# Dilution and molarity calculator

> Solve C₁V₁ = C₂V₂ for any dilution variable, get molarity, % w/v and ppm from a weighed mass, the mass to weigh for a solution, or molality.

Interactive version: https://www.calcopenly.com/science/dilution-concentration-calculator
Subject: Science calculators

Diluting a solution leaves the moles of solute unchanged, so C₁V₁ = C₂V₂: stock concentration times stock volume equals final concentration times final volume. Enter any three and the fourth follows, with the solvent to add and the dilution factor C₁/C₂. The other modes turn a weighed mass into molarity (n = m/M, c = n/V), % w/v and mg/L, give the mass to weigh for a target molarity, or find molality per kilogram of solvent.

The default makes 250 mL of 0.1 mol/L from a 1 mol/L stock: measure 25 mL of stock and make it up to 250 mL, a tenfold dilution.

Volumes of mixed liquids do not always add exactly, so make up to the final volume in a volumetric flask rather than adding the calculated solvent volume. The ppm figure is mg per litre of solution, which equals mg/kg only for dilute water-based solutions.

## Inputs

- **Calculate** (options: Dilution C₁V₁ = C₂V₂, Concentration from a mass, Mass needed for a solution, Molality)
- **Solve for** (options: C₁, V₁, C₂, V₂)
- **Stock concentration C₁**
- **C₁ unit**: Also the unit of the answer when you solve for C₁ (options: µmol/L, mmol/L, mol/L)
- **Stock volume V₁**
- **Final concentration C₂**
- **C₂ unit**: Also the unit of the answer when you solve for C₂ (options: µmol/L, mmol/L, mol/L)
- **Final volume V₂**
- **Molar mass from** (options: Formula, Typed value)
- **Solute formula**
- **Molar mass of the solute**
- **Mass of solute**
- **Volume of solution**
- **Wanted concentration**
- **Concentration unit** (options: µmol/L, mmol/L, mol/L)
- **Mass of solvent**

## Results

- Stock volume V₁ (mL) — main result
- Stock concentration C₁ (mol/L)
- Final concentration C₂ (mol/L)
- Final volume V₂ (mL)
- Solvent to add (mL)
- Dilution factor
- Molarity (mol/L)
- Mass concentration (g/L)
- Percent w/v
- Parts per million (mg/L) (ppm)
- Mass of solute to weigh (g)
- Molality (mol/kg)
- Amount of solute (mol)

## Formula

$$
C_1V_1 = C_2V_2,\qquad c = \frac{m/M}{V},\qquad \%\,w/v = \frac{m\,(\mathrm{g})}{V\,(\mathrm{mL})}\times100,\qquad b = \frac{m/M}{m_{\text{solvent}}}
$$

## Worked examples

### 250 mL of 0.1 M from a 1 M stock

- Calculate: Dilution C₁V₁ = C₂V₂
- Solve for: V₁
- Stock concentration C₁: 1
- C₁ unit: mol/L
- Final concentration C₂: 0.1
- C₂ unit: mol/L
- Final volume V₂: 250 mL
- **Stock volume V₁: 25 mL**
- **Solvent to add: 225 mL**
- **Dilution factor: 10**
- Checked against: Python 3.8 decimal: V₁ = 0.1 × 250 / 1 = 25 mL (OpenStax Chem 2e §3.3 method)

### 10 mL of 12 M HCl made up to 1 L

- Calculate: Dilution C₁V₁ = C₂V₂
- Solve for: C₂
- Stock concentration C₁: 12
- C₁ unit: mol/L
- Stock volume V₁: 10 mL
- C₂ unit: mol/L
- Final volume V₂: 1 L
- **Final concentration C₂: 0.12 mol/L**
- Checked against: Python 3.8 decimal: 12 × 0.010 / 1

### Dilution factor 1: nothing to add

- Calculate: Dilution C₁V₁ = C₂V₂
- Solve for: V₁
- Stock concentration C₁: 0.5
- C₁ unit: mol/L
- Final concentration C₂: 0.5
- C₂ unit: mol/L
- Final volume V₂: 100 mL
- **Stock volume V₁: 100 mL**
- **Solvent to add: 0 mL**
- Checked against: C₁ = C₂ ⇒ V₁ = V₂

