Percentage Concentration to Molarity Calculator
ChemistryConvert percentage concentration (% w/v or % w/w) to molarity (mol/L) using molar mass and solution density. Essential for preparing solutions from commercial reagents.
37 %
%
1.19 g/mL
g/mL
36.46 g/mol
g/mol
Molarity (mol/L)
12.076
Molality (mol/kg)
0.161
Mass Fraction
0.37
What is a % Conc to Molarity?
The Percentage Concentration to Molarity Calculator converts the mass percent concentration (% w/w) printed on commercial reagent labels into the molar concentration (mol/L) required for stoichiometric laboratory calculations. It simultaneously computes molality (mol/kg solvent) and mass fraction โ three concentration expressions from a single data entry.
Commercial laboratory chemicals โ particularly concentrated acids and bases โ are universally labelled in % w/w because mass percent is stable under temperature changes and does not require knowledge of the molar mass. However, laboratory preparations, titrations, and reaction stoichiometry require molarity. A student or analyst receiving a bottle of "37% w/w HCl, density 1.19 g/mL" cannot directly use that label for a calculation requiring 12 mol/L HCl without the conversion this tool provides.
The key insight is that converting from % w/w to mol/L requires density โ the link between mass-based and volume-based concentration. For dilute aqueous solutions (density โ 1 g/mL), % w/w and % w/v are numerically close and molarity is approximately 10 ร % รท molar mass. For concentrated acids and bases with densities of 1.2โ1.8 g/mL, this approximation fails badly: 98% HโSOโ at density 1.84 g/mL is approximately 18.4 mol/L โ not 9.8 mol/L as the density-free approximation would give.
The default values in this calculator (37%, 1.19 g/mL, molar mass 36.46 g/mol) correspond exactly to concentrated hydrochloric acid โ one of the most commonly used reagents in Indian chemistry laboratories and the canonical example in B.Sc. and B.Pharm curricula. Use the Normality Calculator for the normality equivalent, and the Molarity Calculator to plan dilutions from this concentrated stock.
How to use this % Conc to Molarity calculator
- Locate the concentration information on your reagent bottle label or the Certificate of Analysis (CoA). Find the % w/w value and enter it in the Percentage Concentration (% w/w or % w/v) field.
- Find the density of the solution on the same label or in the SDS (Safety Data Sheet). Enter it in the Solution Density field in g/mL. Do not use 1.0 g/mL unless the label confirms it.
- Enter the molar mass of your solute in the Molar Mass of Solute field in g/mol. For HCl = 36.46, HโSOโ = 98.08, HNOโ = 63.01, NaOH = 40.00.
- Read the Molarity (mol/L) output โ this is your working stock concentration for stoichiometric calculations and dilution planning.
- Note the Molality (mol/kg) if you are performing colligative property calculations or working in a non-aqueous system where molality is the preferred unit.
- Use the Mass Fraction when plugging into thermodynamic or activity models that require dimensionless composition input. Cross-check with the PPM to Molarity Calculator if your target concentration is in ppm.
Formula & Methodology
Molarity from % w/w:Molarity (mol/L) = (% w/w ร ฯ ร 10) รท MMolality from % w/w:Molality (mol/kg) = (% w/w ร 10) รท (M ร (100 โ % w/w))Mass fraction:Mass Fraction = % w/w รท 100Where: -% w/w= mass percent of solute (g per 100 g solution) -ฯ= density of solution (g/mL) -M= molar mass of solute (g/mol) - The factor 10 converts (g per 100 g ร g/mL) to (g per L) Worked examples โ three common Indian lab reagents: | Reagent | % w/w | Density (g/mL) | Molar Mass (g/mol) | Molarity | |---|---|---|---|---| | HCl (conc.) | 37 | 1.19 | 36.46 | 12.08 mol/L | | HโSOโ (conc.) | 98 | 1.84 | 98.08 | 18.38 mol/L | | NHโOH (28% as NHโ) | 28 | 0.90 | 17.03 | 14.81 mol/L | Step-by-step for 98% HโSOโ:Molarity = (98 ร 1.84 ร 10) / 98.08 = 1,803.2 / 98.08 = 18.38 mol/L Molality = (98 ร 10) / (98.08 ร (100 โ 98)) = 980 / 196.16 = 5.0 mol/kg Mass Fraction = 98 / 100 = 0.98To prepare 1 mol/L HโSOโ from 18.38 mol/L concentrate: use the Molarity Calculator with Cโ = 18.38 mol/L, Cโ = 1 mol/L, and Vโ = your target volume. For 1 litre: Vโ = (1 ร 1,000) / 18.38 = 54.4 mL of concentrate to make up to 1,000 mL. Always add acid to water slowly and stir continuously โ never the reverse.
Frequently Asked Questions
Percentage concentration expresses the amount of solute as a fraction of the total solution mass (% w/w) or volume (% w/v), multiplied by 100. For laboratory reagents, % w/w (weight per weight) is the most common โ it means x grams of solute per 100 grams of solution. Commercial concentrated acids such as HCl, HโSOโ, and HNOโ are almost always labelled in % w/w because mass ratios are independent of temperature, unlike volume-based concentrations.
