How to Calculate Protons and Neutrons in an Atom

This calculator finds the number of protons and neutrons in an atom or ion from its atomic number and mass number. Enter those two whole-number values to get the proton count and neutron count; the method works for isotopes and charged atoms alike.

Formula

Protons = atomic number, or p = Z. Neutrons = mass number − atomic number, or n = A − Z. Here, Z is the atomic number, a whole-number count of protons; A is the mass number, the whole-number total of protons and neutrons; p is the proton count; and n is the neutron count. The counts are particles, not masses.

The inputs must describe a possible nuclide: the mass number cannot be smaller than the atomic number. This calculator uses the values you supply; it does not look up an element or decide whether a particular isotope is stable.

Worked Example

For the default values, the atomic number is Z = 6 and the mass number is A = 12.

1. Protons: p = Z = 6. The atom has 6 protons.
2. Neutrons: n = A − Z = 12 − 6 = 6. The atom has 6 neutrons.

The calculator therefore returns 6 protons and 6 neutrons. These are the counts for carbon-12.

Assumptions

• The atomic number and mass number are entered correctly as whole numbers.
• The mass number refers to one isotope, not the element’s average atomic mass from a periodic table.
• The calculation counts particles in one nucleus; it does not calculate electrons or isotope abundance.

What You’ll Need

• The element’s atomic number, usually shown above or beside its symbol on a periodic table.
• The isotope’s mass number, provided in the isotope name or notation.

For example, in carbon-14, “14” is the mass number. In isotope notation, the mass number is the upper-left number and the atomic number is the lower-left number beside the element symbol. Use a periodic table to find the atomic number if it is not given.

Step-by-Step

1. Identify the isotope. Find its element symbol and mass number. The mass number is written as a whole number, as in oxygen-16 or uranium-238. Do not use the decimal atomic weight printed on many periodic tables as the mass number.
2. Look up the atomic number. Find the element on a periodic table. Its atomic number is the number of protons in every atom of that element. For instance, oxygen has atomic number 8, so every oxygen nucleus has 8 protons.
3. Enter both numbers. Put the atomic number in the Z field and the isotope’s mass number in the A field. Check that the values are whole numbers and that A is at least as large as Z.
4. Read the proton count. The calculator returns Z as the number of protons. This number identifies the element: changing the proton count means it is a different element.
5. Subtract to find neutrons. The calculator uses n = A − Z. For oxygen-16, for example, there are 16 − 8 = 8 neutrons.
6. Check the result. Add the two counts: protons + neutrons should equal the mass number. If it does not, review the isotope notation and the values entered.

You can do the same calculation without a calculator: write down A, subtract Z, and label the answer as neutrons. The calculator is useful for checking the subtraction and keeping proton and neutron counts distinct.

Common Mistakes

• Using average atomic mass instead of mass number. A periodic table may list chlorine’s atomic weight as about 35.45. That is an abundance-weighted average for naturally occurring chlorine, not the mass number of one chlorine atom. Chlorine-35 has mass number 35; chlorine-37 has mass number 37.
• Mixing up atomic number and mass number. Atomic number is protons only. Mass number is protons plus neutrons. Subtract the atomic number from the mass number, not the other way around.
• Assuming a charge changes the nucleus. A plus or minus charge usually reflects a change in electrons. It does not change the proton count or neutron count. Use the element’s atomic number and isotope’s mass number even for an ion.
• Rounding a decimal atomic weight. Rounding a periodic-table average to the nearest whole number may suggest a likely isotope in some cases, but it does not reliably identify the isotope. Use the isotope’s stated mass number instead.
• Reporting mass rather than count. The answer is a number of protons or neutrons, not grams, atomic mass units, or a decimal mass.

Tips

• Use the hyphen form of an isotope name as a quick guide: the number after the hyphen is A.
• Remember the short checks: protons = Z; protons + neutrons = A.
• If you know the element but not its isotope, you can determine its proton count from the periodic table, but you cannot determine its exact neutron count without the mass number.
• When a worksheet gives isotope notation, read the upper-left superscript as A and the lower-left subscript as Z. The element symbol itself also identifies Z.

Troubleshooting

The calculator says the values are invalid: confirm both inputs are whole numbers and that the mass number is not less than the atomic number. A nucleus cannot contain fewer total protons and neutrons than its protons alone.

The neutron count is unexpectedly large or negative: check that you did not swap A and Z. The mass number is normally the larger value; subtract Z from A.

You have only a periodic-table decimal: that value is generally an average atomic weight. Find the isotope name or notation in the question or reference material before calculating neutrons. If no isotope is specified, the exact neutron count cannot be determined from the average alone.

You have an ion such as O²⁻: the charge concerns electrons. Keep the same proton calculation, and use the mass number if you also need the neutron count.

Frequently Asked Questions

How do you calculate the number of protons?
Use the element’s atomic number. An element with atomic number 11 has 11 protons.

How do you calculate the number of neutrons?
Subtract the atomic number from the isotope’s mass number: neutrons = A − Z.

What is the difference between mass number and atomic mass?
Mass number is a whole-number count of protons and neutrons in one isotope. Atomic mass on a periodic table is usually a decimal average across naturally occurring isotopes.

Do ions have different numbers of protons or neutrons?
Not just because of their charge. Ions gain or lose electrons; their proton and neutron counts remain those of the same isotope.

Can I find neutrons if I only know the element?
Not exactly. The element tells you its proton count, but different isotopes of that element have different neutron counts. You need the isotope’s mass number.

Can the neutron count be zero?
Yes. Ordinary hydrogen-1 has one proton and no neutrons: A = 1, Z = 1, so n = 0.

Related

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

in z | Atomic number (Z) | - | 6 | 1
in a | Mass number (A) | - | 12 | 1
out p | Protons | particles | z | 0
out n | Neutrons | particles | a - z | 0