The same solution can be described in a dozen different ways. A lab recipe asks for molarity, a safety data sheet lists weight percent, a water report gives ppm and a physical chemistry problem wants molality. This calculator converts any one of these into all the others. Enter the solute (as a formula or a molar mass) and the solution’s density, then either a known concentration or the mass of solute and the final volume, and it returns every common unit with the steps shown.
How to use the solution concentration calculator
- Choose to start from A known concentration or from Solute mass and solution volume.
- Enter the Solute as a formula such as
NaCl,C6H12O6orCuSO4·5H2O, or simply type its molar mass in g/mol. - Enter the concentration and pick its unit: M, mM, µM, mol/kg, % w/w, % w/v, g/L, mg/mL, mg/L, ppm by mass, ppm as mg/L, ppb by mass or mole fraction. Or enter the solute mass and the total volume of solution.
- Enter the Density of the solution. Use about 1.00 g/mL for dilute water solutions, or a measured or tabulated value for concentrated ones.
- Keep water’s Solvent molar mass of 18.015 g/mol unless you use another solvent; it is needed only for the mole fraction.
- Pick the unit for the main result. The table lists all of them.
Concentration formulas
Working with 1 L of solution, whose mass is ρ × 1,000 mL, and ms grams of solute of molar mass M:
The mole fraction is nsolute ÷ (nsolute + nsolvent), with the solvent’s moles found from its mass, 1,000ρ − ms. Any unit is first converted to grams of solute per liter, then into every other unit.
Worked example
Normal saline
0.9% w/v NaCl (58.44 g/mol) with a density of about 1.005 g/mL.
0.9% w/v = 0.9 g per 100 mL = 9 g/L
Molarity = 9 ÷ 58.44 = 0.154 M (154 mM)
A liter weighs 1,005 g, so % w/w = 9 ÷ 1,005 × 100 = 0.896%, ppm by mass = 8,955 and molality = 0.154 ÷ 0.996 kg = 0.1546 mol/kg.
Concentrated acid. Commercial hydrochloric acid is 37% HCl by mass with a density of 1.19 g/mL. A liter weighs 1,190 g and contains 440.3 g of HCl, so it is 12.08 M, and its molality is 16.1 mol/kg because only 750 g of each liter is water.
From a weighing. Dissolving 5 g of glucose and making it up to 250 mL gives 20 g/L, which is 2% w/v and 0.111 M (111 mM).
Which unit to use when
| Unit | Based on | Typical use |
|---|---|---|
| Molarity (M) | mol per L of solution | Lab recipes, titrations |
| Molality (mol/kg) | mol per kg of solvent | Freezing and boiling point changes |
| % w/w | g per 100 g of solution | Commercial acids, alloys, food labels |
| % w/v | g per 100 mL of solution | Medical solutions such as saline and dextrose |
| ppm, ppb | parts per million or billion | Drinking water, pollutants, trace metals |
| Mole fraction | mol per total mol | Vapor pressure, gas mixtures |
The EPA sets drinking-water limits in mg/L; for arsenic, the maximum contaminant level is 0.010 mg/L, which is 10 ppb.
Accuracy tips
Volume-based units depend slightly on temperature, because solutions expand when warmed, while mass-based units do not. For concentrated solutions, always use a measured density; assuming 1.00 g/mL for 37% HCl would understate its molarity by about 16%. “Final volume” means the volume after dissolving, so make solutions up to the mark in a volumetric flask rather than adding solute to a measured volume of water.
To prepare a weaker solution from a stock, use the dilution calculator. For moles, mass and volume of a single solution, the molarity calculator is quicker, and the molar mass calculator gives molecular weights for any formula.
Frequently asked questions
Is ppm the same as mg/L?
Only for dilute water solutions, where a liter of solution weighs very close to 1 kg. Strictly, ppm by mass is mg of solute per kg of solution. Water-quality reports use ppm and mg/L interchangeably; for concentrated or non-aqueous solutions, use the density to convert.
How do I convert percent to molarity?
For % w/v, multiply by 10 to get g/L, then divide by the molar mass. For % w/w, multiply by the density in g/mL and by 10, then divide by the molar mass. Concentrated hydrochloric acid at 37% w/w and 1.19 g/mL is 37 × 1.19 × 10 ÷ 36.46 ≈ 12.1 M.
What is the difference between molarity and molality?
Molarity is moles per liter of solution; molality is moles per kilogram of solvent. Molality does not change with temperature because it uses masses, which is why it is used for freezing-point and boiling-point calculations. In dilute water solutions the two are nearly equal.
Why does the calculator need the density?
Molarity, % w/v, g/L and mg/L are per volume of solution, while % w/w, ppm by mass, molality and mole fraction are per mass. Converting between the two families requires the solution's mass per liter, which is its density. For dilute water solutions, 1.00 g/mL is a good estimate.
What concentration is normal saline?
0.9% w/v sodium chloride: 9 g of NaCl per liter. That is 0.154 M, or 154 mmol/L of NaCl, which gives about 308 mOsm/L because each NaCl releases two ions, close to the osmolarity of blood plasma.