Molarity from Density Calculator
When working with concentrated reagents supplied by mass percent (w/w%), you need to convert to molarity (mol/L) to prepare dilutions accurately. This calculator uses the standard formula M = 10 x (mass%) x density / molar mass. For example, concentrated hydrochloric acid is sold as 37% HCl with a density of 1.19 g/mL; entering these values with the molar mass of HCl (36.46 g/mol) gives approximately 12.1 M. Enter the mass percent from the reagent label, the solution density in g/mL, and the molar mass of the solute to get the molarity.
Molarity from density formula
M = (10 x mass% x density) / molar mass
Where mass% is the weight percent (g solute per 100 g solution), density is in g/mL, and molar mass is in g/mol. The result is molarity in mol/L. This formula appears in standard analytical chemistry texts and is consistent with IUPAC definitions.
Common concentrated reagent molarities
- Concentrated HCl: 37 w/w%, density 1.19 g/mL, MW 36.46 g/mol, approximately 12.1 M.
- Concentrated H2SO4: 98 w/w%, density 1.84 g/mL, MW 98.08 g/mol, approximately 18.4 M.
- Concentrated HNO3: 70 w/w%, density 1.42 g/mL, MW 63.01 g/mol, approximately 15.8 M.
- Concentrated NH3 (aq): 28 w/w%, density 0.90 g/mL, MW 17.03 g/mol, approximately 14.8 M.
- Acetic acid (glacial): 100 w/w%, density 1.05 g/mL, MW 60.05 g/mol, approximately 17.5 M.
Molarity from density: frequently asked questions
What is the molarity from density formula?
M = (10 x mass% x density) / molar mass. Here mass% is the weight percent of solute, density is in g/mL, and molar mass is in g/mol. The factor 10 converts g per 100 g solution to moles per litre.
Why is the factor 10 in the formula?
The mass fraction (w/w %) gives grams of solute per 100 g solution. To get per litre: multiply by density (g/mL) to get g solute per 100 mL, then multiply by 10 to get per 1000 mL (1 L), then divide by molar mass to convert grams to moles.
What are typical concentrated acid molarities?
Concentrated HCl (37 w/w%, density 1.19 g/mL, MW 36.46) is approximately 12.1 M. Concentrated H2SO4 (98 w/w%, density 1.84 g/mL, MW 98.08) is approximately 18.4 M. Concentrated HNO3 (70 w/w%, density 1.42 g/mL, MW 63.01) is approximately 15.8 M.
How do I find density and mass percent on a reagent bottle?
Commercial reagent bottles list density (specific gravity) and assay (w/w%) on the label or in the SDS sheet. NIST and ASTM maintain reference tables for common solutions. Use the values from the actual lot certificate for greatest accuracy.
Can I use this for aqueous bases like NaOH?
Yes. Enter the mass percent and density of the NaOH solution from its SDS, along with the molar mass of NaOH (40.00 g/mol), to get the molarity of the solution.
Official sources
- NIST Chemistry WebBook: Thermophysical properties of solutions.
- IUPAC: Quantities, Units and Symbols in Physical Chemistry (Green Book).
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.