About the Concentration Converter
This concentration converter translates a solution concentration from any common unit into all the others at once: molarity (M, mM, µM, nM), mass concentration (mg/mL, g/L, µg/mL or ppm), percent weight/volume, percent weight/weight, molality and mole fraction. Enter the value, pick its unit, and give the solute’s molar mass.
It is built for lab work — converting a protein stock in mg/mL to µM, a reagent label in % w/w to molarity, or a molality from a colligative-property problem into mass percent. Conversions between molar and mass-per-volume units need only the molar mass; conversions involving % w/w, molality or mole fraction also need the solution density, because they relate the solute to the mass of solution or solvent rather than its volume.
The default density of 1.02 g/mL suits roughly 0.5 M salt solutions, and 1.00 g/mL is fine for very dilute ones; for concentrated acids, bases or salt solutions use the measured density from the supplier’s data sheet. The solvent is assumed to be water (18.015 g/mol) unless you change it. ppm here means mg per litre, the usual convention for dilute aqueous solutions.
With the default inputs, the molarity is 0.5 M. Change any value above to recalculate instantly.
How to use the concentration converter
- 1Enter the concentration you have and choose its unit.
- 2Enter the solute’s molar mass in g/mol.
- 3Enter the solution density if you need % w/w, molality or mole fraction.
- 4Read every equivalent unit in the results and table.
Formula and method
Every input is first converted to grams of solute per litre of solution. Molar units divide by the molar mass M (mol/L = g/L ÷ M); mg/mL equals g/L; % w/v is grams per 100 mL, so g/L ÷ 10. These need no density.
For mass-based units the calculator uses the density ρ (g/mL) to find the mass of one litre of solution, 1000·ρ grams. Mass percent is solute grams ÷ solution grams × 100. The solvent mass is solution mass minus solute mass, so molality = moles of solute ÷ kg of solvent, and mole fraction = moles of solute ÷ (moles of solute + moles of solvent). Converting from molality or mole fraction runs these relations backwards.
- c
- Molarity (mol/L)
- M
- Molar mass of the solute (g/mol)
- ρ
- Solution density (g/mL)
- w
- Mass fraction (% w/w ÷ 100)
- b
- Molality (mol/kg solvent)
- x
- Mole fraction of solute
Worked examples
0.5 M sodium chloride (density 1.02 g/mL)
One litre holds 0.5 × 58.44 = 29.22 g NaCl, so the solution is 29.22 mg/mL or 2.922% w/v. That litre weighs 1,020 g, so mass percent is 29.22 ÷ 1,020 = 2.865% and the 990.78 g of water gives a molality of 0.5 ÷ 0.99078 = 0.5047 mol/kg.
Protein stock: 5 mg/mL BSA to micromolar
Bovine serum albumin has a molar mass of about 66,430 g/mol. 5 g/L ÷ 66,430 g/mol = 7.527 × 10⁻⁵ mol/L, or 75.27 µM.
10% w/w sodium hydroxide (density 1.109 g/mL)
A litre weighs 1,109 g, of which 10% (110.9 g) is NaOH: 110.9 ÷ 40.00 = 2.77 M. Per kilogram of water there are 100/90 × 2.5 mol = 2.78 mol, so the molality is 2.778 mol/kg.
1 molal glucose (density 1.06 g/mL)
1 mol (180.16 g) of glucose in 1 kg of water makes 1,180.16 g of solution, or 1,113.4 mL at 1.06 g/mL. That gives 1 ÷ 1.1134 = 0.898 M and a mass percent of 15.27%.
Frequently asked questions
How do I convert mg/mL to molarity?+
Divide the mass concentration in g/L (which equals mg/mL) by the molar mass in g/mol. For example, 10 mg/mL of glucose is 10 ÷ 180.16 = 0.0555 M, or 55.5 mM.
How do I convert percent to molarity?+
For % w/v, multiply by 10 to get g/L and divide by the molar mass. For % w/w, multiply the mass fraction by the density in g/L first: 37% HCl at 1.19 g/mL is 0.37 × 1190 ÷ 36.46 ≈ 12.1 M.
What is the difference between molarity and molality?+
Molarity is moles per litre of solution and changes slightly with temperature because volume changes. Molality is moles per kilogram of solvent and is temperature independent, which is why it is used for boiling-point and freezing-point calculations.
Why do I need the density?+
Converting between volume-based units (M, g/L) and mass-based units (% w/w, molality, mole fraction) requires knowing how much one litre of solution weighs. For dilute aqueous solutions 1.00 g/mL is a fair approximation; concentrated solutions differ considerably.
Is ppm the same as mg/L?+
For dilute water solutions, yes: 1 litre weighs about 1 kg, so 1 mg/L ≈ 1 mg/kg = 1 ppm by mass. In dense or non-aqueous solutions ppm by mass and mg/L diverge, so check which definition you need.