Protons, Neutrons and Electrons Calculator

How to find protons, neutrons and electrons

The number of protons is the atomic number Z, the number of neutrons is the mass number minus the atomic number, and the number of electrons is the atomic number minus the charge: p = Z, n = A − Z and e = Z − q. The atomic number comes from the element, the mass number from the isotope, and the charge from the ion, so a chlorine-37 chloride ion, ³⁷Cl⁻, has 17 protons, 20 neutrons and 18 electrons.

Those three are definitions, not measurements. The atomic number is the number of protons in the nucleus, and it is what makes an atom chlorine rather than argon. The mass number is the number of protons and neutrons together, the nucleons, and differs from one isotope of an element to the next. A charge is the protons minus the electrons, so a positive ion has lost electrons and a negative ion has gained them, while its nucleus is unchanged.

How to use the calculator

Type the isotope or ion the way a textbook writes it. Cl-37 or chlorine-37 is hyphen notation, with the mass number after the name; ³⁷Cl or 37Cl puts it before the symbol; and a charge goes last, as Fe3+, Fe³⁺, O2− or Cl-. Both together read as ³⁷Cl⁻ or Cl-37-. The result gives the three counts, the mass number, atomic number and charge, the full nuclide symbol, and the working with your numbers.

Leave out the mass number and the calculator uses the element’s most abundant natural isotope, from NIST’s isotopic compositions, and says which one it used. To work the other way, choose From particle counts and type the protons, neutrons and electrons: it names the element, gives the mass number and charge, and writes the symbol.

Worked example: the chloride ion ³⁷Cl⁻

Chlorine is element 17, so p = Z = 17. The mass number is 37, so n = A − Z = 37 − 17 = 20. The charge is 1−, one electron more than the protons, so e = Z − q = 17 − (−1) = 18. The answer is 17 protons, 20 neutrons and 18 electrons, the same number of electrons as an argon atom.

Worked example: Fe³⁺ with no mass number

Iron is element 26, and the ion has lost three electrons, so e = 26 − 3 = 23. The symbol names no isotope, so the neutrons need one: the calculator takes iron-56, 91.754 percent of natural iron atoms in NIST’s representative composition, and gives n = 56 − 26 = 30. The answer is 26 protons, 30 neutrons and 23 electrons, written ⁵⁶₂₆Fe³⁺. For an iron-54 ion type Fe-54 3+, and only the neutrons change, to 28.

Worked example: from particle counts

A particle with 8 protons, 10 neutrons and 10 electrons is oxygen, because every atom with 8 protons is. Its mass number is A = 8 + 10 = 18 and its charge is q = 8 − 10 = −2, so it is the oxide ion of oxygen-18, ¹⁸₈O²⁻.

Why the atomic weight does not give the neutrons

Neutrons belong to a mass number, and an atomic weight is not one. It is the average mass of an element’s atoms in a natural sample, weighted by how common each isotope is, so it is rarely a whole number and it describes no single atom. Rounding it and subtracting Z is the commonest wrong method, and it can give a count no atom of the element has.

Chlorine’s atomic weight is 35.45, because natural chlorine is 75.76 percent chlorine-35 and 24.24 percent chlorine-37. Rounded to 35 it gives 35 − 17 = 18 neutrons, right for chlorine-35 and wrong for chlorine-37, which has 20. Copper’s 63.546 rounds to 64 and gives 35 neutrons, but natural copper is copper-63 and copper-65, with 34 and 36: no copper atom in a natural sample has 35. The calculator never rounds the atomic weight, and when the shortcut would have given a different answer it says so under the result.

The atomic weight is the right number for masses of ordinary samples, which is what the molar mass calculator uses it for. The periodic table gives it for every element, and each element’s own page, such as chlorine, gives the neutron count of its most abundant isotope beside it.

Reading isotope notation

In the full nuclide symbol the mass number is written at the top left, the atomic number at the bottom left and the charge at the top right, so ²³⁵₉₂U is uranium-235, with 92 protons and 235 − 92 = 143 neutrons, and ²³⁸₉₂U has 146. The atomic number is often left out, because the symbol already fixes it. Hyphen notation says the same with the name: carbon-14 has 6 protons and 8 neutrons, carbon-12 has 6 and 6.

Isotopes of one element have the same protons and electrons, and so almost the same chemistry, and differ only in their neutrons, which is where their stability can differ: carbon-12 is stable and carbon-14 is radioactive. The radioactive decay simulator follows an unstable nucleus as it decays, and the Rutherford scattering simulator shows the experiment that found the nucleus. For ions made of several atoms, such as sulfate, see the list of polyatomic ions.

What this does not cover

The calculator does not check that a nuclide exists. It knows the most abundant natural isotope of 84 elements and the mass number of one long-lived isotope for the rest, not the full chart of nuclides, so Cl-50 is counted like any other mass number of at least 17. It refuses only what cannot be: a mass number below the atomic number, a positive charge larger than the atomic number, which would remove more electrons than the atom has, and, as a guard against typing slips, a negative charge beyond 4− or a mass number above 300.

It counts particles and nothing else. The mass of an atom in atomic mass units is close to its mass number but, except for carbon-12, which defines the unit as exactly 12 u, not equal to it: a proton and a neutron each weigh a little more than 1 u, the electrons add a little, and binding the nucleus together takes some mass away. How the electrons are arranged in shells and subshells is a separate question, which the electron configuration calculator answers for any atom or ion. One atom or ion is counted here at a time.

Common mistakes

• Taking the neutrons from the rounded atomic weight. Use the mass number of the isotope in the question.
• Changing the protons when an atom becomes an ion. Only the electrons change: Na⁺ still has 11 protons.
• Getting the sign backwards. A positive charge means electrons lost, so fewer electrons than protons; a negative charge means electrons gained.
• Reading O-2 as the oxide ion. In hyphen notation the number is a mass number; for the ion write the number and then the sign, O2−.
• Swapping the mass number and the atomic number. The mass number is the larger, top-left figure in the nuclide symbol, and it is never smaller than the atomic number.