Molecular Weight Calculator (Molar Mass)

Atomic weight, molecular weight, and molar mass are fundamental concepts in chemistry. These measurements are essential for calculating the quantities of substances involved in chemical reactions, determining concentrations, analyzing molecular properties, and many other situations. To understand much of the content below, it is helpful to first be familiar with the following definitions.

Term Definitions

• Atom — the basic particle of chemical elements, made up of a nucleus, protons, neutrons, and electrons. Chemical elements are distinguished by the number of protons they contain; the atomic number of an element is its number of protons.
• Isotope — an atom of an element with the same number of protons but a different number of neutrons. All atoms with 12 protons are magnesium, but magnesium has three stable isotopes: ²⁴Mg, ²⁵Mg, and ²⁶Mg, with 12, 13, and 14 neutrons respectively.
• Mole (mol) — a unit for measuring the amount of a substance. One mole is an aggregate of exactly 6.02214076×10²³ (Avogadro's number) base particles, which can be atoms, molecules, ions, ion pairs, or other particles.
• Sample — a small amount of a material taken from a larger quantity for testing and analysis.
• Molecule — a group of two or more atoms held together by chemical bonds.

Atomic Weight

Atomic weight, more precisely referred to as relative atomic mass (and not to be confused with atomic mass), is defined as the ratio of the average mass of a sample of atoms of an element to the atomic mass constant. Since both have units of mass, the resulting quantity is dimensionless. It represents the weighted average of the masses of individual atoms, including all isotopes, in a sample. Atomic mass, on the other hand, is the mass of a single atom, which can be measured with precision in units of daltons (Da).

The atomic weight of a given element is the weighted average of the atomic masses of its different isotopes. For example, hydrogen has three main isotopes: hydrogen-1, deuterium (²H), and tritium (³H). Hydrogen-1 comprises 99.9855% of naturally occurring hydrogen while deuterium comprises 0.0145%; tritium exists naturally in only negligible trace amounts. Since ²H has a mass of 2.01410177811 Da and ¹H has a mass of 1.007825031898 Da, its atomic weight can be calculated as 1.007825031898 × 99.9855% + 2.01410177811 × 0.0145% ≈ 1.008 Da. Note that this calculator uses standard atomic weights as stated by IUPAC (International Union of Pure and Applied Chemistry); the table of standard atomic weights for each element is provided at the bottom of this page.

Molecular Weight (relative molecular mass)

The molecular weight (more precisely, relative molecular mass) is defined as the ratio of the mass of a molecule to the atomic mass constant. Like the atomic weight, this is a dimensionless quantity. Molecular weight differs from atomic weight simply in that a molecule is made up of multiple atoms, so the sum of the atomic weights of the atoms that make up a compound is its molecular weight. For example, the molecular weight of a water molecule (H₂O), using an atomic weight of 1.008 Da for hydrogen and 15.999 Da for oxygen, is 2 × 1.008 + 15.999 = 18.015 Da. Although the above is the more accurate definition of molecular weight, for the intents of this calculator, molecular weight is used interchangeably with molar mass, defined below.

Molar Mass

Molar mass is defined as the mass of 1 mole of a substance and is typically measured in grams per mole (g/mol). It is frequently used interchangeably with molecular weight, even though they are not exactly the same: molecular weight is the ratio of the mass of a molecule to the atomic mass constant, while molar mass can be defined as the ratio of the mass of any sample of a compound to the amount of substance (measured in moles). Although the two are defined differently and usually expressed in different units, for most purposes — including a high school chemistry class — they have more or less the same value and may be used largely interchangeably. Before the redefinition of certain values, they were numerically equivalent with different units.

Molecular Mass

To make things more confusing, molecular mass is also distinct from molecular weight. Molecular weight (relative molecular mass) takes into account the weighted abundance of the various isotopic compositions of a given compound. For example, the relative molecular mass of water is 18.015 Da, but a given water molecule may have a molecular mass ranging from 18.0106 Da to 22.0277 Da.

Calculate Molecular Weight and Molar Mass

Atomic weight serves as the foundation for calculating molecular weight and molar mass. It provides the mass of individual atoms, which, when combined according to a molecule's chemical formula, yields the mass of the entire molecule. Molecular weight or molar mass can therefore be calculated by:

• Identifying and counting the number of atoms of each element in the molecule.
• Obtaining the atomic weights of each element using the standard atomic weights from the periodic table or the table provided below.
• Multiplying the atomic weight of each element by the number of atoms of that element, then summing the results.

Table of abridged standard atomic weights

Below is a table of the abridged standard atomic weights of the elements. The abridged version is commonly used in practical scenarios, as it simplifies calculations by providing values rounded to a fixed number of decimal places, ignoring the typically small natural variations in isotope ratios from different sources or samples. These values are published by the International Union of Pure and Applied Chemistry (IUPAC). The calculations of this calculator are based on this data.

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