Percent to molarity calculator
Enter percent, density and molar mass, get the molarity.
How do I convert mass percent to molarity?
Molarity = mass percent × density (g/mL) × 1,000 ÷ (100 × molar mass). One liter of solution weighs density × 1,000 g; the percent of that is solute, and dividing by the molar mass gives moles.
Example: concentrated hydrochloric acid
OpenStax describes concentrated HCl as 37.2% HCl with a density of 1.19 g/mL: 500 mL holds 221 g of HCl. Per liter that is 37.2 × 1.19 × 1,000 ÷ (100 × 36.46) = 12.1 M.
Why do I need the density?
Mass percent compares masses, but molarity is per liter. The density links the mass of the solution to its volume.
Where do I find the density and percent?
On the reagent bottle or its safety data sheet. The molar mass calculator gives the molar mass from a formula.
Can I go the other way?
Yes: mass percent = molarity × molar mass ÷ (10 × density). The calculator shows grams of solute per liter as well.
What if the label gives a percent weight per volume (w/v)?
Then no density is needed. A mass-volume percent is grams of solute per 100 mL of solution (OpenStax Chemistry 2e, section 3.4), so grams per liter is the percent × 10 and molarity is that divided by the molar mass. Physiological saline, 0.9% (m/v) sodium chloride, is 9 g/L, and 9 ÷ 58.44 = 0.154 M. This calculator is for mass percent (w/w), where the density does matter.
Does the formula work for percent by volume, like rubbing alcohol?
No. A label such as 70% isopropyl alcohol is a volume percentage: 70 mL of alcohol in 100 mL of solution (OpenStax section 3.4). To get molarity from it, first multiply the volume of pure alcohol by its own density to get grams of solute, then divide by the molar mass and by the solution volume in liters.
How the conversion works
Mass percent is the mass of solute divided by the mass of the whole solution, times 100 (OpenStax Chemistry 2e, section 3.4). Molarity is moles of solute per liter of solution (section 3.3). The two differ in what they divide by, a mass in one case and a volume in the other, so the density of the solution links them. One liter of solution has a mass of 1,000 × density grams; the percent of that mass is solute; dividing by the molar mass gives moles. That is M = percent × density × 1,000 ÷ (100 × molar mass), with the density in g/mL and the molar mass in g/mol. The formula holds for any solute; the only inputs are three numbers, all of which usually appear on the reagent label or its safety data sheet.
Worked example: a volume percent
The concentrated hydrochloric acid in the first answers above is a mass percent, so the formula applies directly. A volume percent needs one more step. OpenStax section 3.4 lists wine at 12% ethanol by volume, 750 mL, with an ethanol density of 0.789 g/mL and a molar mass of 46.06 g/mol. The ethanol volume is 0.12 × 750 = 90 mL, its mass is 90 × 0.789 = 71.0 g, and the amount is 71.0 ÷ 46.06 = 1.54 mol, the textbook’s 1.5 mol. In 0.750 L of wine that is 2.06 M. The denominator is the volume of the whole drink, 0.750 L, not of the ethanol.
Common mistakes
The density must be that of the solution, in g/mL, not of the pure solute or of water. Leaving it at 1.00 turns the acid above into 10.2 M instead of 12.1 M. Entering the density in g/L (1190) overstates the result by 1,000, giving 12,142 M. Another trap is mixing up percent types: w/w (mass percent) is what this calculator expects, whereas labels for alcohols and some cleaning products use volume percent, and some biological solutions use w/v. Finally, use the molar mass of the compound on the label, not that of an ion or of the element it contains.
Sources: OpenStax Chemistry 2e, section 3.4 “Other Units for Solution Concentrations” (mass, volume and mass-volume percent, Example 3.23, density as the link), section 3.3 “Molarity” and section 3.1 (molar mass). Related: molarity calculator, dilution calculator, ppm calculator and grams to moles calculator.