Molarity Calculator - Solution Concentration (mol/L)

What is molarity?

Molarity is a way of measuring how much of a substance is dissolved in a liquid. It is defined as the number of moles of solute per liter of solution, written as mol/L or the symbol M. A solution labeled "1 M" contains one mole of dissolved substance in every liter.

Molarity formula

Molarity is calculated with a simple division:

$\text{Molarity (M)} = \frac{\text{Moles of solute (mol)}}{\text{Volume of solution (L)}}$

• Moles of solute is the amount of dissolved substance, measured in moles.
• Volume of solution is the total volume of the liquid after the solute is fully dissolved, measured in liters.
• Molarity is the result, in moles per liter (mol/L), also called M.

Worked example

Dissolving 2 moles of sodium chloride (NaCl) in enough water to make 0.5 liters of solution gives:

$\text{Molarity} = \frac{2 \text{ mol}}{0.5 \text{ L}} = 4 \text{ M}$

The solution has a concentration of 4 moles per liter, written as 4 M.

How to calculate molarity from grams

Solute is often weighed in grams rather than measured in moles directly. An extra step converts grams to moles before applying the molarity formula.

1. Find the molar mass of the compound, in grams per mole.
2. Divide the mass, in grams, by the molar mass to get moles.
3. Divide the moles by the volume of solution, in liters.

Example: 10 g of NaCl is dissolved to make 500 mL (0.5 L) of solution.

• Molar mass of NaCl: 22.99 + 35.45 = 58.44 g/mol
• Moles: 10 g ÷ 58.44 g/mol ≈ 0.171 mol
• Molarity: 0.171 mol ÷ 0.5 L ≈ 0.342 M

How this calculator works

The calculator on this page takes two entries: the amount of solute in moles and the volume of solution in liters. It divides moles by volume and shows the result rounded to four decimal places.

Both entries must be greater than zero. A value of zero or less for either field triggers an error message instead of a result, since a negative amount of solute or a zero volume has no physical meaning and would make the division undefined.

Preparing a solution of a known molarity

Chemists commonly work backward from a target molarity to find how much solute to weigh out.

Example: Prepare 250 mL (0.25 L) of a 0.1 M sodium hydroxide (NaOH) solution.

1. Moles needed = molarity × volume = 0.1 M × 0.25 L = 0.025 mol
2. Mass needed = moles × molar mass = 0.025 mol × 40 g/mol = 1 g
3. Dissolve 1 g of NaOH in water and add water until the solution measures exactly 250 mL.

Diluting a stock solution

A concentrated "stock" solution can be diluted to a lower molarity using the equation M₁V₁ = M₂V₂, where M₁ and V₁ are the concentration and volume of the stock solution, and M₂ and V₂ are the concentration and volume wanted after dilution.

Example: Make 500 mL of a 0.2 M solution from a 2 M stock solution.

$V_1 = \frac{M_2 \times V_2}{M_1} = \frac{0.2 \text{ M} \times 0.5 \text{ L}}{2 \text{ M}} = 0.05 \text{ L} = 50 \text{ mL}$

Adding 50 mL of the 2 M stock to enough water to reach 500 mL total gives the target concentration.

Molarity in titration

In a titration, one solution of known concentration is added to another until a reaction finishes. Molarity connects the volumes measured to the amount of substance reacting.

Example: 20 mL of 0.1 M NaOH neutralizes 25 mL of an HCl solution of unknown concentration.

1. Moles of NaOH used: 0.1 M × 0.020 L = 0.002 mol
2. HCl and NaOH react in a 1:1 ratio (HCl + NaOH → NaCl + H₂O), so moles of HCl = 0.002 mol.
3. Molarity of HCl = 0.002 mol ÷ 0.025 L = 0.08 M

Other units of concentration

Molarity is one of several ways to express concentration. Each is suited to different situations.

History

The idea of a fixed counting unit for atoms and molecules traces back to Amedeo Avogadro's 1811 hypothesis linking gas volume to particle number. Chemists built on this over the following century to define the mole, and molarity became the standard way to describe solution concentration once the mole was adopted as an SI base unit in 1971. In 2019, the International Union of Pure and Applied Chemistry (IUPAC) redefined the mole using a fixed value of the Avogadro constant, 6.02214076 × 10²³, rather than a mass-based standard.

Frequently asked questions

What is the difference between molarity and molality?

Molarity divides moles of solute by liters of solution. Molality divides moles of solute by kilograms of solvent. Because liquids expand slightly when heated, molarity changes a little with temperature, while molality does not.

Can molarity be higher than 1 M?

Yes. Concentrated hydrochloric acid is about 12 M, and concentrated sulfuric acid is about 18 M. The maximum possible molarity depends on how much of the solute can dissolve in the solvent at that temperature.

What is the molarity of pure water?

About 55.3 M. Water's density at 25°C is about 997 g/L, and its molar mass is 18.02 g/mol, so 997 ÷ 18.02 ≈ 55.3 mol/L. This number is used in equilibrium calculations because removing a small amount of water from a large volume barely changes its concentration.

Does temperature affect molarity?

Slightly. Most liquids expand as they warm, so the same amount of solute occupies a larger volume, lowering the molarity. Molality is unaffected by temperature because it is based on mass rather than volume.

How is molarity used in titration?

In a titration, the volume of a solution with known molarity needed to react completely with another solution is measured. The reaction's mole ratio, from the balanced chemical equation, is then used to calculate the unknown solution's molarity.

How many decimal places does this calculator show?

The result is shown to four decimal places. The number of digits that are actually meaningful depends on the precision of the moles and volume entered; a result should not be reported with more significant figures than the least precise input allows.