# Atomic Mass Calculator URL: https://speedycalculator.com/calculators/chemistry/atomic-mass/ Last updated: 2026-10-30 > The atomic mass calculator estimates the mass of a single atom from its numbers of protons and neutrons. It gives the mass number, the quick “mass number in daltons” approximation and a better estimate that subtracts the nuclear binding energy, in u, kg, g or MeV/c². ## Inputs - Number of protons (Z) — The atomic number – 26 for iron. - Number of neutrons (N) — Mass number minus atomic number. ## Results - Estimated atomic mass (with binding energy) - Element - Mass number (A = Z + N) - Quick estimate (A × 1 u) - Sum of free hydrogen atoms and neutrons - Nuclear binding energy (estimate) - Binding energy per nucleon - Mass defect - Mass defect as a share of the free mass ## Formula ``` A = Z + N · m ≈ A u (quick estimate) m = Z·m(¹H) + N·mₙ − B/c² · B = aᵥA − aₛA^(2/3) − a_c·Z(Z−1)/A^(1/3) − a_a(A − 2Z)²/A ± δ ``` ## Explanation The mass of one atom is tiny – a carbon-12 atom weighs 1.993 × 10⁻²⁶ kg – so chemists measure it in unified atomic mass units (u, also called daltons, Da). One u is defined as one twelfth of the mass of a carbon-12 atom, 1.66054 × 10⁻²⁷ kg. On this scale protons and neutrons each weigh just over 1 u and an electron only 0.00055 u, which is why the mass number A = Z + N is already a good first guess for the atomic mass. The guess is not exact because a nucleus weighs less than its separate protons and neutrons. When nucleons bind together, energy is released, and by E = mc² that energy is missing from the mass. This mass defect is about 0.8–0.9% of the total for most nuclei – roughly 0.5 u for iron-56. This calculator gives all three numbers: the mass number, the sum of the free hydrogen atoms and neutrons, and a corrected atomic mass that subtracts the binding energy estimated with the semi-empirical (Weizsäcker) mass formula. For medium and heavy nuclei the estimate is usually within about 0.01 u of the measured value. ### How to use the Atomic Mass Calculator - **Number of protons (Z)** — The atomic number – 26 for iron. - **Number of neutrons (N)** — Mass number minus atomic number. Results update as you type, every field has its own unit menu, and everything is calculated in your browser. ### How it works Enter the number of protons Z and neutrons N. The calculator adds Z hydrogen-atom masses (which include the electrons) and N neutron masses, estimates the binding energy B from the volume, surface, Coulomb, asymmetry and pairing terms of the liquid-drop model, and subtracts B/931.494 MeV per u. Use the unit menu to show the result in kilograms, grams or MeV/c². ### Worked example Iron-56 has Z = 26 and N = 30, so A = 56 and the quick estimate is 56 u. The separate particles weigh 26 × 1.007825 + 30 × 1.008665 = 56.4634 u. The binding-energy terms (MeV) are: volume 15.8 × 56 = 884.80, surface −18.3 × 56^(2/3) = −267.87, Coulomb −0.714 × 26 × 25 / 56^(1/3) = −121.31, asymmetry −23.2 × (56 − 52)² / 56 = −6.63 and pairing (even–even) +12/√56 = +1.60, so B ≈ 490.6 MeV (measured: 492.3 MeV) or 8.76 MeV per nucleon. Dividing by 931.494 MeV/u gives a mass defect of 0.5267 u, and the atomic mass is 56.4634 − 0.5267 = **55.9367 u** – only 0.0018 u above the measured 55.9349 u. In kilograms that is 9.2885 × 10⁻²⁶ kg. ### Constants used QuantityValueMass of a hydrogen-1 atom1.00782503223 uNeutron mass1.00866491595 u1 u in kg1.66053906660 × 10⁻²⁷ kg1 u in energy931.49410242 MeV/c²Liquid-drop coefficients (MeV)aᵥ 15.8 · aₛ 18.3 · a_c 0.714 · a_a 23.2 · a_p 12.0 ### Tips - Type formulas with normal capitals and numbers, e.g. Ca(OH)2 or CuSO4·5H2O – brackets and hydrates work. - Atomic masses are IUPAC standard atomic weights; radioactive elements use the mass number of their longest-lived isotope. - Electronegativity values are on the Pauling scale. - Everything is calculated in your browser. ### Common mistakes