# How much stock for this dilution?

Solves the dilution equation C₁V₁ = C₂V₂ for the stock volume, the final volume or either concentration, and gives the solvent to add and the dilution factor.

- Page: https://www.acalculator.org/chemistry/dilution-calculator
- JSON spec: https://www.acalculator.org/chemistry/dilution-calculator.json
- Version: 91f17c63fee0

## Default answer

Example with the default inputs (Stock concentration (C₁) 1, Final concentration (C₂) 0.1, Final volume (V₂) 100 mL): To make 100 mL at 0.1 from a stock at 1, use 10 mL of stock.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| c1 | Stock concentration (C₁) | The concentration of the stock solution you start from. |
| v1 | Stock volume (V₁) | The volume of stock solution to use. |
| c2 | Final concentration (C₂) | The concentration you want after diluting, in the same unit as the stock concentration. |
| v2 | Final volume (V₂) | The total volume after diluting: stock plus solvent. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| c1 | Stock concentration (C₁) | The concentration of the stock solution you start from. |
| v1 | Stock volume (V₁) | The volume of stock solution to use. |
| c2 | Final concentration (C₂) | The concentration you want after diluting, in the same unit as the stock concentration. |
| v2 | Final volume (V₂) | The total volume after diluting: stock plus solvent. |
| solvent | Solvent to add | The volume of solvent to add to the stock: V₂ − V₁. Shown only when the final volume is larger. |
| factor | Dilution factor | How many times the stock is diluted: C₁ ÷ C₂, which equals V₂ ÷ V₁. |

## Method

C₁ × V₁ = C₂ × V₂; solvent to add = V₂ − V₁; dilution factor = C₁ ÷ C₂ = V₂ ÷ V₁.

## Assumptions

- Both concentrations use the same unit (mol/L, mmol/L, % or mg/mL). The volumes may be in any units.
- Only solvent is added, so the amount of solute does not change.
- Volumes add up: the final volume is the stock volume plus the solvent volume. For mixtures such as alcohol and water this is only approximate.

## Worked examples

1. c1 = 1, c2 = 0.1, v2 = 0.0001 gives v1 = 0.00001, solvent = 0.00009, factor = 10. Source: hand calculation in content.mdx: V₁ = 0.1 × 100 ÷ 1 = 10 mL; solvent = 100 − 10 = 90 mL; factor = 1 ÷ 0.1 = 10.
2. c1 = 12, v1 = 0.000025, v2 = 0.00025 gives c2 = 1.2, factor = 10. Source: hand calculation in content.mdx: C₂ = 12 × 25 ÷ 250 = 1.2 M.
3. c1 = 70, v1 = 0.0001, c2 = 25 gives v2 = 0.00028, solvent = 0.00018, factor = 2.8. Source: hand calculation in content.mdx: V₂ = 70 × 100 ÷ 25 = 280 mL; solvent = 280 − 100 = 180 mL.

## FAQ

### What is the dilution formula?

C₁ × V₁ = C₂ × V₂. C₁ and V₁ are the concentration and volume of the stock solution, and C₂ and V₂ are the concentration and volume after diluting. Adding solvent does not change the amount of solute, so concentration times volume stays the same.

### How much stock solution do I need?

V₁ = C₂ × V₂ ÷ C₁. For 100 mL of 0.1 M from a 1 M stock: 0.1 × 100 ÷ 1 = 10 mL of stock, then add 90 mL of solvent.

### What units can I use?

Any concentration unit, as long as C₁ and C₂ are in the same one: mol/L, mmol/L, percent, or mg/mL. The volumes may be in different units; the calculator converts them.

### What is a dilution factor?

How many times the solution is diluted: C₁ ÷ C₂, which equals V₂ ÷ V₁. Diluting 10 mL of stock to 100 mL is a 10-fold dilution, often written 1:10.

### How do I dilute an acid safely?

Add the acid slowly to the water, never water to acid, and wear eye protection. The mixing gives off heat, and water added to concentrated acid can boil and spatter.

## Sources

- IUPAC Compendium of Chemical Terminology (the Gold Book), amount concentration: c = n ÷ V. https://doi.org/10.1351/goldbook.A00295
- NIST Special Publication 811 (2008), Appendix B.8: 1 US gallon = 3.785411784 L and 1 US fluid ounce = 29.5735295625 mL. https://www.nist.gov/pml/special-publication-811