Planning a one-step solution dilution
For a simple dilution with no solute loss or reaction, the amount of solute before dilution equals the amount after dilution. This gives the familiar relationship C₁V₁ = C₂V₂.
The concentration units must match each other and the volume units must match each other. The calculated stock volume is the aliquot transferred; diluent is then added to reach final total volume, not simply added in that same amount.
How to use the dilution calculator
- Select the unknown: Choose the concentration or volume to calculate.
- Enter three known values: Use matching concentration units and matching volume units.
- Calculate: Review the positive result and its implied dilution factor.
- Prepare appropriately: Transfer the calculated stock aliquot and bring the solution to final volume using suitable laboratory technique.
Formula and variables
The equation conserves solute amount for a direct dilution when concentration is proportional to amount per volume.
C₁V₁ = C₂V₂- C₁ — Initial concentration
- Stock-solution concentration
- V₁ — Stock volume
- Volume of stock solution transferred
- C₂ — Final concentration
- Target concentration after dilution
- V₂ — Final volume
- Total solution volume after dilution
Tenfold dilution
Prepare 100 mL of 0.1 M solution from a 1.0 M stock.
- C₁
- 1.0 M
- C₂
- 0.1 M
- V₂
- 100 mL
- V₁ = C₂V₂/C₁
- V₁ = 0.1 × 100/1.0 = 10 mL
Result: Use 10 mL of stock and dilute to a final total volume of 100 mL.
This generally means adding less than 90 mL initially, mixing, then bringing exactly to volume.
Understanding your results
Distinguish final volume from diluent volume
V₂ is the total final solution volume.
- The stock aliquot is part of the final volume.
- For accurate work, use calibrated volumetric equipment.
- If C₂ exceeds C₁, the requested operation is concentration rather than dilution.
Assumptions
- Solute amount is conserved during transfer and dilution.
- Volumes and concentrations are defined consistently.
- Mixing does not cause a relevant chemical reaction or non-additive model failure.
Limitations
- Does not calculate serial dilution chains, uncertainty, density-based preparation, purity correction, or reaction stoichiometry.
- Does not account for pipetting losses or volumetric glassware tolerances.
- May not apply to activities, strongly nonideal solutions, or concentrations whose volume basis changes incompatibly.
Common mistakes
- Adding the calculated final volume as diluent instead of bringing the mixture to that total volume.
- Mixing concentration or volume units.
- Reversing stock and final concentration.
- Using C₁V₁ = C₂V₂ for a chemical reaction rather than a dilution.
Practical use cases
Stock-solution preparation
Calculate the aliquot required for a target concentration and final volume.
Laboratory teaching
Check direct-dilution arithmetic and conservation of solute amount.
Frequently asked questions
How much diluent should I add?
The ideal geometric difference V₂ − V₁ is only approximate for preparation; accurately bring the mixture to the final total volume.
Can concentration units differ?
Convert them to the same concentration unit before using the equation.
Can this calculate serial dilutions?
It handles one step at a time. Plan and document each serial-dilution step separately.
Sources and review
- Dilute solution — IUPAC Gold Book. Accessed 2026-07-13.
Reviewed 2026-07-13.