Molar Mass Calculator

About the Molar Mass Calculator

Almost every quantitative problem in chemistry passes through molar mass. Converting a mass on a balance into moles, finding how much product a reaction can make, preparing a solution of known concentration and working out an empirical formula all start with adding up atomic weights correctly.

The arithmetic is simple, but long formulas make it easy to miss an atom, especially when brackets or water of crystallisation multiply part of the formula. This calculator reads the formula, expands every bracket and hydrate, counts each element, multiplies by its standard atomic weight and adds the contributions. It shows the mass percent of each element and, if you enter a sample mass, the number of moles and formula units it contains.

What is molar mass?

The molar mass $M$ of a substance is the mass of one mole of its formula units, measured in grams per mole. One mole contains exactly $6.02214076 \times 10^{23}$ particles, the Avogadro constant. Because the mole is defined this way, the molar mass in g/mol has the same numerical value as the mass of one formula unit in daltons, which is why the terms molecular weight and formula mass are often used interchangeably.

To find the molar mass, multiply the atomic weight of each element by the number of its atoms in the formula and add the results. Water, $\mathrm{H_2O}$ , has two hydrogen atoms at 1.008 and one oxygen atom at 15.999, giving $2(1.008) + 15.999 = 18.015$ g/mol.

How to use the Molar Mass Calculator

Type the formula using correct capitalisation, for example NaCl, Fe2O3 or (NH4)2SO4.
Use round brackets, square brackets or braces for groups, and · or * between the parts of a hydrate.
Optionally enter the mass of your sample in grams to convert it to moles.
Press Calculate molar mass.
Read the atom count for each element, each contribution, the total in g/mol and the mass percentages.

Formulas

Molar mass

M = \sum_i n_i A_i

n is the number of atoms of an element in the formula and A is its atomic weight.

Moles from mass

n = \frac{m}{M}

Mass percent

\%X = \frac{n_X A_X}{M} \times 100\%

Number of particles

N = n \cdot N_A

Worked example: Water, H₂O

The worked example is water, $\mathrm{H_2O}$ . It has 2 hydrogen atoms contributing $2 \times 1.008 = 2.016$ and 1 oxygen atom contributing $15.999$ , so $M = 18.015$ g/mol.

The mass percentages follow from the same numbers: hydrogen is $2.016 / 18.015 \approx 11.19\%$ and oxygen is $15.999 / 18.015 \approx 88.81\%$ of the mass of water.

The solution below is generated by the same engine that powers the calculator above.

Final answer

M = 18.015\ \text{g/mol}

How we read your problem

Add the atomic weights of all 3 atoms in one formula unit of H2O.

M(\mathrm{H_{2}O})

Step-by-step solution

Count the atoms of each element
Subscripts multiply everything inside the brackets before them, and a hydrate coefficient multiplies the whole water (or other) unit.
$\text{H}: 2,\quad \text{O}: 1$
Look up each atomic weight (g/mol)
IUPAC standard atomic weights (abridged, conventional values).
$\text{H} = 1.008,\quad \text{O} = 15.999$
Multiply each count by its atomic weight
$2 \times 1.008 = 2.016 \\ 1 \times 15.999 = 15.999$
Add the contributions
$M = 2.016 + 15.999 = 18.015\ \text{g/mol}$
Mass percent of each element
$\%\text{H} = \frac{2.016}{18.015} \times 100 \approx 11.19\% \\ \%\text{O} = \frac{15.999}{18.015} \times 100 \approx 88.81\%$

Formulas used

Molar mass
$M = \sum_i n_i \, A_i$
Moles from mass
$n = \frac{m}{M}$
Mass percent
$\%X = \frac{n_X A_X}{M} \times 100$

The molar mass is the mass of one mole of formula units. It equals the sum of the atomic weights of every atom in the formula, and numerically matches the formula mass in daltons (u).

Verification

Percent composition adds to 100.00%.
Elements: hydrogen ×2, oxygen ×1.

Detailed explanation

Reading brackets and hydrates

A subscript after a bracket multiplies every atom inside it. In calcium hydroxide, $\mathrm{Ca(OH)_2}$ , there is one calcium, two oxygens and two hydrogens, so $M = 40.078 + 2(15.999) + 2(1.008) = 74.092$ g/mol. Brackets can be nested, as in potassium ferrocyanide, $\mathrm{K_4[Fe(CN)_6]}$ , where the 6 multiplies both carbon and nitrogen.

