What this calculator does
The dilution equation says that the moles of solute do not change when you add solvent, so the concentration times the volume is the same before and after. Making 1,000 mL of 0.5 mol/L from a 5 mol/L stock needs 100 mL of stock and 900 mL of diluent.
The diluent volume is the answer people actually need, and it is the one the equation does not give directly. C₁V₁ = C₂V₂ returns the stock volume; the diluent is the final volume minus that. Adding the full final volume of solvent to the stock is a common and easily avoided error.
The formula
The stock volume required is the target concentration times the target volume, divided by the stock concentration. The diluent is the difference between the final volume and the stock volume. The units of concentration cancel, so any consistent pair works: mol/L, percent, ppm or anything else.
| Term | Meaning |
|---|---|
| C₁V₁ = C₂V₂ | The dilution equation, expressing conservation of solute. |
| Stock solution | The concentrated starting solution. |
| Diluent | The solvent added, usually water. |
| Dilution factor | The ratio of final volume to stock volume, so a 10× dilution uses one part stock in ten parts total. |
The inputs explained
| Field | What to enter |
|---|---|
| Stock concentration (mol/L) | Stock concentration. |
| Target concentration (mol/L) | Target concentration, in the same units as the stock. |
| Target final volume (mL) | Final volume you want to end up with. |
When to use it
Preparing a working solution
Laboratory stocks are kept concentrated and diluted fresh, which is the most common use of this equation.
Diluting a cleaning or garden chemical
Product labels give a target concentration and the same arithmetic applies.
Checking a dilution ratio
Translating between a stated ratio such as 1:10 and an actual volume to measure.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How much stock does each target need?
A range of target concentrations from the same stock.
| Target concentration | Stock volume needed | Diluent to add | Dilution factor |
|---|---|---|---|
| 0.1 mol/L | 20.00 mL | 980.00 mL | 50.000× |
| 0.5 mol/L | 100.00 mL | 900.00 mL | 10.000× |
| 1 mol/L | 200.00 mL | 800.00 mL | 5.000× |
| 2.5 mol/L | 500.00 mL | 500.00 mL | 2.000× |
Questions
Does a 1:10 dilution mean 1 part in 10 or 1 part plus 10?
Usage genuinely differs, which is why it causes errors. In most laboratory contexts 1:10 means one part in ten total, so 1 mL of stock plus 9 mL of diluent. Some fields mean one part to ten parts, giving 11 total. Where it matters, state the volumes rather than the ratio.
Do the concentration units matter?
Only that both are the same. The units cancel in the equation, so mol/L, percent, ppm or mg/mL all work identically as long as C₁ and C₂ use the same one. Mixing units is the error to watch for.
Should I add stock to water or water to stock?
Stock to water, generally, and always for concentrated acids where the reverse can generate enough heat to spatter. Adding acid to water disperses the heat through the larger volume. The old mnemonic is to do as you oughta and add acid to water.
What if I need several dilution steps?
Use a serial dilution when the total factor is large. Diluting 10,000-fold in one step needs an impractically small stock volume, so it is done as repeated tenfold steps, each of which can be measured accurately.
For repeated dilution steps, see the serial dilution calculator. For making a solution from solid, see the molarity calculator.