to avoid - Writing CO (carbon monoxide) when you mean Co (cobalt) – capitals matter. - Forgetting to multiply the bracket contents by the subscript after the bracket. - Mixing up atomic number (protons) and mass number (protons + neutrons). ### Inputs explained FieldWhat to enterNumber of protons (Z)A number. The atomic number – 26 for iron.Number of neutrons (N)A number. Mass number minus atomic number. ### What each result means - **Mass number (A = Z + N)** = [Number of protons (Z)] + [Number of neutrons (N)] - **Quick estimate (A × 1 u)** = [Number of protons (Z)] + [Number of neutrons (N)] - **Sum of free hydrogen atoms and neutrons** = [Number of protons (Z)]×1.00782503223 + [Number of neutrons (N)]×1.00866491595 - **Binding energy per nucleon** = [Nuclear binding energy (estimate)]÷([Number of protons (Z)] + [Number of neutrons (N)]) - **Mass defect** = [Nuclear binding energy (estimate)]÷931.49410242 - **Mass defect as a share of the free mass** = [Nuclear binding energy (estimate)]÷931.49410242÷[Sum of free hydrogen atoms and neutrons]×100 ## Worked example Inputs — Number of protons (Z): 26; Number of neutrons (N): 30. Results — **Estimated atomic mass (with binding energy) = 55.936709 u (Da)**; Element = Iron (Fe); Mass number (A = Z + N) = 56; Quick estimate (A × 1 u) = 56 u (Da); Sum of free hydrogen atoms and neutrons = 56.463398 u (Da); Nuclear binding energy (estimate) = 490.61 MeV; Binding energy per nucleon = 8.761 MeV; Mass defect = 0.52669 u; Mass defect as a share of the free mass = 0.933 %. ## Key terms - **Unified atomic mass unit (u, Da)**: One twelfth of the mass of a carbon-12 atom, 1.66054 × 10⁻²⁷ kg. - **Mass defect**: The difference between the mass of the separate nucleons and the mass of the nucleus, Δm = B/c². - **Binding energy**: The energy needed to pull a nucleus apart into free protons and neutrons. - **Semi-empirical mass formula**: The liquid-drop model of the nucleus (Weizsäcker, 1935) that estimates binding energy from five terms. ## FAQ **What is the atomic mass of carbon-12?** Exactly 12 u by definition – the dalton is one twelfth of a carbon-12 atom. Its 6 protons, 6 neutrons and 6 electrons weigh 12.0989 u when separate; the 0.0989 u difference is the binding energy (92.2 MeV). **How do I calculate atomic mass from protons and neutrons?** A quick answer is the mass number in daltons: Z + N. Iron with 26 protons and 30 neutrons is about 56 u. The measured value is 55.9349 u; this calculator's binding-energy estimate gives 55.9367 u. **Why is atomic mass not a whole number?** Protons and neutrons each weigh slightly more than 1 u, electrons add a little, and the binding energy removes some mass. Only carbon-12 is exactly whole by definition. **What is the difference between atomic mass and atomic weight?** Atomic mass belongs to one isotope (chlorine-35: 34.969 u). The standard atomic weight on the periodic table averages all natural isotopes by abundance (chlorine: 35.45). **How much does one atomic mass unit weigh?** 1 u = 1.66053906660 × 10⁻²⁷ kg, which is also 931.494 MeV/c² of energy. **How accurate is the semi-empirical estimate?** For nuclei heavier than about oxygen it is usually within 0.01 u (a few MeV of binding energy). For very light nuclei such as ²H, ³He or ⁴He it is poor, because the liquid-drop model assumes a large nucleus. **Which nucleus has the most binding energy per nucleon?** Nickel-62, with about 8.79 MeV per nucleon, closely followed by iron-58 and iron-56. That peak is why fusion releases energy below iron and fission above it. **What formula does the Atomic Mass Calculator use?** A = Z + N · m ≈ A u (quick estimate). ## Sources - [NIST – Fundamental physical constants (CODATA)](https://physics.nist.gov/cuu/Constants/) - [IUPAC Compendium of Chemical Terminology (Gold Book)](https://goldbook.iupac.org/) - [OpenStax – Chemistry 2e](https://openstax.org/details/books/chemistry-2e)