Concentration Calculator
Enter your solute and solution amounts to calculate concentration in six common units: molarity (mol/L), molality (mol/kg), mass percent (w/w), volume percent (v/v), parts per million (ppm), and parts per billion (ppb). Switch the calculation mode to instead solve for the solute mass or volume needed to hit a target concentration. Results update instantly with a full show-your-work panel.
Formula
Worked example
Dissolving 5.844 g of NaCl (molar mass 58.44 g/mol) in enough water to make 1000 mL of solution: moles = 5.844 / 58.44 = 0.1000 mol; molarity = 0.1000 mol / 1.000 L = 0.1000 M. In ppm: 5844 mg / 1.000 L = 5844 ppm.
What is solution concentration?
Concentration describes how much solute is dissolved in a given amount of solvent or solution. Expressing it as a number requires a unit, and the choice of unit depends on the application. Molarity (mol/L) is the standard for volumetric reactions and titrations because it ties directly to the stoichiometry of equations. Molality (mol/kg) is used when temperature or pressure may change the volume, such as in colligative property calculations for boiling-point elevation and freezing-point depression. Mass percent appears on reagent bottles and in food science. Parts per million (ppm) and parts per billion (ppb) are the units of choice for trace-level analysis in environmental monitoring and water quality testing.
How to use this calculator
Choose a calculation mode from the drop-down. In the default mode, enter the mass of solute (grams), the mass of solvent (grams), and the total volume of solution (millilitres), plus the molar mass of your solute in g/mol. The calculator returns molarity, molality, mass percent, volume percent, ppm and ppb simultaneously. Switch to "Solute mass needed" mode to find how many grams of solute to weigh out for a target molarity and volume. Switch to "Volume needed" mode to find what final volume you must prepare if you already have a fixed mass of solute. The step-by-step panel shows the arithmetic at each stage so you can follow the working through.
Molarity vs molality: which should you use?
Molarity is the most commonly used unit in analytical and synthetic chemistry because volumes are easy to measure with glassware and molarity fits directly into stoichiometric calculations. However, molarity changes with temperature because liquids expand and contract, altering the volume. Molality does not change with temperature because it is defined per kilogram of solvent, not per litre of solution. For colligative properties such as the depression of the freezing point (using the formula delta-Tf = Kf x m), molality is the correct unit. For dilute aqueous solutions at room temperature the two values are nearly identical, but for concentrated solutions or work at elevated temperatures they diverge significantly.
ppm and ppb: mass/volume convention
Parts per million has more than one definition. In liquid analysis the most common convention is mass per volume: 1 ppm = 1 mg of solute per litre of solution. This calculator uses that definition. The mass/mass convention (1 ppm = 1 mg per kg of solution) is used in soil science and food labelling and gives a slightly different number unless the solution density is exactly 1 g/mL. Parts per billion (ppb) is simply the same idea at a thousand times greater dilution: 1 ppb = 1 microgram per litre. Regulatory drinking-water limits for contaminants such as lead and arsenic are set in ppb, so this unit matters practically as well as academically.
Common solution concentration types
| Type | Symbol | Formula | Best used for |
|---|---|---|---|
| Molarity | M or c | mol solute / L solution | Volumetric reactions, titrations |
| Molality | m | mol solute / kg solvent | Boiling/freezing point changes |
| Mass percent | w/w % | (mass solute / mass soln) × 100 | Industrial and food chemistry |
| Volume percent | v/v % | (vol solute / vol soln) × 100 | Alcohol content, solvents |
| ppm (m/v) | ppm | mg solute / L solution | Environmental, trace analysis |
| ppb (m/v) | ppb | μg solute / L solution | Ultra-trace analysis, water quality |
A quick-reference guide to the six most-used concentration expressions in chemistry.
Frequently asked questions
What is the formula for molarity?
Molarity (M) = moles of solute divided by litres of solution. You convert grams of solute to moles by dividing by the molar mass: moles = mass (g) / molar mass (g/mol). Then divide by the volume in litres. For example, 5.85 g of NaCl (molar mass 58.5 g/mol) in 250 mL: moles = 5.85 / 58.5 = 0.100 mol; molarity = 0.100 mol / 0.250 L = 0.400 mol/L.
What is the difference between molarity and molality?
Molarity is moles of solute per litre of solution. Molality is moles of solute per kilogram of solvent (not solution). Molarity is more convenient in the lab because you measure volumes with glassware, but molality is independent of temperature and is therefore used for colligative properties such as boiling-point elevation and freezing-point depression. For dilute aqueous solutions at room temperature the numerical values are very close.
How do I convert ppm to molarity?
Using the mass/volume ppm convention (mg per litre): molarity = ppm / (molar mass x 1000). For example, 100 ppm of NaCl (molar mass 58.44 g/mol) = 100 mg/L = 0.100 g/L; moles per litre = 0.100 / 58.44 = 0.00171 mol/L. Alternatively, enter the solute mass (in grams) and volume (1000 mL) into this calculator and read off both molarity and ppm at once.
What does w/w percent mean?
Mass percent, written w/w %, is the mass of solute divided by the total mass of the solution, multiplied by 100. A 5% w/w NaCl solution contains 5 g of NaCl in every 100 g of solution (not 100 mL). It is independent of density and temperature, which is why it appears on concentrated reagent bottles. To convert to molarity you also need the solution density.
How do I prepare a 0.1 mol/L solution?
Use the "Solute mass needed" mode. Enter 0.1 as the target molarity, your desired volume (e.g. 500 mL), and the molar mass of your compound. The calculator gives you the grams to weigh out. Weigh the solute into a beaker, dissolve it in a small amount of distilled water, transfer the solution to a volumetric flask of the correct size, and then add water to the graduation mark. Never fill the flask to volume before dissolving, as this changes the final volume.