This guide is for students learning about solutions in school science, anyone revising concentration calculations, and anyone preparing a solution in a lab or kitchen.
“Is the denominator the water or the whole solution?” “Is 20 g of salt in 100 g of water 20%?” “How do I convert mass percent to molarity?” Two ideas resolve most of the confusion: what the denominator is and which quantities you already know. This guide covers the definition, preparing solutions, mixing and evaporation, conversion to molarity, and a free calculator for checking your work.
The formula: the denominator is the whole solution
Mass percent is the percentage of the solution’s mass that is solute.
| Term | Meaning | Brine example |
|---|---|---|
| Solute | The substance that dissolves | Salt |
| Solvent | The liquid that does the dissolving | Water |
| Solution | Solute + solvent (the finished liquid) | Brine |
| Mass percent | Solute mass ÷ solution mass × 100 | e.g. 10% |
Mass percent (%) = mass of solute (g) ÷ mass of solution (g) × 100
The denominator is not the water. Dissolving 10 g of salt in 90 g of water gives a solution of 100 g, so the concentration is 10 ÷ 100 × 100 = 10%. Using 10 ÷ 90 × 100 = 11.1% is the classic mistake (OpenStax).
Example 1: 20 g of salt in 100 g of water
- Solution mass = 100 g + 20 g = 120 g
- Concentration = 20 ÷ 120 × 100 ≈ 16.7%
Reading “100 g of water” and answering 20% is the most common error. Always compute the solution mass as solute + solvent. In practice, solubility also limits how much dissolves: about 36 g of salt dissolves in 100 g of water at 20 °C, and the limit varies greatly between substances. Anything beyond the limit stays undissolved (solubility and saturation).
Example 2: preparing 200 g of 8% brine
Work backwards from the target mass and concentration.
- Solute = solution × percent ÷ 100 = 200 × 8 ÷ 100 = 16 g
- Water = solution − solute = 200 − 16 = 184 g
Dissolve 16 g of salt in 184 g of water so the finished mass is 200 g. Adding 16 g of salt to 200 g of water would give 216 g of solution at about 7.4% instead.
Example 3: mixing and evaporation
Mixing two solutions
Mix 100 g of 10% brine with 200 g of 5% brine. The total solute mass is unchanged.
- Solute A = 100 × 10 ÷ 100 = 10 g, solute B = 200 × 5 ÷ 100 = 10 g
- Solution = 100 + 200 = 300 g, solute = 20 g
- Concentration = 20 ÷ 300 × 100 ≈ 6.67%
The result is not the simple average of 10% and 5% (7.5%) because the larger mass pulls the concentration towards 5%. Only equal masses give a simple average.
Evaporating water
Evaporating 50 g of water from 200 g of 8% brine leaves the 16 g of solute behind while the solution falls to 150 g.
- Solute = 200 × 8 ÷ 100 = 16 g (unchanged)
- Solution = 200 − 50 = 150 g
- Concentration = 16 ÷ 150 × 100 ≈ 10.7%
Once the solution becomes saturated, further evaporation causes crystals to form instead of raising the concentration.
Example 4: converting to and from molarity
Mass percent is mass-based, while molarity is volume-based (mol/L), so the solution density and the solute molar mass are needed. Taking 1 L (1000 mL) of solution as the basis:
| Conversion | Formula | Variables |
|---|---|---|
| Mass % → molarity | c = 10wρ / M | w: mass percent (%), ρ: density (g/mL), M: molar mass (g/mol) |
| Molarity → mass % | w = cM / (10ρ) | c: molarity (mol/L) |
- 5% sodium chloride solution (density 1.033 g/mL, M = 58.44 g/mol): c = 10 × 5 × 1.033 ÷ 58.44 ≈ 0.884 mol/L
- 98% concentrated sulfuric acid (density 1.8 g/mL, M = 98 g/mol): c = 10 × 98 × 1.8 ÷ 98 = 18 mol/L
- 12 mol/L concentrated hydrochloric acid (density 1.20 g/mL, M = 36.5 g/mol): w = 12 × 36.5 ÷ (10 × 1.20) = 36.5%
Density varies with temperature and concentration, so use a measured value for accurate work. Dilution calculations (C₁V₁ = C₂V₂) are covered in the molarity and dilution guide.
