Dilution Calculator
Work out any one value in a dilution — starting concentration, starting volume, final concentration, or final volume — using C₁V₁ = C₂V₂.
The formula
C₁V₁ = C₂V₂, where C₁ and V₁ are the concentration and volume of the starting (stock) solution, and C₂ and V₂ are the concentration and volume after dilution. Diluting doesn't change the total amount of solute — only the volume it's dissolved in — so this product stays constant.
Worked example
To dilute 10 mL of a 5 mol/L stock solution down to 1 mol/L: V₂ = (5 × 10) ÷ 1 = 50 mL. Since you already have 10 mL, add 40 mL of diluent (usually water) to reach exactly 50 mL total.
The four solve-for modes
- Final volume (V₂) = C₁ × V₁ ÷ C₂. This mode also reports the diluent to add, V₂ − V₁.
- Final concentration (C₂) = C₁ × V₁ ÷ V₂.
- Starting volume (V₁) = C₂ × V₂ ÷ C₁, the amount of stock to measure out.
- Starting concentration (C₁) = C₂ × V₂ ÷ V₁, the strength the stock must have.
- Results are shown to four decimals. Concentrations can be in any unit as long as C₁ and C₂ match, and the same goes for volumes.
Worked examples with the tool's output
Final volume: a 12-unit stock, 25 units of it, diluted to 0.5 gives V₂ = 600.0000, so 575.0000 units of diluent are added to the 25 of stock.
Final concentration: 20 units of a 10-strength stock made up to 250 gives C₂ = 0.8000.
Stock to measure: to make 500 units at strength 1 from a 12-strength stock, take V₁ = 41.6667 units of stock and make up to 500.
Required stock: 5 units diluted to 100 at strength 2 needs a stock of C₁ = 40.0000.
Checks and limits
The tool refuses a final concentration above the starting one, and a final volume below the starting volume. If both are equal, the result is simply no dilution, with 0.0000 diluent. Zero and negative values are rejected. Diluent is shown only in final-volume mode. Serial dilutions are not built in; run the calculation once per step and use each answer as the next stock.
Frequently asked questions
Do the units of concentration matter?
No, as long as C₁ and C₂ use the same units (both mol/L, both %, etc.) — the formula works with any consistent concentration unit, and the same logic applies to volume units.
Can dilution increase concentration?
No — adding diluent only ever increases volume and decreases concentration. If you need a higher concentration, you need a different (stronger) stock solution or need to remove solvent, which this calculator doesn't model.
Is V₂ the amount of water to add?
No. V₂ is the total volume after dilution. The water to add is V₂ minus V₁, which the tool prints on its own line when you solve for V₂.
Why does it say my final concentration is too high?
Adding diluent can only lower concentration, so a C₂ larger than C₁ is blocked. Check that the two values are in the same unit and not swapped.
How do I plan a two-step dilution?
Calculate the first step, then enter its final concentration as the starting concentration of the second. Each step is a separate calculation.