# What is the concentration?

Computes the concentration of a solution as molarity, grams per litre, % w/v, mass percent, ppm, ppb and molality from the solute mass, its molar mass and the solution volume or mass.

- Page: https://www.acalculator.org/chemistry/concentration-calculator
- JSON spec: https://www.acalculator.org/chemistry/concentration-calculator.json
- Version: 02e7cbdebd3d

## Default answer

Example with the default inputs (Mass of solute 25.2 g, Molar mass of solute (g/mol) 60.052, I know the solution’s Volume, Volume of solution 0.5 L, Density of solution 1 g/mL): 25.2 g of solute in 500 mL of solution is 0.839273 mol/L (5.04% by mass).

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| m | Mass of solute | The mass of the substance dissolved. |
| mm | Molar mass of solute (g/mol) | The mass of one mole of the solute, in grams per mole: 58.44 for sodium chloride. |
| by | I know the solution’s | Whether you know the volume or the mass of the whole solution. |
| v | Volume of solution | The volume of the whole solution (solute and solvent together). |
| ms | Mass of solution | The mass of the whole solution (solute and solvent together). |
| d | Density of solution | The density of the whole solution; dilute water solutions are close to 1 g/mL. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| molarity | Molarity | Moles of solute per litre of solution (mol/L, M). |
| gramsPerLiter | Mass concentration | Grams of solute per litre of solution (equal to mg/mL). |
| wv | Mass/volume percent | Grams of solute per 100 mL of solution (% w/v). |
| ww | Mass percent | Mass of solute ÷ mass of solution × 100 (% w/w). |
| ppm | Parts per million | Mass of solute ÷ mass of solution × 1,000,000. |
| ppb | Parts per billion | Mass of solute ÷ mass of solution × 1,000,000,000. |
| molality | Molality | Moles of solute per kilogram of solvent (solution mass − solute mass). |
| moles | Moles of solute | Mass of solute ÷ molar mass. |
| solutionMass | Mass of solution | Volume × density, or the mass you typed. |
| solutionVolume | Volume of solution | The volume you typed, or mass ÷ density. |

## Method

moles = mass ÷ molar mass; molarity = moles ÷ litres; g/L = grams ÷ litres; % w/v = grams ÷ mL × 100; mass percent = solute mass ÷ solution mass × 100; ppm = × 10⁶; ppb = × 10⁹; molality = moles ÷ (solution kg − solute kg).

## Assumptions

- The solution mass is volume × density (or the mass you type); its volume is mass ÷ density when you type the mass.
- Dilute water solutions have a density close to 1 g/mL, the default.
- Molality uses the solvent mass: the solution mass less the solute mass.

## Worked examples

1. m = 0.0252, mm = 60.052, by = volume, v = 0.0005, d = 1,000 gives molarity = 0.839273, gramsPerLiter = 50.4, wv = 5.04, molality = 0.883817. Source: OpenStax Chemistry 2e, section 3.3, Molarity, Example 3.16: 25.2 g of acetic acid (60.052 g/mol) in 0.500 L is 0.839 M (https://openstax.org/books/chemistry-2e/pages/3-3-molarity, retrieved 2026-10-01).
2. m = 0.000004, mm = 180.156, by = mass, ms = 0.005, d = 1,000 gives ww = 0.075, ppm = 750. Source: OpenStax Chemistry 2e, section 3.4, Other Units for Solution Concentrations, Example 3.22: 3.75 mg of glucose in 5.0 g is 0.075% by mass (https://openstax.org/books/chemistry-2e/pages/3-4-other-units-for-solution-concentrations, retrieved 2026-10-01).
3. m = 0, mm = 207.2, by = volume, v = 0.0003, d = 1,000 gives ppb = 15, ppm = 0.015. Source: OpenStax Chemistry 2e, section 3.4, Example 3.25: 15 ppb of lead in 300 mL of water (density ~1.00 g/mL) is 4.5 µg (https://openstax.org/books/chemistry-2e/pages/3-4-other-units-for-solution-concentrations).

## FAQ

### How do I calculate the concentration of a solution?

It depends on the unit. Molarity is moles of solute per litre of solution: 25.2 g of acetic acid (60.052 g/mol) is 0.41964 mol, and in 0.500 L that is 0.839 mol/L. Mass percent is the solute mass divided by the solution mass, times 100.

### What is the difference between molarity and molality?

Molarity divides the moles of solute by the litres of solution. Molality divides them by the kilograms of solvent, which is the solution mass less the solute mass. Molality does not change with temperature, because it uses masses only.

### How do I calculate mass percent?

Divide the mass of solute by the mass of the whole solution and multiply by 100. 3.75 mg of glucose in a 5.0 g sample is 0.00375 ÷ 5.0 × 100 = 0.075%.

### What does ppm mean?

Parts per million by mass: the solute mass divided by the solution mass, times 1,000,000. For water at about 1 g/mL, 1 ppm is about 1 mg per litre. 4.5 µg of lead in 300 mL of water is 15 ppb, or 0.015 ppm.

### What is % w/v?

Mass/volume percent: grams of solute per 100 mL of solution. Saline at 0.9% w/v has 0.9 g of sodium chloride in every 100 mL.

### Why does the calculator ask for density?

Mass percent, ppm, ppb and molality need the mass of the solution, and molarity needs its volume. The density converts one to the other. Dilute water solutions are close to 1 g/mL, the default.

## Sources

- OpenStax, Chemistry 2e, section 3.3, Molarity (M = mol solute ÷ L solution; Example 3.16), CC BY 4.0, retrieved 2026-10-01. https://openstax.org/books/chemistry-2e/pages/3-3-molarity
- OpenStax, Chemistry 2e, section 3.4, Other Units for Solution Concentrations (mass percentage, mass-volume percentage, ppm, ppb; Examples 3.22 and 3.25), CC BY 4.0, retrieved 2026-10-01. https://openstax.org/books/chemistry-2e/pages/3-4-other-units-for-solution-concentrations