A hydrate contains water molecules locked into the crystal. In copper(II) sulfate pentahydrate, $\mathrm{CuSO_4 \cdot 5H_2O}$ , the 5 multiplies the whole water unit, adding 10 hydrogens and 5 oxygens. The molar mass is about 249.68 g/mol, compared with about 159.60 g/mol for anhydrous copper sulfate, a difference that matters when weighing out the blue crystals in a lab.

From grams to moles and particles

Dividing a mass by the molar mass gives the amount in moles. Ten grams of sodium chloride, with $M = 58.44$ g/mol, is $10 / 58.44 \approx 0.1711$ mol. Multiplying by the Avogadro constant gives about $1.03 \times 10^{23}$ formula units. Enter the mass in the optional field and the calculator performs both steps.

The reverse conversion, moles to grams, uses $m = nM$ . For instance, 0.25 mol of glucose, $M = 180.156$ g/mol, has a mass of about 45.04 g. Keeping the molar mass to at least three decimal places prevents rounding errors from building up in multi-step stoichiometry problems.

Where the atomic weights come from

The calculator uses IUPAC standard atomic weights in their abridged, conventional form, such as 1.008 for hydrogen, 12.011 for carbon and 35.45 for chlorine. These values average the natural mix of isotopes found on Earth. Your textbook may round them differently, for example 35.5 for chlorine, which can shift the last decimal of an answer.

Elements such as technetium, radon and plutonium have no stable isotopes and therefore no standard atomic weight. For these, the mass number of the longest-lived isotope is used and shown in brackets, a common convention on periodic tables.

Common mistakes

Writing element symbols in the wrong case: Co is cobalt, but CO is carbon monoxide.
Applying a bracket subscript only to the last atom inside the bracket.
Forgetting to multiply the water in a hydrate by its coefficient.
Using atomic numbers instead of atomic weights.
Rounding molar masses to whole numbers too early in a multi-step calculation.

Tips

Count atoms element by element and write the counts down before multiplying.
Check that mass percentages add to 100% as a quick test of your arithmetic.
Subscript digits such as H₂O can be pasted directly; they are read as normal numbers.
For ions, the electron mass is negligible, so the molar mass of $\mathrm{SO_4^{2-}}$ is the same as that of $\mathrm{SO_4}$ ; enter the formula without the charge.
Keep units in every step: grams divided by grams per mole leaves moles.

Frequently asked questions

How do you calculate molar mass?

Multiply the atomic weight of each element by the number of atoms of that element in the formula, then add all the results. For carbon dioxide, CO2: 12.011 + 2 × 15.999 = 44.009 g/mol.

What is the difference between molar mass and molecular weight?

Molar mass is the mass of one mole of a substance in g/mol. Molecular weight (relative molecular mass) is the mass of one molecule relative to one twelfth of a carbon-12 atom and has no unit. The two have the same numerical value.

How do I enter a hydrate like CuSO4·5H2O?

Type the anhydrous part, then a middle dot (·), an asterisk (*) or a period, then the coefficient and the water: CuSO4·5H2O, CuSO4*5H2O or CuSO4.5H2O all give the same result.

How do I convert grams to moles?

Divide the mass in grams by the molar mass in g/mol. Enter a sample mass in the optional field and the calculator shows the moles and the number of formula units using the Avogadro constant.

Why does my textbook give a slightly different molar mass?

Books and periodic tables round atomic weights differently, for example chlorine as 35.5 or 35.45. The calculator uses IUPAC abridged standard atomic weights, so small differences in the last decimal are expected.

What is mass percent composition?

It is the share of a compound's mass contributed by each element: the element's total mass in the formula divided by the molar mass, times 100. In water, oxygen makes up about 88.81% of the mass.

Does the calculator accept charges or states like (aq)?

No. Enter only the formula of the neutral unit. Charges barely change the mass because electrons are so light, and state symbols such as (aq) or (s) do not affect the molar mass.

Find a molar mass

Enter any chemical formula above to get its molar mass, the contribution of each element and the mass percentages.

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