Common mistakes
- Using the solvent mass as the denominator: 10 g of salt in 90 g of water is 10 ÷ 100 × 100 = 10%, not 10 ÷ 90 × 100 = 11.1%
- Adding 16 g of salt to 200 g of water for 8%: the solution becomes 216 g at about 7.4%; the target mass is the solution mass
- Averaging mixed concentrations: different masses do not average simply
- Confusing mass and volume percent: mass percent is w/w; v/v and w/v are different definitions
- Skipping density when converting to molarity: mass percent to mol/L requires density
- Ignoring solubility: solute beyond the limit precipitates, so the calculated concentration is not reached
Check your work with the calculator
The Tools Hub mass percent calculator mirrors the examples above across three modes.
Examples 1 and 2
With the type set to "Basics (solute, solvent, solution)", press "10 g salt + 90 g water" to get 10%, solution 100 g, solute 10 g and solvent 90 g. Switch "What you know" to "Solution mass and target percent" and press "Make 200 g of 8% brine" to get 16 g of salt and 184 g of water.
Example 3 (mixing and evaporation)
Select "Mixing, adding water, evaporation" and press "10% 100 g + 5% 200 g" to get 6.667%. Press "Evaporate 50 g from 8%" to see 10.67% with the water change set to −50. Positive water values add water; negative values evaporate it.
Example 4 (molarity conversion)
Choose "Mass percent ↔ molarity" and press "5% NaCl → molarity" to get 0.8838 mol/L from density 1.033 g/mL and molar mass 58.44 g/mol. "12 mol/L HCl → mass %" gives 36.5%. The direction selector switches the conversion.
Tool used in this guide
Mass Percent Concentration Calculator
Work out concentrations, prepare solutions, mix or evaporate them, and convert to molarity with the working shown. Free, no sign-up, and everything runs in your browser.
Applicability and limits
- Mass percent is a mass (w/w) basis. Volume percent (v/v) and mass/volume percent (w/v) are different definitions
- Because it is mass-based, the value does not change with temperature (volume-based molarity does)
- If the solute cannot all dissolve, the excess precipitates and the calculated concentration is not reached; saturated solutions also shift with temperature
- When a reaction occurs, or when using hydrates such as CuSO₄·5H₂O, count the solute mass according to the actual composition
- Density used for molarity conversion varies with temperature and concentration; use measured values for accurate work
FAQ
What is the denominator in mass percent?
The total mass of the solution (solute + solvent). For 10 g of salt in 90 g of water the denominator is 100 g, giving 10%. Using 90 g gives 11.1%, which is wrong.
What percentage is 20 g of salt in 100 g of water?
20 ÷ (100+20) × 100 ≈ 16.7%, not 20%. Whether all of it dissolves depends on solubility, which varies with substance and temperature.
How much salt and water do I need for 200 g of 8% brine?
16 g of salt and 184 g of water. Use solute = solution × percent ÷ 100 and water = solution − solute. Adding 16 g of salt to 200 g of water would give 216 g of solution, not 8%.
When do I use mass percent rather than molarity?
Mass percent is common for preparation, product labels and school science. For stoichiometry, molarity (mol/L) is usually more convenient. Converting between them needs density and molar mass.
Is the concentration after mixing a simple average?
Only when the masses are equal. In general it is total solute ÷ total solution × 100, so the result moves towards the concentration of the larger mass.
Can evaporation raise the concentration indefinitely?
No. The solute does not evaporate, but once saturation is reached the excess precipitates instead of raising the concentration. Check the solute’s solubility and the temperature.
How this guide was checked
On 6 October 2026 the definition and formulas were checked against the sources above, and the examples were recalculated by hand (10 g salt in 90 g water giving 10%, 20 g in 100 g water giving about 16.7%, 200 g of 8% brine needing 16 g salt and 184 g water, 10% 100 g plus 5% 200 g giving about 6.67%, evaporating 50 g from 8% giving about 10.7%, 5% NaCl giving 0.8838 mol/L, 98% H₂SO₄ giving 18 mol/L and 12 mol/L HCl giving 36.5%). The examples are teaching calculations, not measurements. The calculator inputs and outputs were also verified.
