Last updated: July 3, 2026
Percentage Concentration to Molarity Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Quick Answer
This calculator converts a mass percent solution to molarity with M = (10 × percent × density) / molarMass. Percent is entered as the label value such as 37 for 37% w/w, density is in g/mL, and molar mass is in g/mol. It also reports the intermediate mass concentration in g/L.
To convert mass percent to molarity, multiply ten by the percent and by the solution density in grams per millilitre, then divide by the solute molar mass in grams per mole.
Key Takeaways
- Mass percent to molarity requires percent, solution density, and solute molar mass.
- The working equation is M = (10 × percent × density) / molarMass.
- The factor 10 converts % w/w and g/mL density into grams per litre.
- A 37% w/w HCl solution at 1.19 g/mL is about 12.08 mol/L.
- Use density and assay values from the same certificate or label for accurate stock molarity.
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
M = (10 × percent × density) / molarMass
Where:
- M=Molarity or amount concentration(mol/L)
- % w/w=Mass percent of solute in solution(%)
- ρ=Solution density(g/mL)
- M_W=Molar mass of solute(g/mol)
- 10=Conversion factor from percent and g/mL to g/L(mL·% conversion)
Worked Examples
Concentrated hydrochloric acid
A typical reagent bottle lists hydrochloric acid as 37% w/w with density 1.19 g/mL.
- 1Convert percent and density to mass concentration: 10 × 37 × 1.19 = 440.3 g/L.
- 2Divide by molar mass: 440.3 g/L ÷ 36.46 g/mol.
- 3The molarity is about 12.08 mol/L.
Concentrated sulfuric acid
Commercial concentrated sulfuric acid is often near 98% w/w and density 1.84 g/mL.
- 1Mass concentration = 10 × 98 × 1.84 = 1803.2 g/L.
- 2Molarity = 1803.2 ÷ 98.079.
- 3The solution is approximately 18.39 mol/L.
Concentrated nitric acid
A 70% w/w nitric acid solution with density 1.42 g/mL is converted to molarity.
- 1Mass concentration = 10 × 70 × 1.42 = 994 g/L.
- 2Divide by molar mass: 994 ÷ 63.01.
- 3The molarity is approximately 15.77 mol/L.
Introduction
This percentage concentration to molarity calculator converts a mass percent (% w/w) reagent label into molarity using density and molar mass. It is designed for solutions such as concentrated hydrochloric acid, sulfuric acid, nitric acid, ammonia, and sodium hydroxide where labels often give percent by mass plus density. Use it with the molarity calculator for mole-per-litre work and the mass percent calculator when solute and solution masses are known directly. The terminology follows IUPAC amount concentration and mass fraction definitions.
What does the calculator convert?
The calculator converts percent by mass into amount concentration. A 37% w/w solution contains 37 g solute per 100 g of final solution. Density tells you how many grams of that solution occupy one millilitre, and molar mass converts grams of solute into moles.
Percent must be entered as the label number, for example 37 not 0.37.
Density is for the complete solution, not the pure solvent.
Molar mass must match the solute species on the label.
The final unit is mol/L, commonly written M.
Formula explained
The formula is M = (10 × percent × density) / molarMass. One litre of solution has mass 1000 × density grams. The solute mass is percent/100 of that mass, giving 10 × percent × density grams per litre. Dividing by molar mass changes grams per litre into moles per litre.
The factor 10 combines 1000 mL/L with the percent-to-fraction divisor of 100.
How to calculate molarity from % w/w
First read the mass percent and density from the reagent certificate, safety data sheet, or bottle label. Next find the molar mass from a reliable formula mass. Multiply 10 by percent and density to get g/L, then divide by molar mass. For 37% HCl at 1.19 g/mL, 10 × 37 × 1.19 = 440.3 g/L, and 440.3 ÷ 36.46 = 12.08 M.
Enter mass percent as a percent value.
Enter density in g/mL.
Enter molar mass in g/mol.
Read molarity and g/L together to check the conversion.
Relationship to mass percent, density, and g/L
Mass percent alone cannot determine molarity because it lacks volume information. Density supplies the missing mass-to-volume conversion. The calculator therefore also reports mass concentration in g/L. If you need to prepare a dilution from the concentrated stock, pair the molarity result with the dilution factor calculator or a C1V1 dilution workflow.
| Known data | Extra data needed | Result |
|---|---|---|
| % w/w only | density and molar mass | molarity |
| % w/w + density | molar mass | g/L and mol/L |
| g/L | molar mass | mol/L |
| mol/L | target volume | moles needed |
Practical reagent examples
Concentrated acid bottles commonly use percent by mass because the solution is made and certified by weight. Hydrochloric acid near 37% w/w and density 1.19 g/mL is about 12 M; sulfuric acid near 98% and density 1.84 g/mL is about 18.4 M; nitric acid near 70% and density 1.42 g/mL is about 15.8 M. Reference definitions for amount concentration and mass fraction explain the underlying quantities.
Use the density at the same temperature as the certificate or lab conditions when precision matters.
Accuracy, assumptions, and safety
The conversion assumes the percent is % w/w and the density applies to the same solution composition. It does not correct for temperature, impurities, assay uncertainty, or volume contraction after mixing. For regulated work, use certificate-of-analysis assay and density values, calibrated volumetric glassware, and uncertainty propagation. See the BIPM SI Brochure for unit conventions and NIST Chemistry WebBook for reference chemical data.
Do not treat % v/v or % m/v as % w/w.
Do not use pure-water density for concentrated acids.
Check whether the label gives assay, nominal concentration, or minimum purity.
Handle concentrated reagents with appropriate safety controls.
Quick Reference Card
Mass Percent to Molarity — Quick Reference
Quick reference • Percentage Concentration to Molarity Calculator
M = (10 × percent × density) / molarMassValid range: percent 0–100% w/w; density > 0 g/mL; molar mass > 0 g/mol
Common Values
⚠ Watch Out
- •Use % w/w only; % v/v and % m/v need different formulas.
- •Do not substitute water density for concentrated reagent density.
- •Molarity depends on temperature because solution volume and density change.
- •Check whether commercial acid assay is nominal, minimum, or certified.
- •Use the molar mass of the solute species, not the solvent or hydrate unless intended.
Pro Tips
- →Compute g/L first to sanity-check the conversion before dividing by molar mass.
- →Use certificate-of-analysis density for analytical standards.
- →Round final molarity according to the least precise input, often density or assay.
- →After finding stock molarity, use C1V1 or dilution factor calculations for working solutions.
- →Record density temperature with the calculated molarity in lab notebooks.
FAQs
How do I convert percent concentration to molarity?
For mass percent solutions, multiply 10 by the percent and the solution density in g/mL, then divide by the solute molar mass in g/mol: M = (10 × percent × density) / molarMass.
Why is density required?
Mass percent tells grams of solute per 100 g solution, while molarity needs moles per litre. Density converts the solution mass basis into a volume basis.
Should I enter 37 or 0.37 for 37% HCl?
Enter 37. The formula already includes the percent-to-fraction conversion through the factor 10.
Can I use this for volume percent solutions?
No. The formula is for % w/w solutions. Volume percent and mass/volume percent use different definitions and need different conversions.
What molarity is 37% hydrochloric acid?
Using density 1.19 g/mL and molar mass 36.46 g/mol, 37% w/w HCl is about 12.08 mol/L.
Why might my bottle value differ from the calculator?
Real bottles may have a certified assay, density at a specified temperature, and impurity limits. Use certificate values for high-accuracy analytical work.