Concentrated acids, bases and many lab reagents are sold with a mass percentage on the label – 37% hydrochloric acid, 96% sulfuric acid, 28% ammonia – but most calculations in the lab need molarity, the number of moles of solute in one litre of solution. Converting between the two needs one extra piece of information: the density of the solution, because a percentage tells you mass of solute per mass of solution while molarity is per volume.
The conversion is short. One litre of solution weighs 1000 × ρ grams; w% of that is solute; dividing by the molar mass turns grams into moles. That gives c = w% × ρ × 10 ÷ M. Working the other way, multiply molarity by the molar mass to get grams per litre, then divide by the mass of a litre of solution.
This calculator also gives the mass concentration in g/L, the molality (moles per kilogram of solvent, which does not change with temperature) and the mole fraction of the solute when the solvent is water – handy for colligative property and vapour pressure problems.
How to use the Percentage Concentration to Molarity Calculator
- Convert
- Solute
- Molar mass of the solute
- Density of the solution
- Percentage concentration (w/w)
- Molarity
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose the solute (or enter its molar mass), enter the density of the solution and either the percentage or the molarity. The calculator converts the percentage to a mass fraction, multiplies by the mass of one litre of solution to get grams of solute per litre, and divides by the molar mass. Use the density of the solution, not of the pure solute.
Worked example
Concentrated hydrochloric acid is 37% HCl by mass with a density of 1.19 g/mL. One litre weighs 1190 g, of which 37% – 440.3 g – is HCl. Dividing by 36.458 g/mol gives 12.08 mol/L. The remaining 749.7 g is water, so the molality is 12.08 ÷ 0.7497 ≈ 16.11 mol/kg, and the mole fraction of HCl is 0.0101 ÷ (0.0101 + 0.0350) ≈ 0.225 (per gram of solution). To make 1 L of 1 M HCl you need 1000 ÷ 12.08 ≈ 82.8 mL of the concentrate.
Common concentrated reagents
Typical commercial concentrations and densities at about 20 °C (check your own bottle – grades differ):
| Reagent | Typical % (w/w) | Density (g/mL) | Molarity | Volume for 1 L of 1 M |
|---|---|---|---|---|
| Hydrochloric acid | 37% | 1.19 | 12.08 M | 82.8 mL |
| Sulfuric acid | 96% | 1.84 | 18.01 M | 55.5 mL |
| Nitric acid | 70% | 1.41 | 15.66 M | 63.8 mL |
| Glacial acetic acid | 99.7% | 1.049 | 17.42 M | 57.4 mL |
| Ammonia solution | 28% | 0.9 | 14.80 M | 67.6 mL |
| Phosphoric acid | 85% | 1.685 | 14.62 M | 68.4 mL |
| Hydrogen peroxide | 30% | 1.11 | 9.79 M | 102.1 mL |
| Sodium hydroxide solution | 50% | 1.52 | 19.00 M | 52.6 mL |
Tips
- Use the final volume of the solution, not the volume of solvent added, for molarity.
- For dilutions, C₁V₁ = C₂V₂ only holds when both concentrations use the same unit.
- Add acid to water, never water to acid.
- Everything is calculated in your browser.
Common mistakes to avoid
- Mixing w/w, w/v and v/v percentages.
- Forgetting that pH is logarithmic – one unit is a tenfold change in [H⁺].
- Using pKa where Ka is asked for (or the other way round).
Inputs explained
| Field | What to enter |
|---|---|
| Convert | Choose one: Percentage (w/w) → molarity, Molarity → percentage (w/w) |
| Solute | Choose one: Hydrochloric acid – HCl (36.458 g/mol), Sulfuric acid – H₂SO₄ (98.072 g/mol), Nitric acid – HNO₃ (63.012 g/mol), Phosphoric acid – H₃PO₄ (97.994 g/mol) … |
| Molar mass of the solute | Units: g/mol, kg/mol, Da (u), kDa |
| Density of the solution | Units: g/mL, g/cm³, kg/m³, kg/L, lb/ft³ |
| Percentage concentration (w/w) | In % |
| Molarity | Units: mol/L (M), mmol/L (mM), µmol/L (µM), nmol/L (nM), mol/m³ |
What each result means
- Molarity = [Mass fraction]×[Density of the solution]×1000÷[Molar mass used]
- Percentage concentration (w/w) = [Mass fraction]×100
- Mass concentration = [Mass fraction]×[Density of the solution]×1000
- Mole fraction of solute (water as solvent) = ([Mass fraction]÷[Molar mass used])÷(([Mass fraction]÷[Molar mass used]) + (1 – [Mass fraction])÷18.015)
- Volume needed to make 1 L of 1 M = [Molar mass used]÷([Mass fraction]×[Density of the solution]×1000)
Formula
Molarity c = (w% × ρ × 10) ÷ M (ρ in g/mL, M in g/mol)w% = c × M ÷ (10 × ρ)Molality b = (w/M) ÷ (1 − w) × 1000 (w as a fraction)Worked example
Inputs — Convert: Percentage (w/w) → molarity; Solute: Hydrochloric acid – HCl (36.458 g/mol); Density of the solution: 1.19 g/mL; Percentage concentration (w/w): 37 %.
Results — Molar mass used = 36.458 g/mol; Molarity = 12.0769 mol/L (M); Mass concentration = 440.3 g/L; Molality (mol per kg of solvent) = 16.109 mol/kg; Mole fraction of solute (water as solvent) = 0.22493; Volume needed to make 1 L of 1 M = 0.0828 L.
Key terms
- Mass percentage (w/w)
- Grams of solute in 100 g of solution.
- Molarity (M)
- Moles of solute per litre of solution.
- Molality (m)
- Moles of solute per kilogram of solvent.
- Density (ρ)
- Mass of one millilitre of the solution, in g/mL.
- Molar mass (M)
- Mass of one mole of the substance, in g/mol.
Frequently asked questions
How do I convert 37% HCl to molarity?
With a density of 1.19 g/mL: 37 × 1.19 × 10 ÷ 36.458 = 12.08 M. Concentrated hydrochloric acid is therefore about 12 M.
What is the molarity of 96% sulfuric acid?
With density 1.84 g/mL and M = 98.072 g/mol, c = 96 × 1.84 × 10 ÷ 98.072 ≈ 18.0 M.
Why do I need the density?
A percentage compares masses, molarity compares moles with volume. The density links the mass of solution to its volume.
Is this for w/w or w/v percent?
For w/w (mass of solute per 100 g of solution), the way reagent bottles are labelled. For w/v percent (g per 100 mL) you do not need density: molarity = w/v% × 10 ÷ M.
What is the percentage of a 1 M NaOH solution?
Taking a density of about 1.04 g/mL: 1 × 39.997 ÷ (10 × 1.04) ≈ 3.85% w/w.
What is the difference between molarity and molality?
Molarity is moles per litre of solution and changes slightly with temperature; molality is moles per kilogram of solvent and does not.
Where do I find the density?
On the supplier's label or safety data sheet, or in density tables such as the CRC Handbook, which list density against concentration for common solutions.
What formula does the Percentage Concentration to Molarity Calculator use?
Molarity c = (w% × ρ × 10) ÷ M (ρ in g/mL, M in g/mol).