Calculate Protons, Neutrons, and Electrons in an Atom

Calculate an atom’s protons, neutrons, and electrons from its atomic number, mass number, and charge. Enter those three values to get the particle counts; the calculator uses the mass number as a whole-number count of protons plus neutrons.

Formula

The formulas are: protons = Z; neutrons = A − Z; electrons = Z − q. Here, Z is the atomic number, A is the mass number, and q is the atom’s signed charge in units of the elementary charge. All three outputs are whole-number particle counts. A positive q means the atom has lost electrons; a negative q means it has gained electrons. For a neutral atom, q = 0, so the electron count equals the proton count.

The atomic number is a count, not a mass. The mass number is also a count: it adds the protons and neutrons in one nucleus. The charge records the net imbalance between positive protons and negative electrons. For example, a charge of +2 means two fewer electrons than protons; a charge of −1 means one more electron than protons.

Worked Example

With the default values Z = 6, A = 12, and q = 0:

• Protons = Z = 6.
• Neutrons = A − Z = 12 − 6 = 6.
• Electrons = Z − q = 6 − 0 = 6.

The calculator therefore returns 6 protons, 6 neutrons, and 6 electrons. This is a neutral carbon-12 atom.

Assumptions

• Atomic number and mass number are supplied as whole-number counts.
• Charge is in elementary-charge units: for example, +1 or −2.
• The result describes a single atom or ion, not a bulk sample or a molecule’s total particle count.

What the Three Numbers Mean

Protons and neutrons make up the nucleus, while electrons occupy regions around it. Protons carry positive electric charge, neutrons have no net electric charge, and electrons carry negative charge. The number of protons determines the element: every carbon atom has six protons, whereas every oxygen atom has eight. Changing the number of neutrons makes a different isotope of the same element; changing the number of electrons makes an ion.

These distinctions are useful because the counts answer different questions. The atomic number identifies the element. The mass number identifies a particular isotope when combined with the element symbol. The charge distinguishes a neutral atom from an ion. A notation such as ¹²C represents carbon-12: carbon gives Z = 6, and the superscript 12 gives A = 12.

How to Use the Calculator

1. Enter the atomic number Z, which is the element’s number of protons.
2. Enter the isotope’s mass number A, a whole number equal to protons plus neutrons.
3. Enter the signed charge q. Use zero for a neutral atom, a positive number for a cation, and a negative number for an anion.
4. Read the three calculated counts. Check that A is at least Z and that the electron count is not negative.

For a neutral sodium-23 atom, Z = 11, A = 23, and q = 0. It has 11 protons, 12 neutrons, and 11 electrons. For a sodium ion with a +1 charge, the proton and neutron counts stay the same, but it has 10 electrons. The nucleus has not changed simply because an electron was removed.

Isotopes, Ions, and Common Mistakes

Isotopes share the same atomic number but have different mass numbers. Carbon-12 and carbon-14 each have six protons. Carbon-12 has 12 − 6 = 6 neutrons; carbon-14 has 14 − 6 = 8. Both are carbon because the proton count remains six. An isotope’s mass number is not its atomic mass in atomic mass units: it is the integer count of nucleons in that isotope’s nucleus.

A frequent error is using the element’s decimal atomic weight from a periodic table as A. The listed atomic weight is generally a weighted average across naturally occurring isotopes and is not the mass number of a particular atom. To calculate neutrons, use an isotope’s stated whole-number mass number. If only an element name is given, the neutron count cannot be uniquely determined without specifying an isotope.

Another common mistake is reversing the charge sign. A positive ion has fewer electrons than protons, so subtract a positive q from Z. A negative ion has extra electrons: for example, a −1 charge gives Z − (−1), or Z + 1, electrons. Do not subtract the absolute size of a negative charge.

These formulas describe ordinary atoms and ions, whose proton and electron counts are whole numbers. If the inputs produce a negative number of neutrons, the values are inconsistent: a nucleus cannot have a mass number smaller than its proton count. Likewise, an electron count below zero signals an invalid combination of atomic number and charge. The calculator does not determine whether a particular isotope is stable or naturally occurring.

Frequently Asked Questions

How do I find the number of protons?
The number of protons equals the atomic number Z. Find the element on the periodic table or use the atomic number given in the isotope notation.

How do I calculate neutrons?
Subtract the atomic number from the mass number: neutrons = A − Z. You need a specific isotope’s mass number; a decimal atomic weight is not a substitute.

How do I calculate electrons in an ion?
Use electrons = Z − q, with the charge written as a signed number. A +2 ion has two fewer electrons than protons; a −1 ion has one extra electron.

Does changing the number of electrons change the element?
No. The element is defined by its proton count. Changing electrons changes the atom’s charge, while changing neutrons changes its isotope.

Can I calculate neutrons from the periodic-table atomic weight?
Not exactly for a particular atom. Atomic weight is typically an isotope-weighted average; use the isotope’s whole-number mass number to calculate its neutron count.

Related

• Molecules to Moles Calculator: Divide by the Avogadro Constant
• Mass to Mole Calculator: Grams to Moles From the Molar Mass
• Moles to Grams Calculator: Mass of a Compound From Moles

in z | Atomic number (Z) | - | 6 | 0
in a | Mass number (A) | - | 12 | 1
in q | Atomic charge | elementary charge units | 0 | -
out p | Number of protons | particles | z | 0
out n | Number of neutrons | particles | a - z | 0
out e | Number of electrons | particles | z - q | 0