Mass Number
The mass number is the total count of protons and neutrons in the nucleus of one atom; it is a whole number specific to each isotope.
Formula
A = Z + N
Definition
The mass number is the number of protons plus the number of neutrons in one atom, always a whole number. Written $A$, it satisfies $A = Z + N$ and appears after the element name (carbon-14) or as a superscript before the symbol ($^{14}C$); different isotopes of an element have different mass numbers. Because $A$ counts nucleons in a specific nuclide, it is conserved in every nuclear reaction, and full nuclide notation $^{A}_{Z}X$ places $A$ above $Z$ before the symbol. The actual mass of a nuclide in atomic mass units is close to $A$ but not equal to it, because nuclear binding energy converts a little mass to energy.
Example
A carbon atom with $6$ protons and $6$ neutrons has a mass number of $12$, hence carbon-12. Chlorine-35 has $17$ protons and $18$ neutrons ($A = 35$) and chlorine-37 has $20$ neutrons ($A = 37$). Uranium-235 is $^{235}_{92}U$, with $N = 235 - 92 = 143$ neutrons and a measured atomic mass of $235.044\text{ amu}$, slightly off from $235$ because of the mass defect.
Key Insight
Electrons are so light that they do not count toward the mass number; only the nucleus matters. Mass number is a count for one atom, while the atomic mass on the periodic table is an average across isotopes, which is why it has decimals. Balancing a nuclear equation means making both $A$ and $Z$ add up on each side: in $^{235}_{92}U + ^{1}_{0}n \rightarrow ^{141}_{56}Ba + ^{92}_{36}Kr + 3\,^{1}_{0}n$, the mass numbers sum to $236$ on both sides.