Every atom is built from three kinds of particles. Protons and neutrons sit in the tiny nucleus, electrons fill the space around it. The number of protons, called the atomic number Z, decides which element you have: six protons is always carbon, 26 is always iron. The mass number A counts protons and neutrons together, and the charge q is the difference between protons and electrons.
That gives three simple relationships – N = A − Z, e = Z − q and A = Z + N – so any three of the six quantities determine the other three. Atoms of one element with different neutron numbers are isotopes (carbon-12 and carbon-14), and atoms that have gained or lost electrons are ions: anions carry a negative charge, cations a positive one.
Pick how you want to describe the particle, and the calculator returns the full set of numbers, the nuclide symbol such as ⁵⁶Fe³⁺, the ground-state electron configuration of that atom or ion, the neutron-to-proton ratio and the approximate mass from the masses of the free particles.
How to use the Atom Calculator
- I know
- Element (symbol, name or Z) — Type a symbol (Fe), a name (iron) or an atomic number (26).
- Mass number (A)
- Charge (q) — Use a negative number for anions, e.g. −2 for S²⁻.
- Number of protons (p)
- Number of neutrons (N)
- Number of electrons (e)
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
Choose an input mode, enter the element (or the proton count) with the other two values, and the calculator applies N = A − Z and e = Z − q. The element is looked up from the atomic number, the ion’s electron configuration is built by removing electrons from the outermost shell first (or adding them for anions), and the particle mass is the sum of the proton, neutron and electron masses (CODATA 2018), ignoring nuclear binding energy.
Worked example
What is inside the ion ⁵⁶Fe³⁺? Iron has atomic number Z = 26, so it has 26 protons. Neutrons: N = A − Z = 56 − 26 = 30. Electrons: e = Z − q = 26 − 3 = 23. The neutral iron atom is [Ar] 3d⁶ 4s²; removing three electrons (first the two 4s, then one 3d) gives [Ar] 3d⁵. The free particles weigh 26 × 1.007276 + 30 × 1.008665 + 23 × 0.000549 ≈ 56.4618 u – about 0.53 u more than a real ⁵⁶Fe nucleus with its electrons, because the binding energy of the nucleus is released as mass.
Second example: an ion with 16 protons, 16 neutrons and 18 electrons is sulfur (Z = 16), A = 32 and q = 16 − 18 = −2, so it is the sulfide ion ³²S²⁻ with the argon configuration [Ne] 3s² 3p⁶.
The three particles
| Particle | Charge | Mass (u) | Where it is |
|---|---|---|---|
| Proton | +1 | 1.007276 | Nucleus |
| Neutron | 0 | 1.008665 | Nucleus |
| Electron | −1 | 0.000549 (1/1836 of a proton) | Orbitals around the nucleus |
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).
Formula
Protons p = Z · Neutrons N = A − Z · Electrons e = Z − qZ = p · A = p + N · q = p − eWorked example
Inputs — I know: Element, mass number and charge; Element (symbol, name or Z): Fe; Mass number (A): 56; Charge (q): 3.
Results — Nuclide / ion symbol = ⁵⁶Fe³⁺ · iron-56 ion; Element = Iron (Fe); Protons = 26; Neutrons = 30; Electrons = 23; Atomic number (Z) = 26.
Key terms
- Atomic number (Z)
- The number of protons in the nucleus; it identifies the element.
- Mass number (A)
- The total number of protons and neutrons (nucleons) in the nucleus.
- Isotope
- Atoms of the same element with different numbers of neutrons, such as ¹²C and ¹⁴C.
- Ion
- An atom or group of atoms with unequal numbers of protons and electrons; cations are positive, anions negative.
- Nuclide symbol
- Notation such as ⁵⁶Fe³⁺, with the mass number at the top left and the charge at the top right.
Frequently asked questions
How do I find the number of neutrons?
Subtract the atomic number from the mass number: N = A − Z. Iron-56 has 56 − 26 = 30 neutrons, and chlorine-37 has 37 − 17 = 20.
How do I find the number of electrons in an ion?
Subtract the charge from the atomic number: e = Z − q. Fe³⁺ has 26 − 3 = 23 electrons; S²⁻ has 16 − (−2) = 18 electrons.
What decides which element an atom is?
Only the number of protons. Change the neutrons and you get another isotope of the same element; change the electrons and you get an ion of the same element.
Is the mass number the same as the atomic mass?
No. The mass number is a whole count of protons plus neutrons (56 for iron-56); the atomic mass is the real mass in daltons (55.9349 u for iron-56) and the standard atomic weight averages all natural isotopes (55.845 for iron).
Why does a cation have fewer electrons?
A positive charge means protons outnumber electrons. Na⁺ has 11 protons but only 10 electrons, the same number as neon.
Can the number of neutrons be zero?
Yes – ordinary hydrogen (¹H, protium) is a single proton with no neutron. It is the only stable nuclide without neutrons.
What does the neutron-to-proton ratio tell me?
Light stable nuclei have N/Z close to 1 (¹²C, ¹⁶O, ⁴⁰Ca), while heavy ones need more neutrons – about 1.5 for lead-208. Nuclides far from this band are radioactive.
What formula does the Atom Calculator use?
Protons p = Z · Neutrons N = A − Z · Electrons e = Z − q.