Concentration describes how much of a substance is dissolved in a given amount of solution, but chemists, pharmacists and engineers use many different measures for it. Molarity (mol/L) is the workhorse of the laboratory, mass percent (w/w) is used for commercial acids and alloys, mass/volume percent (w/v) is common in medicine (0.9% saline is 0.9 g NaCl per 100 mL), molality is preferred when temperature changes, and ppm suits trace amounts.
Converting between these units needs two extra facts. The molar mass links grams and moles, and the density of the solution links its volume and its mass. With both, any measure can be converted to any other: for example, concentrated hydrochloric acid labelled 37% w/w with a density of 1.18 g/mL is about 12 M. The calculator assumes the solvent is water when it reports molality, mass of solute per 100 g water and mole fraction.
Choose what you know – the solute mass and solution volume, the solute and solvent masses, a molarity or a mass percent – and the calculator fills in the rest.
How to use the Solution Concentration Calculator
- I know
- Mass of solute
- Volume of solution
- Mass of solvent
- Molarity
- Mass percent
- Mass/volume percent
- Molar mass of the solute — NaCl 58.44, glucose 180.16, H₂SO₄ 98.08, HCl 36.46 g/mol.
- Density of the solution — About 1 g/mL for dilute water solutions.
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Every starting point is first turned into two base quantities: the mass concentration (g of solute per litre of solution) and the mass fraction w. Density links the two (w = ρ ÷ (1,000·d)), and the molar mass converts grams to moles for molarity, molality and mole fraction.
Worked example
Dissolve 20 g of NaCl (58.44 g/mol) and make up to 250 mL; the solution density is 1.05 g/mL. Mass concentration = 20 / 0.250 = 80 g/L, so molarity = 80 / 58.44 = 1.369 M and w/v = 8.0%. The solution mass is 250 × 1.05 = 262.5 g, so w/w = 20 / 262.5 = 7.62%. The water mass is 242.5 g, giving 8.25 g NaCl per 100 g water and a molality of 0.342 mol / 0.2425 kg = 1.41 mol/kg.
Going the other way, 3 M NaCl with density 1.116 g/mL contains 175.3 g/L, which is 15.7% w/w and 18.6 g per 100 g water.
Commercial concentrated reagents
| Reagent | Typical % w/w | Density (g/mL) | Approx. molarity |
|---|---|---|---|
| Hydrochloric acid | 37% | 1.18 | 12.0 M |
| Sulfuric acid | 96% | 1.84 | 18.0 M |
| Nitric acid | 70% | 1.41 | 15.7 M |
| Acetic acid (glacial) | 99.7% | 1.05 | 17.4 M |
| Ammonia solution | 28% NH₃ | 0.90 | 14.8 M |
Molarities calculated with c = 10·d·w%/M; check the label of your bottle, as strengths vary by grade.
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 |
|---|---|
| I know | Choose one: Mass of solute and volume of solution, Mass of solute and mass of solvent, Molarity, Mass percent (w/w) … |
| Mass of solute | Units: g, mg, µg, kg, oz, lb |
| Volume of solution | Units: L, mL, µL, m³, dm³, cm³ … |
| Mass of solvent | Units: g, mg, µg, kg, oz, lb |
| Molarity | Units: mol/L (M), mmol/L (mM), µmol/L (µM), nmol/L (nM), mol/m³ |
| Mass percent | In % |
| Mass/volume percent | In % |
| Molar mass of the solute | Units: g/mol, kg/mol, Da (u), kDa. NaCl 58.44, glucose 180.16, H₂SO₄ 98.08, HCl 36.46 g/mol. |
| Density of the solution | Units: g/mL, g/cm³, kg/m³, kg/L, lb/ft³. About 1 g/mL for dilute water solutions. |
What each result means
- Molarity = [gL]÷[Molar mass of the solute]
- Mass percent (w/w) = ([w])×100
- Mass/volume percent (w/v) = [gL]÷10
- Mass concentration = [gL]
- Molality (water as solvent) = [w]÷((1 – [w])×[Molar mass of the solute])×1000
- Solute per 100 g of water = [w]÷(1 – [w])×100
- Parts per million (w/w) = [w]×1e6
- Mole fraction of solute (water as solvent) = ([w]÷[Molar mass of the solute])÷(([w]÷[Molar mass of the solute]) + (1 – [w])÷18.015)
Formula
Mass concentration ρ = m_solute ÷ V · Molarity c = ρ ÷ M · w/v % = m ÷ V(mL) × 100 · wt % = m_solute ÷ m_solution × 100 = c·M ÷ (10·d) · molality b = w ÷ ((1 − w)·M) · g per 100 g water = w ÷ (1 − w) × 100Worked example
Inputs — I know: Mass of solute and volume of solution; Mass of solute: 20 g; Volume of solution: 0.25 L; Molar mass of the solute: 58.44 g/mol; Density of the solution: 1.05 g/mL.
Results — Molarity = 1.3689 mol/L (M); Mass percent (w/w) = 7.619 %; Mass/volume percent (w/v) = 8 %; Mass concentration = 80 g/L; Molality (water as solvent) = 1.4113 mol/kg; Solute per 100 g of water = 8.247 g; Parts per million (w/w) = 76,190 ppm; Mole fraction of solute (water as solvent) = 0.02479; Check = Consistent.
Key terms
- Molarity (M)
- Moles of solute per litre of solution.
- Mass percent (w/w)
- Grams of solute per 100 g of solution.
- Mass/volume percent (w/v)
- Grams of solute per 100 mL of solution.
- Molality (b)
- Moles of solute per kilogram of solvent.
- Mole fraction (x)
- Moles of solute divided by total moles of all components.
Frequently asked questions
How do I calculate molarity from grams?
Divide the mass by the molar mass to get moles, then divide by the solution volume in litres. 20 g NaCl in 250 mL: 20 / 58.44 = 0.342 mol, / 0.250 L = 1.37 M.
How do I convert molarity to mass percent?
wt % = c × M / (10 × d), with c in mol/L, M in g/mol and d in g/mL. For 3 M NaCl with d = 1.116 g/mL: 3 × 58.44 / 11.16 = 15.7%.
How do I convert mass percent to molarity?
c = 10 × d × wt % / M. Concentrated HCl (37%, 1.18 g/mL): 10 × 1.18 × 37 / 36.46 ≈ 12.0 M.
What is the difference between w/w and w/v percent?
w/w is grams of solute per 100 g of solution; w/v is grams per 100 mL of solution. They are equal only when the density is 1 g/mL.
What is the difference between molarity and molality?
Molarity is moles per litre of solution; molality is moles per kilogram of solvent. Molality does not change with temperature because it uses masses only.
Why do I need the density?
Density turns a volume of solution into a mass. Without it you cannot convert between volume-based units (molarity, w/v) and mass-based ones (w/w, molality).
What does 0.9% saline mean?
0.9 g NaCl per 100 mL of solution (w/v), which is 9 g/L or about 0.154 M.