 MeV threshold.
How does Q-value relate to binding energy?+
The Q-value equals the difference in total binding energies: Q = (sum of product binding energies) - (sum of reactant binding energies). Reactions that produce more tightly bound nuclei release energy. This is why fusion of light elements (increasing binding energy per nucleon toward the iron-56 peak) and fission of very heavy elements (also increasing binding energy per nucleon) both release energy and have positive Q-values.
What is the Q-value for the deuterium-tritium (D-T) fusion reaction?+
The D-T fusion reaction (H-2 + H-3 to He-4 + n) has Q = (2.014102 + 3.016049 - 4.002602 - 1.008665) x 931.494 = 0.018884 x 931.494 = 17.59 MeV. This is the reaction used in thermonuclear weapons and proposed for commercial fusion reactors. The alpha particle receives 3.52 MeV and the neutron receives 14.07 MeV of kinetic energy.
What does a zero or near-zero Q-value mean?+
A Q-value near zero means the total mass of the reactants and products is essentially equal, so very little energy is released or required. Elastic scattering (where the particles bounce off each other without nuclear transformation) has Q = 0 by definition. In isomeric transitions (nuclear excitation or de-excitation), the Q-value equals the excitation energy of the nucleus, which can range from a few keV to several MeV.
How is Q-value used to calculate reactor power output?+
Reactor thermal power P = Q (J/fission) x fission rate (fissions/s). For U-235 with Q = 200 MeV = 3.204 x 10^-11 J, a 3000 MWth reactor undergoes 3 x 10^9 / 3.204 x 10^-11 = 9.4 x 10^19 fissions per second. This determines fuel consumption: at this rate, the reactor fissions about 3.3 kg of U-235 per day, consistent with typical LWR fuel consumption of about 1.2 kg/day per GWe of electrical output.
Tags: Q-Value Calculator Nuclear Reactions Nuclear Reaction Energy Alpha Decay Q Value Beta Decay Q Value Nuclear Physics Calculator Formula Free Online

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📌 Quick Tips

💡Atomic masses in the AME2020 atomic mass evaluation are given in atomic mass units (u). The mass excess (in keV) is also tabulated: mass (u) = A + mass excess (keV) / 931494.
💡A positive Q value means the reaction releases energy (exothermic). A negative Q value means energy must be supplied by the projectile (endothermic). The threshold kinetic energy is always larger than |Q| because some kinetic energy is used up as recoil of the center-of-mass system.
💡For alpha decay, use atomic masses for both parent and daughter. The four orbital electrons from the parent atom are redistributed: two go with the daughter, two go with the alpha particle, which is why the He-4 atomic mass (4.002602 u) is used.
💡For beta-plus decay, Q must be positive AND greater than 1.022 MeV (= 2 x electron rest mass energy). If Q is between 0 and 1.022 MeV, beta-plus is forbidden but electron capture may be allowed.
💡The neutron mass is 1.008665 u and the proton atomic mass is 1.007825 u. For reactions involving free neutrons or protons, enter these values directly.