Molar Mass

Summing Atomic Weights From a Chemical Formula

Molar mass is the mass of one mole of a substance, in grams per mole (g/mol), found by adding up the standard atomic weight of every atom in its chemical formula. Type a formula using plain element symbols and digits — subscripts as ordinary numbers (H2O, C6H12O6), parentheses with a trailing number for a repeated group (Ca(OH)2, Al2(SO4)3), and a period or middle dot before a hydrate’s water count (CuSO4.5H2O) — and this calculator adds up every atom’s contribution using the current IUPAC standard atomic weights.

The Formula

For a formula with atoms of elements $\vA{1}, \vA{2}, \ldots$, each present in count $\vB{n_1}, \vB{n_2}, \ldots$:

$$\vC{\text{Molar Mass}} = \sum \vB{n_i} \times \vA{\text{atomic weight}_i}$$

Each element’s own standard atomic weight — the average mass of one mole of its naturally occurring atoms, accounting for the relative abundance of its isotopes — comes from the current IUPAC/CIAAW Standard Atomic Weights table (2021, with 2024 revisions), the internationally recognized reference for this data.

Worked Example

Molar mass of water, H2O (2 hydrogen atoms, 1 oxygen atom):

1. Look up each element’s atomic weight: hydrogen $\vA{1.008}$ g/mol, oxygen $\vA{15.999}$ g/mol.
2. Multiply by each element’s atom count: hydrogen $\vB{2} \times \vA{1.008} = 2.016$ g/mol, oxygen $\vB{1} \times \vA{15.999} = 15.999$ g/mol.
3. Add every element’s contribution: $2.016 + 15.999 = \vC{18.015}$ g/mol.

Molar mass of copper(II) sulfate pentahydrate, CuSO4·5H2O (a hydrate — the parenthesis-free sulfate group plus 5 water molecules):

1. Add up the anhydrous copper sulfate (CuSO4): copper $63.546$ + sulfur $32.06$ + 4 oxygen $\vB{4} \times \vA{15.999} = 63.996$, totaling $\vC{159.602}$ g/mol.
2. Add up the 5 water molecules: $\vB{5} \times \vA{18.015} = 90.075$ g/mol.
3. Add both parts together: $159.602 + 90.075 = \vC{249.677}$ g/mol — matching the widely published reference value of 249.685 g/mol (the small difference comes from rounding each element’s abridged atomic weight to 3-4 decimal places).

Key Factors to Consider

• Molar mass is the key conversion factor between mass and moles, the unit chemists use to count particles. Since counting individual atoms or molecules directly is impractical, chemists work in moles (a fixed, enormous number of particles) instead — molar mass is what lets a lab measurement in grams be converted into a mole count for a chemical reaction, and vice versa.
• A capital letter always starts a new element symbol — capitalization matters in a chemical formula. “Co” means cobalt (one element), while “CO” means carbon monoxide (carbon plus oxygen, two elements) — getting the capitalization wrong changes which atoms are actually being totaled.
• Standard atomic weights are themselves averages across an element’s naturally occurring isotopes, not a single fixed number. Because most elements exist in nature as a mix of isotopes with slightly different masses, the standard atomic weight reflects their typical relative abundance — this is why atomic weights (like chlorine’s 35.45) often aren’t whole numbers.
• Molar mass and molecular weight are numerically the same value, just with different units. Molecular weight is technically a dimensionless ratio (relative to 1/12 the mass of carbon-12), while molar mass carries units of grams per mole — in practice, the two terms are frequently used interchangeably since they share the same numeric value.

Common Mistakes

• Getting element capitalization wrong. A formula’s letters aren’t case-insensitive — “Co” (cobalt) and “CO” (carbon monoxide) total completely different atoms, so a lowercase letter where an uppercase one belongs can silently change which element is being counted.
• Forgetting the trailing number on a parenthesized group. Ca(OH)2 means one calcium plus two full hydroxide groups (2 oxygen, 2 hydrogen) — typing Ca(OH) without the closing “2” leaves out half the formula’s actual atoms.
• Missing the dot before a hydrate’s water count. CuSO4 and CuSO4.5H2O are different substances with very different masses — the water of crystallization only gets counted when the period (or middle dot) and water count are actually present.
• Assuming every element on the periodic table is supported. This calculator covers the roughly 60 elements most common in everyday and classroom formulas — a formula using an element outside that set shows a clear error rather than silently miscalculating.

Useful to Know

• Need to know a solution’s concentration once you know a solute’s molar mass? Molarity & Dilution Calculator converts between grams, moles, and molarity.
• Working with an acid or base’s concentration instead of a solid compound’s formula? pH Calculator calculates pH from concentration.
• Need trigonometric, logarithmic, or other general-purpose math alongside a chemistry calculation? Scientific Calculator covers that broader toolkit.