Percentage Concentration to Molarity Calculator
Enter a percentage concentration and the calculator converts it to molarity (mol/L). Choose the percentage type (w/w, w/v, or v/v), pick a common reagent from the preset list or enter any molar mass manually, and add the solution density when needed. The reverse direction works too: type a known molarity to find the percentage concentration. Step-by-step working shows the full arithmetic with your numbers.
What is percentage concentration and why convert it to molarity?
Percentage concentration expresses how much solute is present in a solution as a fraction of the total, expressed as a percentage. Three variants are common in the laboratory. Weight-by-weight (w/w) gives grams of solute per 100 g of solution and is the standard form on bottle labels for concentrated mineral acids. Weight-by-volume (w/v) gives grams of solute per 100 mL of solution, which is the form used in most biological and pharmaceutical standards. Volume-by-volume (v/v) gives millilitres of solute per 100 mL of solution, most often used for alcohol mixtures. Molarity (M, mol/L) expresses concentration in moles per litre. Because most stoichiometric calculations involve moles, converting from a percentage to molarity is one of the first steps when preparing a reaction or a standard solution from a bottle-labelled reagent. For example, a 37% w/w hydrochloric acid bottle gives no hint of how many moles of HCl are in each litre until you run the calculation.
How to convert percentage concentration to molarity - the formula
The conversion depends on which percentage type you are working with. For w/v percentage: M = (p x 10) / Mm, where p is the percentage, Mm is the molar mass in g/mol, and the factor 10 converts "per 100 mL" to "per 1000 mL" (one litre). No density is required because the percentage already relates mass of solute to volume of solution. For w/w and v/v percentages: M = (p x density x 10) / Mm, where density is in g/mL. The density is needed to convert the mass-based fraction into a volume-based one. For v/v, use the density of the pure solute (not the mixture). The reverse direction is just algebra: p% = M x Mm / 10 for w/v, or p% = M x Mm / (density x 10) for w/w and v/v. Worked example - concentrated HCl: p = 37%, Mm = 36.46 g/mol, density = 1.19 g/mL. Molarity = (37 x 1.19 x 10) / 36.46 = 440.3 / 36.46 = 12.08, rounded to 12.1 mol/L. This matches the value on most reagent-grade HCl labels.
Molality and mass concentration as companion outputs
This calculator also reports two companion concentration measures. Mass concentration (g/L) is simply M x Mm, giving grams of solute per litre of solution. It is useful when gravimetric preparation is more convenient than volumetric. Molality (mol/kg solvent) is calculated from w/w percentage only: m = (p x 1000) / (Mm x (100 - p)). Unlike molarity, molality does not change with temperature because it is referenced to the mass of solvent rather than the volume of solution. It appears directly in equations for boiling point elevation and freezing point depression: delta-Tb = Kb x m x i and delta-Tf = Kf x m x i, where i is the van't Hoff factor and Kb, Kf are solvent constants.
When density matters and how to find it
The density of a solution increases with solute concentration, so using a density value for the wrong concentration can introduce significant error. For example, the density of sulfuric acid changes from 1.00 g/mL (pure water) to 1.84 g/mL (fuming, 98% H2SO4). Always match the density to the percentage concentration on the label. Density data can be found in standard reference tables such as the Merck Index, the CRC Handbook of Chemistry and Physics, or supplier safety data sheets. Preset values in this calculator are for typical concentrated reagent-grade solutions and may differ from your actual bottle. For precise work, measure the density of your batch using a calibrated pycnometer or densitometer.
Common laboratory reagents: typical concentration data
| Substance | Molar mass (g/mol) | Typical % (w/w) | Density (g/mL) | Approx. molarity (mol/L) |
|---|---|---|---|---|
| Hydrochloric acid (HCl) | 36.46 | 37 | 1.19 | 12.1 |
| Sulfuric acid (H2SO4) | 98.08 | 96 | 1.84 | 18.0 |
| Nitric acid (HNO3) | 63.01 | 70 | 1.51 | 16.8 |
| Phosphoric acid (H3PO4) | 97.99 | 85 | 1.69 | 14.7 |
| Acetic acid (CH3COOH) | 60.05 | 100 | 1.05 | 17.5 |
| Sodium hydroxide (NaOH) | 40.00 | 50 | 1.53 | 19.1 |
| Ammonia (NH3) | 17.03 | 28 | 0.90 | 14.8 |
| Hydrogen peroxide (H2O2) | 34.01 | 30 | 1.11 | 9.8 |
| Ethanol (C2H5OH) | 46.07 | 70 | 0.89 | 13.5 |
Density and molar mass values for concentrated reagent-grade solutions at approximately 20 degrees C. Exact values vary by manufacturer and temperature.
Frequently asked questions
Why do I need the solution density for w/w but not w/v?
A w/v percentage already connects mass of solute to volume of solution, so you can go straight to mol/L by dividing grams per 100 mL by molar mass and multiplying by 10. A w/w percentage only tells you the mass ratio. To reach molarity you need to know how many millilitres one gram of solution occupies, which is the inverse of the density. Without the density there is no way to express the result in units of moles per litre.
What units should the density be in?
Enter density in g/mL (which is the same numerical value as g/cm3). To convert from kg/m3, divide by 1000: for example, 1190 kg/m3 = 1.19 g/mL. Water at 20 degrees C has a density of approximately 0.998 g/mL, often rounded to 1.00 g/mL for dilute aqueous solutions.
What is the difference between molarity and molality?
Molarity (M) is moles of solute per litre of solution. Molality (m) is moles of solute per kilogram of solvent. Molarity changes with temperature because liquid volumes expand with heat, while molality is temperature-independent. Molality is used in colligative property equations (freezing point depression, boiling point elevation, osmotic pressure) and in precise thermodynamic calculations.
How do I use the result to make a dilute solution?
Use the dilution equation C1 x V1 = C2 x V2, where C1 is the stock molarity you calculated, V1 is the volume of stock you need to take, C2 is the target molarity, and V2 is the final solution volume. For example, to make 500 mL of 1.0 mol/L HCl from 12.1 mol/L stock: V1 = (1.0 x 500) / 12.1 = 41.3 mL of concentrated HCl, made up to 500 mL with water.
Is percentage concentration the same as parts per million (ppm)?
No. One percent (w/v) equals 10 000 ppm (mg/L) for dilute aqueous solutions. For very dilute solutions such as trace contaminants, ppm, ppb (parts per billion), or mg/L are more practical. Convert ppm to molarity using M = ppm / (Mm x 1000), where Mm is in g/mol and ppm is in mg/L.
What does normality mean and how does it relate to molarity here?
Normality (N, eq/L) is molarity multiplied by the number of equivalents per mole of solute, called the n-factor. For a simple monoprotic acid like HCl the n-factor is 1 so normality equals molarity. For sulfuric acid (H2SO4, which can donate two protons) the n-factor is 2 so a 1 mol/L solution has a normality of 2 eq/L. This calculator shows the n=1 normality as a reference; multiply by the actual n-factor for your compound.