### 5.844 g NaCl in 100 mL

- Calculate: Concentration from a mass
- Molar mass from: Formula
- Solute formula: NaCl
- Mass of solute: 5.844 g
- Volume of solution: 100 mL
- **Molarity: 1 mol/L**
- **Percent w/v: 5.844%**
- **Mass concentration: 58.44 g/L**
- **Parts per million (mg/L): 58,440 ppm**
- Checked against: Python 3.8 decimal: 5.844/58.440 g/mol/0.1 L = 1 M (NaCl = 22.990 + 35.45)

### Mass of glucose for 500 mL of 0.2 M

- Calculate: Mass needed for a solution
- Molar mass from: Formula
- Solute formula: C6H12O6
- Volume of solution: 500 mL
- Wanted concentration: 0.2
- Concentration unit: mol/L
- **Mass of solute to weigh: 18.0156 g**
- Checked against: Python 3.8 decimal: 0.2 × 0.5 × 180.156

### Molality: 58.44 g NaCl in 2 kg water

- Calculate: Molality
- Molar mass from: Typed value
- Molar mass of the solute: 58.44 g/mol
- Mass of solute: 58.44 g
- Mass of solvent: 2 kg
- **Molality: 0.5 mol/kg**
- Checked against: Python 3.8 decimal: 1 mol / 2 kg

## Questions

### How do you use C1V1 = C2V2?

Write down the three values you know, use the same concentration unit on both sides and the same volume unit on both sides, and rearrange for the unknown. For 250 mL of 0.1 M from a 1 M stock, V₁ = C₂V₂ ÷ C₁ = 0.1 × 250 ÷ 1 = 25 mL of stock, made up to 250 mL with 225 mL of solvent. Because the units cancel, mmol/L or % work too.

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

Molarity (mol/L) is moles of solute per litre of solution; molality (mol/kg) is moles of solute per kilogram of solvent. Molality does not change with temperature because mass does not expand, which is why freezing-point and boiling-point calculations use it. For dilute water solutions the two are close: 58.44 g of NaCl in 2 kg of water is 0.5 mol/kg.

### How do you calculate the mass needed to make a solution?

Multiply the target molarity by the volume in litres to get moles, then by the molar mass: m = c × V × M. For 500 mL of 0.2 M glucose (180.156 g/mol), 0.2 × 0.5 × 180.156 = 18.016 g. Dissolve it in less solvent than the final volume, then make up to the mark so the total is exactly 500 mL.

### How do you convert molarity to ppm?

Multiply the molarity by the molar mass to get grams per litre, then by 1000 to get mg/L, which is ppm for dilute water solutions. A 0.001 M NaCl solution is 0.001 × 58.44 = 0.05844 g/L, or 58.44 ppm. Reading mg/L as ppm assumes a density of about 1 g/mL, so the two drift apart for concentrated or non-aqueous solutions.

### What is a dilution factor?

It is the stock concentration divided by the final concentration, C₁/C₂, which equals the final volume divided by the stock volume, V₂/V₁. Making 25 mL up to 250 mL is a dilution factor of 10, often written 1:10, meaning 1 part stock in 10 parts total. Some labs write the same dilution as 1:9, meaning 1 part stock to 9 parts diluent, so check which convention a protocol uses.

### How accurate is the dilution and molarity calculator?

Accuracy depends on your inputs and the method's assumptions. Decimal arithmetic uses 50 significant digits, but estimates, numerical methods and source data can be less precise; the displayed rounding does not remove those limits. It is checked against 6 worked examples whose answers come from independent sources; for example, “250 mL of 0.1 M from a 1 M stock” is checked against Python 3.8 decimal: V₁ = 0.1 × 250 / 1 = 25 mL (OpenStax Chem 2e §3.3 method).

### Where does the method come from?

OpenStax Chemistry 2e, §3.3 Molarity (dilution of solutions) and §3.4 Other units for solution concentrations; IUPAC Gold Book — amount concentration; molality.

## Sources

- [OpenStax Chemistry 2e, §3.3 Molarity (dilution of solutions) and §3.4 Other units for solution concentrations](https://openstax.org/books/chemistry-2e/pages/3-3-molarity)
- [IUPAC Gold Book — amount concentration; molality](https://goldbook.iupac.org/terms/view/A00295)