Molarity = (% w/w ร ฯ ร 10) รท M, where % w/w is the mass percent of the solute, ฯ is the density of the solution in g/mL, and M is the molar mass of the solute in g/mol. The factor of 10 converts g per 100 g into g per 1,000 mL (g/L) using the density, then divides by molar mass to get mol/L. For 37% w/w HCl (ฯ = 1.19 g/mL, M = 36.46 g/mol): Molarity = (37 ร 1.19 ร 10) / 36.46 โ 12.08 mol/L.
Percentage concentration (% w/w) is mass-based and density-independent, while molarity is volume-based. Density bridges the two: it converts grams of solute per 100 grams of solution into grams per litre of solution. For concentrated acids, density is significantly greater than 1 g/mL โ concentrated HโSOโ (98%) has ฯ โ 1.84 g/mL, meaning a given volume contains much more mass (and hence more moles) than an equal volume of water. An error in density of even 0.01 g/mL changes the calculated molarity by about 0.1%.
% w/w (weight per weight) is grams of solute per 100 grams of total solution. % w/v (weight per volume) is grams of solute per 100 mL of solution โ the unit commonly used in pharmacy for liquid medicines. For dilute aqueous solutions (density โ 1 g/mL), % w/w โ % w/v. For concentrated solutions or non-aqueous solvents, the two differ substantially. This calculator uses % w/w with the actual solution density and is more accurate than assuming % w/v for concentrated reagents.
Molarity (mol/L) measures moles of solute per litre of solution โ a volume-based measure that changes with temperature. Molality (mol/kg solvent) measures moles of solute per kilogram of solvent โ a mass-based measure that is temperature-independent. For dilute aqueous solutions the two are nearly equal, but they diverge significantly for concentrated solutions or non-aqueous solvents. Molality is preferred for colligative property calculations (boiling point elevation, freezing point depression) while molarity is used for stoichiometric reaction calculations.
Use % w/w when specifying a reagent for purchase or labelling a stock bottle โ most commercial suppliers label concentrated reagents this way because mass percent is stable under temperature fluctuations and does not require knowing the molar mass. Use molarity when performing stoichiometric calculations, titrations, or preparing solutions of specific molar concentration. This calculator converts the supplier's % w/w label into the molarity you need for laboratory use.
Solution density is printed on the reagent label or in the Safety Data Sheet (SDS) provided by the supplier. For common Indian laboratory reagents, approximate densities at 20ยฐC are: concentrated HCl (37%) โ 1.19 g/mL; HโSOโ (98%) โ 1.84 g/mL; HNOโ (70%) โ 1.42 g/mL; NaOH (50% w/w solution) โ 1.53 g/mL; NHโOH (28% as NHโ) โ 0.90 g/mL. Never use 1.0 g/mL as an approximation for concentrated acids โ the error can be 20โ80% in the calculated molarity.
Enter the percentage concentration from the reagent label in the 'Percentage Concentration (% w/w or % w/v)' field. Enter the solution density from the label or SDS in the 'Solution Density' field in g/mL. Enter the molar mass of the solute in the 'Molar Mass of Solute' field in g/mol. The calculator returns molarity (mol/L), molality (mol/kg solvent), and mass fraction simultaneously.
Standard laboratory-grade concentrated acids available from suppliers such as Merck, SD Fine-Chem, and Rankem in India have the following typical % w/w values: HCl (hydrochloric acid) โ 35โ37% w/w; HโSOโ (sulphuric acid) โ 95โ98% w/w; HNOโ (nitric acid) โ 68โ70% w/w; HClOโ (perchloric acid) โ 70โ72% w/w; HโPOโ (phosphoric acid) โ 85% w/w; CHโCOOH (glacial acetic acid) โ ~99.5% w/w. Always check the actual certificate of analysis for the batch-specific concentration before calculating.
Concentrated HCl is typically 37% w/w with density 1.19 g/mL, giving a molarity of approximately 12.08 mol/L. To prepare 1 mol/L HCl, the dilution factor is 12.08 โ meaning approximately 82.8 mL of concentrated HCl per litre of final solution. Use the [Molarity Calculator](/molarity-calculator/) or a dilution calculator to scale this. Always add acid to water slowly in a fume cupboard โ never water to acid โ to prevent violent exothermic splashing.
The calculator assumes % w/w input with a solution density. For % v/v solutions like 70% v/v ethanol, the calculation pathway differs โ you would need the density of the ethanol-water mixture at that specific concentration. If you treat 70% v/v as approximately equivalent to % w/w (which is only valid near density = 1 g/mL), you will get an approximate result. For precise work with % v/v alcohol solutions, use the actual mixture density for that volume fraction from a published table.
Molality (mol/kg solvent) = (% w/w ร 10) รท (M ร (100 โ % w/w)), where M is the molar mass in g/mol. This formula uses only % w/w and molar mass โ no density required โ because molality is already mass-based. For 37% w/w HCl: Molality = (37 ร 10) รท (36.46 ร 63) = 370 รท 2,297 โ 16.1 mol/kg solvent. Molality is higher than molarity for concentrated solutions because the denominator (solvent mass) is smaller than the solution volume in litres ร density.