Neutrons Calculated: Formula, Examples, and Isotopes

To calculate the number of neutrons in an atom, subtract its atomic number (the number of protons) from its mass number: neutrons = mass number − atomic number. Enter those two whole-number values in the calculator below; it returns the neutron count for one atom or isotope.

Formula

N = A − Z, where N is the number of neutrons in one nucleus (a count, with no unit), A is the mass number (the total number of protons and neutrons, a whole-number count), and Z is the atomic number (the number of protons, also a whole-number count). The expression includes a validity check: the mass number cannot be smaller than the atomic number, because a nucleus cannot contain a negative number of neutrons.

Worked Example

For the calculator’s default values, A = 23 and Z = 11:

1. Write the relation: N = A − Z.
2. Substitute the values: N = 23 − 11.
3. Subtract: N = 12 neutrons per nucleus.

Assumptions

• The inputs describe one nuclide, meaning a specific isotope of an element.
• Mass number and atomic number are exact whole-number counts, not measured masses in grams or atomic mass units.
• The result counts neutrons in the nucleus; it does not include electrons or describe the number of atoms in a sample.

What the Numbers Mean

Atoms are identified by the particles in their nuclei. The atomic number, conventionally written Z, fixes the element: every atom with 11 protons is sodium, and every atom with 6 protons is carbon. Changing the neutron count does not change the element, but it makes a different isotope of that element.

The mass number, written A, is the total number of nuclear protons and neutrons. Thus, A = Z + N, and rearranging gives the calculator’s subtraction formula. Sodium-23, for example, has atomic number 11 and mass number 23, so its nucleus has 23 − 11 = 12 neutrons. The notation sodium-23 names the element and its mass number; it does not mean the atom weighs exactly 23 grams or 23 atomic mass units.

The calculation is simple because both quantities are counts. No conversion factor, periodic-table average, or neutron mass is needed. The challenging part is often identifying the correct mass number for the isotope being asked about.

How to Find the Inputs

• Find the atomic number. Look up the element on a periodic table. It is the whole number that identifies the element and equals its proton count.
• Find the mass number. Use the isotope name or notation, such as carbon-14 or ¹⁴C. The number 14 is the mass number.
• Subtract the atomic number from the mass number. The difference is the number of neutrons in each nucleus of that isotope.

For isotope notation written ^A_ZX, the upper-left number is the mass number, the lower-left number is the atomic number, and X is the element symbol. Some formats show only the element name and mass number, such as uranium-235; the periodic table supplies uranium’s atomic number, 92. Therefore uranium-235 has 235 − 92 = 143 neutrons.

Worked Isotope Examples

These examples show how the same rule applies across elements:

• Carbon-12: carbon has atomic number 6, so 12 − 6 = 6 neutrons.
• Carbon-14: 14 − 6 = 8 neutrons. Carbon-12 and carbon-14 are both carbon because each has six protons; they differ in neutron count.
• Chlorine-37: chlorine has atomic number 17, so 37 − 17 = 20 neutrons.
• Hydrogen-1: hydrogen has atomic number 1, so 1 − 1 = 0 neutrons. Its nucleus is a single proton.

For a neutral atom, the electron count equals the proton count, but electrons do not enter this calculation. For an ion, the number of electrons can differ from the proton count; the neutron calculation remains mass number minus atomic number.

Mass Number Versus Atomic Mass

A common source of mistakes is using an element’s average atomic mass from a periodic table as the mass number. They are different quantities. The mass number is a whole-number count for one isotope. The periodic-table atomic mass is generally a weighted average reflecting the naturally occurring isotopes of an element, and it is commonly shown as a decimal.

For instance, chlorine’s periodic-table atomic mass is about 35.45, while common chlorine isotopes have mass numbers 35 and 37. Subtracting 17 from 35.45 would produce 18.45, which cannot be the neutron count of a single nucleus. Chlorine-35 has 18 neutrons; chlorine-37 has 20. An average atomic mass can help describe a natural sample, but it does not identify the neutron count of an individual isotope.

Likewise, “mass number” is not a laboratory measurement of an atom’s mass. The actual mass of a nucleus is not simply an integer number of atomic mass units because nuclear binding energy affects the total mass. That detail does not change the counting rule: use the isotope’s stated mass number and the element’s atomic number.

Common Errors and Limits

• Subtracting in the wrong order: use mass number minus atomic number, not the reverse.
• Using the decimal atomic mass: identify a particular isotope and use its mass number.
• Counting electrons: electrons affect charge, not the neutron count. An ion still uses the same two nuclear numbers.
• Assuming every atom of an element has the same neutron count: isotopes of one element have the same number of protons but different numbers of neutrons.

If the entered mass number is below the atomic number, the inputs do not describe a physically possible nuclide, so the calculator reports that it cannot compute the result. A nonnegative answer alone does not establish that a proposed isotope is stable or commonly found; nuclear stability is a separate question that requires isotope data. The arithmetic calculates a count once a valid isotope has been specified, rather than predicting which isotopes exist.

Frequently Asked Questions

How do you calculate neutrons from the periodic table?
Take the isotope’s mass number and subtract the element’s atomic number from the periodic table. The periodic table’s decimal atomic mass is not a substitute for an isotope’s mass number.

How many neutrons does carbon-14 have?
Carbon’s atomic number is 6. Carbon-14 therefore has 14 − 6 = 8 neutrons.

Can an atom have zero neutrons?
Yes. The most common hydrogen isotope, hydrogen-1, has one proton and no neutrons, so its mass number and atomic number are both 1.

Do ions have a different number of neutrons?
Not when only the atom becomes charged. Gaining or losing electrons changes the electron count, while the nucleus—and therefore its neutron count—remains unchanged.

Can you find neutrons without knowing the isotope?
Not usually. An element’s atomic number gives its proton count, but different isotopes of that element can have different neutron counts. You need the mass number of the isotope as well.

Related

• Moles Calculation: Formula and Worked Example
• How to Calculate Moles in Chemistry
• Standard Free Energy: Formula and Calculation

in a | Mass number | - | 23 | 0
in z | Atomic number (protons) | - | 11 | 0
out n | Neutrons | particles | a - z | 0