Percentage concentration to molarity calculator
Convert mass percentage and solution density into molarity, or solve the same relationship in reverse.
Inputs
Live result
Calculation basis
| Step | Value | Unit |
|---|---|---|
| Mass of 1 L solution | 1,100.00 | g |
| Mass of solute | 110.00 | g |
| Amount of solute | 1.8823 | mol |
| Molarity | 1.8823 | mol/L |
How to use this percentage concentration to molarity calculator
What this calculator does
This calculator converts between mass percentage concentration and molarity when the solution density and the solute's molar mass are known. It treats percentage as mass percent, written % w/w: grams of solute per 100 grams of solution. Molarity is amount concentration in moles per liter of final solution. The tool is useful for preparing laboratory solutions, translating a supplier specification into a molar concentration, checking textbook exercises, and comparing concentration labels that use different units. It does not determine density, identify an unknown compound, account for chemical reaction, or replace a measured certificate of analysis.
When to use it
Use it when a reagent bottle reports mass percent but an experiment protocol requires mol/L; when a formulation sheet gives molarity but quality control uses % w/w; when checking whether a dilution starts from the expected stock concentration; or when teaching how density connects a mass-based fraction to a volume-based concentration. The underlying definition of amount concentration is described in the IUPAC Gold Book entry for amount concentration.
How to calculate
The calculator opens with a complete demonstration using sodium chloride, a molar mass of 58.44 g/mol, density of 1.10 g/mL, and 10.00% w/w. A validated example workbook is immediately available through Download Excel. To use your own data:
- Choose Solve for: Molarity or Percentage concentration.
- Select a Solute preset or choose Custom molar mass.
- Enter the Molar mass in g/mol and the Density of solution in g/mL.
- Enter either Percentage concentration in % w/w or Molarity in mol/L, depending on the selected mode.
- Read the primary result, the one-liter calculation basis, and the step table. Select Download Excel to export the current typed inputs and outputs.
Reset clears the demonstration and all calculated content. Download Excel is then disabled until a complete valid state is entered again.
Input guide
Solve for is required and selects the unknown. Choose Molarity when percentage is known; choose Percentage concentration when molarity is known. Solute is a convenience selector. A preset supplies a standard molar mass, while Custom molar mass lets you type another compound. Molar mass is required, must be a positive decimal in g/mol, and may be entered as 58.44. A common error is entering molecular mass in kilograms per mole without converting it to g/mol.
Density of solution is required and must be positive. Enter it in g/mL, for example 1.10. Because 1 g/mL equals 1,000 g/L, the calculator converts it internally. Do not enter the density of the pure solute unless it is also the density of the final solution. Percentage concentration is required in molarity mode, accepts a decimal from 0 through 100, and represents % w/w. A value of 10 means 10 g solute per 100 g solution, not 10 g per 100 mL. Molarity is required in percentage mode, accepts a nonnegative decimal in mol/L, and may be entered as 1.8823. Scientific notation and decimal commas are rejected to avoid ambiguous parsing.
Output guide
Molarity or Percentage concentration is the primary result. Molarity is an estimated conversion in mol/L; percentage is an estimated mass fraction expressed as % w/w. Solution mass in 1 L is density multiplied by 1,000 mL. Solute mass in 1 L applies the mass percentage to that solution mass. Amount of solute divides solute mass by molar mass. The Calculation basis table repeats these values in order. Zero percentage or zero molarity produces zero solute and zero converted concentration; unusually high results should prompt a check of density, units, and whether the stated percentage is truly w/w.
Worked example
For the startup example, one liter of solution has a mass of 1.10 g/mL × 1,000 mL = 1,100 g. At 10.00% w/w, the solute mass is 1,100 × 0.10 = 110 g. Dividing by the sodium chloride molar mass gives 110 ÷ 58.44 = 1.8823 mol. Because the basis is one liter, the displayed molarity is exactly 1.8823 mol/L at four decimals. This matches the initial result, table, and workbook.
Formula and interpretation
With density expressed in g/mL, the calculator first multiplies density by 1,000 to obtain g/L. The forward conversion is molarity = percentage × density(g/L) ÷ (molar mass × 100). The reverse conversion is percentage = molarity × molar mass × 100 ÷ density(g/L). The relationship follows the standard definition of mass percentage, summarized by LibreTexts' units of concentration overview, and the mole is grounded in the exact Avogadro constant described by NIST's SI amount-of-substance guidance.
Practical cautions
Temperature matters because solution density can change with temperature. Use density measured or specified at conditions close to your application. Also distinguish % w/w from % w/v and % v/v; they are different concentration definitions and cannot be substituted without additional information. For corrosive, toxic, or reactive materials, use the supplier's safety data and laboratory procedures rather than relying on a concentration conversion alone.