Atomic Mass Calculator
This calculator works in two modes. In the proton-neutron mode, enter the number of protons (atomic number Z) and neutrons (N) to get the mass number and approximate atomic mass of any nuclide. In the average atomic mass mode, enter up to five isotopes with their fractional abundances to compute the weighted average atomic mass that appears on the periodic table. Results are shown in atomic mass units (u/Da) and in kilograms.
Formula
Worked example
Carbon-12: Z = 6, N = 6, so A = 12. The mass defect from free nucleon masses is (6 x 1.007276 + 6 x 1.008665 + 6 x 0.000549) - 12 = 0.098940 u, equivalent to ~92 MeV of nuclear binding energy. For the average atomic mass of chlorine: Cl-35 (34.969 u, 75.76%) and Cl-37 (36.966 u, 24.24%) give 0.7576 x 34.969 + 0.2424 x 36.966 = 26.503 + 8.960 = 35.45 u.
What is atomic mass?
Atomic mass is the mass of a single atom measured in atomic mass units (u), also called daltons (Da). One atomic mass unit is defined as exactly 1/12 the mass of an unbound carbon-12 atom in its nuclear and electronic ground state, which equals approximately 1.66054 x 10^-27 kg. Atomic mass is not the same as atomic number (Z), which merely counts protons, or mass number (A), which counts protons plus neutrons. The true atomic mass of any nuclide is slightly less than its mass number because nuclear binding energy removes a tiny fraction of the free-particle mass - a phenomenon called the mass defect.
Mass number, mass defect, and binding energy
The mass number A = Z + N is the integer count of nucleons and serves as the superscript in isotope notation (e.g. C-12, U-238). Real atomic masses deviate from A by the mass defect: the difference between the sum of free proton and neutron masses and the actual nuclear mass. This missing mass has been converted into nuclear binding energy via E = mc^2. Iron-56 has the highest binding energy per nucleon among all nuclides (~8.8 MeV), which is why stellar nucleosynthesis stalls there. Hydrogen-1 has no neutrons and its atomic mass is essentially 1.00794 u, very close to 1 u but not exactly.
Average atomic mass and the periodic table
Most elements exist as a mixture of stable isotopes in nature. The number shown on the periodic table is the standard atomic weight: a weighted average of all naturally occurring isotope masses, using their terrestrial abundance as weights. Chlorine, for example, is 75.76% Cl-35 (34.969 u) and 24.24% Cl-37 (36.966 u), giving a standard atomic weight of 35.45 u. IUPAC periodically revises these values as measurement precision improves. Twenty elements are monoisotopic in nature (only one stable isotope), so their standard atomic weight equals the exact mass of that isotope.
How to use the two calculator modes
In nuclide mode, enter the atomic number Z (number of protons, which identifies the element) and the neutron count N. The calculator returns the mass number A = Z + N, the approximate atomic mass in u (equal to A for most practical purposes), the SI mass in kilograms, and the mass defect from free-particle masses. In average atomic mass mode, enter the exact mass and natural abundance for each isotope you want to include. The calculator computes the weighted sum and flags whether your abundances add up to 100%. Up to five isotopes are supported, covering elements like tin (which has 10 stable isotopes) when grouped by pairs.
Standard atomic weights of common elements
| Symbol | Element | Atomic number (Z) | Standard atomic weight (u) |
|---|---|---|---|
| H | Hydrogen | 1 | 1.008 |
| He | Helium | 2 | 4.003 |
| Li | Lithium | 3 | 6.941 |
| Be | Beryllium | 4 | 9.012 |
| B | Boron | 5 | 10.81 |
| C | Carbon | 6 | 12.011 |
| N | Nitrogen | 7 | 14.007 |
| O | Oxygen | 8 | 15.999 |
| F | Fluorine | 9 | 18.998 |
| Ne | Neon | 10 | 20.18 |
| Na | Sodium | 11 | 22.99 |
| Mg | Magnesium | 12 | 24.305 |
| Al | Aluminum | 13 | 26.982 |
| Si | Silicon | 14 | 28.086 |
| P | Phosphorus | 15 | 30.974 |
| S | Sulfur | 16 | 32.06 |
| Cl | Chlorine | 17 | 35.45 |
| Ar | Argon | 18 | 39.948 |
| K | Potassium | 19 | 39.098 |
| Ca | Calcium | 20 | 40.078 |
| Fe | Iron | 26 | 55.845 |
| Cu | Copper | 29 | 63.546 |
| Zn | Zinc | 30 | 65.38 |
| Br | Bromine | 35 | 79.904 |
| Ag | Silver | 47 | 107.868 |
| Sn | Tin | 50 | 118.71 |
| I | Iodine | 53 | 126.904 |
| Au | Gold | 79 | 196.967 |
| Pb | Lead | 82 | 207.2 |
| U | Uranium | 92 | 238.029 |
IUPAC 2021 standard atomic weights. Values in atomic mass units (u = Da). Monoisotopic elements marked with (***).
Frequently asked questions
What is the difference between atomic mass and atomic number?
Atomic number (Z) is simply the number of protons in the nucleus and identifies the element. Atomic mass is the total mass of one atom measured in atomic mass units and depends on both proton and neutron counts. Carbon always has Z = 6, but C-12 has mass 12 u (6 neutrons) while C-14 has mass 14 u (8 neutrons).
Why is 1 atomic mass unit defined relative to carbon-12?
By international agreement (IUPAC/BIPM), 1 u is defined as 1/12 of the mass of a free carbon-12 atom at rest in its ground state. Carbon-12 was chosen in 1961 to replace two conflicting earlier standards (one based on oxygen-16, one on natural oxygen) because carbon compounds are easy to handle, and a 1/12 fraction gives hydrogen a mass very close to 1 u, keeping chemical calculations intuitive.
What is the mass defect and why does it matter?
The mass defect is the difference between the sum of the individual free-nucleon masses and the actual measured mass of the nucleus. That "missing" mass has been converted into nuclear binding energy (E = mc^2). The larger the mass defect per nucleon, the more tightly bound the nucleus. For carbon-12 the mass defect is about 0.099 u, corresponding to roughly 92 MeV of binding energy.
What is a dalton and is it the same as an atomic mass unit?
Yes. The dalton (Da) and the atomic mass unit (u) are the same unit. "Dalton" is the preferred name in biochemistry and molecular biology (where protein masses are often given in kilodaltons, kDa), while "u" is more common in physics and nuclear chemistry.
How do I calculate the average atomic mass if I only know percentages?
Divide each percentage by 100 to get the fractional abundance, multiply each fraction by the corresponding isotope mass, then add the products. The result is the weighted average atomic mass. This calculator does that automatically: enter percentages directly and it converts them internally.
Why do the periodic table values for atomic mass have so many decimals?
The values are weighted averages of isotope masses measured to very high precision by mass spectrometry. Because natural abundances and isotope masses are both known with many significant figures, the result inherits those digits. IUPAC now recommends expressing standard atomic weights as intervals (e.g. carbon is [12.0096, 12.0116]) to reflect natural variation in terrestrial samples.