Solution Concentration & Dilution Calculator

What is solution concentration?

Solution concentration describes how much of a constituent is present in a specified amount or volume of a mixture. Common forms include amount concentration, mass concentration and volume concentration. They use different units and should not be interchanged without the appropriate conversion. The IUPAC Gold Book defines amount concentration in terms of amount of substance divided by mixture volume.

The dilution equation

The standard dilution relationship is C₁V₁ = C₂V₂. Here, C₁ is the starting stock concentration, V₁ is the amount of stock solution used, C₂ is the target concentration, and V₂ is the final total solution volume.

The equation expresses the conservation of solute during dilution: the amount of solute in the stock aliquot equals the amount in the resulting diluted solution. Use compatible concentration units and identical volume units on both sides of the equation.

Molarity from moles

Amount concentration (commonly called molarity in educational contexts) is calculated by dividing the amount of solute, in moles, by the total solution volume, in litres:

c = n / V

Molarity from mass

If the solute mass and molar mass are known, first calculate the amount of substance. Divide the mass in grams by the molar mass in grams per mole, then divide the resulting moles by the total solution volume in litres.

n = m / M

c = m / (M × V)

In the second formula, m is the solute mass in grams, M is the molar mass in grams per mole, and V is the solution volume in litres.

Required solute mass for a target molarity

To prepare a specified molarity, multiply the target amount concentration by the final solution volume in litres and then by the solute's molar mass:

m = c × V × M

Weighing the calculated mass is only one step of solution preparation. The final solution must be made up to the specified total volume.

Mass concentration

Mass concentration reports mass per volume, for example mg/mL or g/L. It can be calculated by dividing solute mass by solution volume after converting both quantities into compatible units. It is not the same quantity as molarity, which uses moles per volume.

Important assumptions and lab safety

• Concentrations and volumes must describe the same solute and the intended final solution.
• The dilution calculation treats the solute amount as conserved and assumes the entered concentrations are applicable. It does not account for chemical reactions, degradation, precipitation or temperature-dependent volume effects.
• Solvent volume is not always exactly additive. In practical dilution, add solvent until the solution reaches the desired final volume rather than assuming that measured liquid volumes always sum exactly.
• Follow the chemical's safety data sheet, suitable PPE, and the applicable laboratory procedure. This calculator is not a substitute for safe handling or validated preparation instructions.

Frequently asked questions